Dynamic multi-objective optimization problems (DMOPs) with a changing number of objectives may have Pareto-optimal set (PS) manifold expanding or contracting over time. Knowledge transfer has been used for solving DMOPs, since it can transfer useful information from solving one problem instance to solve another related problem instance. However, we show that the state-of-the-art transfer approach based on heuristic lacks diversity on problem with extremely strong bias and loses convergence on problems with multi-modality and variable correlation, after the number of objectives increases and decreases, respectively. Therefore, we propose a novel transfer strategy based on learning, called learning to expand and contract PS (denoted as LEC) for enhancing diversity and convergence after number of objective increases and decreases, respectively. It firstly learns potentially good directions for expansion and contraction separately via principal component analysis. Then, the most promising expansion and contraction directions are selected from their candidates according to whether they help diversity and convergence, respectively. Lastly, PS is learnt to be expanded and contracted based on these most promising directions. Comprehensive studies using 13 DMOP benchmarks with a changing number of objectives demonstrate that our proposed LEC is effective on improving solution quality, not only right after changes but also after optimization of different generations, compared to state-of-the-art algorithms.

How can a robot provide unobtrusive physical support within a group of humans? We present Attentive Support, a novel interaction concept for robots to support a group of humans. It combines scene perception, dialogue acquisition, situation understanding, and behavior generation with the common-sense reasoning capabilities of Large Language Models (LLMs). In addition to following user instructions, Attentive Support is capable of deciding when and how to support the humans, and when to remain silent to not disturb the group. With a diverse set of scenarios, we show and evaluate the robot’s attentive behavior, which supports and helps the humans when required, while not disturbing if no help is needed.

Complex optimization problems with hundreds or even thousands of decision variables and dozens of conflicting objectives are not uncommon in the real world. In the past five years, increased research efforts have been dedicated to large-scale multiobjective optimization problems (LSMOPs) by using a variety of search strategies, including variable grouping, variable analysis, problem transformation, dimensionality reduction, and novel recombination operators. Despite the success of these efforts in solving some general LSMOPs, there still remains a big gap between the LSMOPs that have been addressed and those encountered in real life, such as sparse, highly constrained, dynamic, and expensive LMOPs, as well as very large-scale and many-objective optimization problems that are widely seen and of paramount importance for solving scientific and engineering problems. Due to the significant practical importance of large-scale multiobjective optimization, there is a high demand for computationally efficient and effective evolutionary algorithms for solving LSMOPs.

The dynamic capacitated arc routing problem (DCARP) aims at re-scheduling the service plans of agents, such as vehicles in a city scenario, when dynamic events deteriorate the quality of the current schedule. Various algorithms have been proposed to solve DCARP instances in different dynamic scenarios. However, most existing work evaluated their algorithms' performance based on artificially constructed dynamic environments instead of using more realistic traffic simulations which are built on actual traffic data. In this paper, we constructed a novel DCARP benchmarking framework based on the Simulation of Urban MObility (SUMO) transportation simulation software, which allows to include real-world traffic environments for generating a set of DCARP instances from dynamic events, such as road congestion or task changes. The flexibility of the framework allows to develop DCARP optimization algorithms and evaluate their effectiveness more comprehensively. We use the benchmarking framework to generate 12 different dynamic instances using real-world traffic data of Dublin City. We then demonstrate the value of our framework by using these instances to compare our previously proposed hybrid local search algorithm (HyLS) with a state-of-the-art meta-heuristic optimization algorithm. The generated benchmark scenarios indicate that HyLS is a very effective optimizer on DCARP scenarios with real traffic data for reducing the total service cost. They also demonstrate the importance of our DCARP benchmarking framework for the development and benchmarking of optimization algorithms in more realistic scenarios.

The Capacitated Arc Routing Problem (CARP) aims at assigning vehicles to serve tasks which are located at different arcs in a graph. However, the originally planned routes are easily affected by different dynamic events like newly added tasks. This gives rise to Dynamic CARP (DCARP) instances, which need to be efficiently optimized for new high-quality service plans in a short time. However, it is unknown which dynamic events make DCARP instances especially hard to solve. Therefore, in this paper, we provide an investigation of the influence of different dynamic events on DCARP instances from the perspective of fitness landscape analysis based on a recently proposed hybrid local search (HyLS) algorithm. We generate a large set of DCARP instances based on a variety of dynamic events and analyze the fitness landscape of these instances using several different measures such as fitness correlation length. From the empirical results we conclude that cost-related events have no significant impact on the difficulty of DCARP instances, but instances which require more new vehicles to serve the remaining tasks are harder to solve. These insights improve our understanding of the DCARP instances and pave the way for future work on improving the performance of DCARP algorithms.

Traditional methods for solving problems within computer science rely mostly upon the application of handcrafted algorithms. As however manual engineering of them can be considered to be a tedious process, it is interesting to consider how far internal mechanisms can be directly learned in an end-to-end manner instead. This is especially tempting to consider for metaheuristic and evolutionary optimization routines which inherently rely upon creating abundant amounts of data during run-time. To implement such an approach for these types of algorithms, it effectively requires a pipeline to first acquire deran-domized algorithm components in a domain-dependent manner and secondly a mapping to select them based upon characteristic features which unveil the black box character of an optimization problem. While in principle, within our prior work we proposed methods for extracting spatial features from metadata, these unfortunately fail to acknowledge the time-dependent nature of it. Thus, fail in scenarios when the inputs generated from initial iterations are not expressive enough. For this reason we specifically develop within this work architectures for spatio-temporal data processing. Particularly, we find that our proposed GCN-GRU and LSTM architectures, which take inspiration from CNN-LSTMs originally proposed for activity recognition in multimedia data-streams, demonstrate high efficiency and most consistent performance on time series of variable length. Further, we can also demonstrate that the class activation map (CAM) for interpretable learning with time series data helps to understand and reflects problem-dependent properties of the search behavior of an optimization algorithm.

Recent advancements in machine learning comprise generative models such as autoencoders (AE) for learning and compressing 3D data to generate low-dimensional latent representations of 3D shapes. Learning latent representations that disentangle the underlying factors of variations in 3D shapes is an intuitive way to achieve generalization in generative models. However, it remains an open problem to learn a generative model of 3D shapes such that the latent variables are disentangled and represent different interpretable aspects of 3D shapes. In this paper, we propose Split-AE, which is an autoencoder-based architecture for partitioning the latent space into two sets, named as content and style codes. The content code represents global features of 3D shapes to differentiate between semantic categories of shapes, while style code represents distinct visual features to differentiate between shape categories having similar semantic meaning. We present qualitative and quantitative experiments to verify feature disentanglement using our Split-AE. Further, we demonstrate that, given a source shape as an initial shape and a target shape as a style reference, the trained Split-AE combines the content of a source and style of a target shape to generate a novel augmented shape, that possesses the distinct features of the target shape category yet maintains the similarity of the global features with the source shape. We conduct a qualitative study showing that the augmented shapes exhibit a realistic interpretable mixture of content and style features across different shape classes with similar semantic meaning.

Benchmarking provides an essential ground base for adequately assessing and comparing evolutionary computation methods and other optimization algorithms. It allows us to gain insights into strengths and weaknesses of different existing techniques, and consequently design more efficient optimization approaches. The need for good benchmarking practices opens up a broad range of complementary research questions, arising as a byproduct of challenges encountered when optimization methods are assessed. From the selection of representative benchmark problem instances, different algorithms, and suitable performance metrics, over efficient experimentation, to a sound evaluation of the benchmark data, these research questions lie at the core of establishing a well-designed and standardized benchmarking procedure.

The choice of design representations, as of search operators, is central to the performance of evolutionary optimization algorithms, in particular, for multitask problems. The multitask approach pushes further the parallelization aspect of these algorithms by solving simultaneously multiple optimization tasks using a single population. During the search, the operators implicitly transfer knowledge between solutions to the offspring, taking advantage of potential synergies between problems to drive the solutions to optimality. Nevertheless, in order to operate on the individuals, the design space of each task has to be mapped to a common search space, which is challenging in engineering cases without clear semantic overlap between parameters. Here, we apply a 3-D point cloud autoencoder to map the representations from the Cartesian to a unified design representation: the latent space of the autoencoder. The transfer of latent space features between design representations allows the reconstruction of shapes with interpolated characteristics and maintenance of common parts, which potentially improves the performance of the designs in one or more tasks during the optimization. Compared to traditional representations for shape optimization, such as free-form deformation, the latent representation enables more representative design modifications, while keeping the baseline characteristics of the learned classes of objects. We demonstrate the efficiency of our approach in an optimization scenario where we minimize the aerodynamic drag of two different car shapes with common underbodies for cost-efficient vehicle platform design.

The capacitated arc routing problem (CARP) is a challenging combinatorial optimization problem abstracted from many real-world applications, such as waste collection, road gritting, and mail delivery. However, few studies considered dynamic changes during the vehicles’ service, which can cause the original schedule infeasible or obsolete. The few existing studies are limited by the dynamic scenarios considered, and by overly complicated algorithms that are unable to benefit from the wealth of contributions provided by the existing CARP literature. In this article, we first provide a mathematical formulation of dynamic CARP (DCARP) and design a simulation system that is able to consider dynamic events while a routing solution is already partially executed. We then propose a novel framework which can benefit from the existing static CARP optimization algorithms so that they could be used to handle DCARP instances. The framework is very flexible. In response to a dynamic event, it can use either a simple restart strategy or a sequence transfer strategy that benefits from the past optimization experience. Empirical studies have been conducted on a wide range of DCARP instances to evaluate our proposed framework. The results show that the proposed framework significantly improves over state-of-the-art dynamic optimization algorithms.

Methods for learning on 3D point clouds became ubiquitous due to the popularization of 3D scanning technology and advances of machine learning techniques. Among these methods, point-based deep neural networks have been utilized to explore 3D designs in optimization tasks. However, engineering computer simulations require high-quality meshed models, which are challenging to automatically generate from unordered point clouds. In this work, we propose Point2FFD: A novel deep neural network for learning compact geometric representations and generating simulation-ready meshed models. Built upon an autoencoder architecture, Point2FFD learns to compress 3D point clouds into a latent design space, from which the network generates 3D polygonal meshes by selecting and deforming simulation-ready mesh templates. Through benchmark experiments, we show that our proposed network achieves comparable shape-generative performance than existing state-of-the-art point-based generative models. In real world-inspired vehicle aerodynamic optimizations, we demonstrate that Point2FFD generates simulation-ready meshes of realistic car shapes and leads to better optimized designs than the benchmarked networks.

Methods for learning and compressing high-dimensional data allow designers to generate novel and low-dimensional design representations for shape optimization problems. By using compact design spaces, global optimization algorithms require less function evaluations to characterize the problem landscape. Furthermore, data-driven representations are often domain-agnostic and independent of the user expertise, and thus potentially capture more relevant design features than a human designer would suggest. However, more factors than the dimensionality play a role in the efficiency of design representations. In this paper, we perform a comparative analysis of design representations for 3D shape optimization problems obtained with principal component analysis, kernel-principal component analysis and a 3D point cloud autoencoder, which we apply on a benchmark data set of computer aided engineering car models. We evaluate the shape-generative capabilities of these methods and show that we can modify the geometries more locally with the autoencoder than with the remaining methods. In a vehicle aerodynamic optimization framework, we verify that this property of the autoencoder representation improves the optimization performance by enabling potentially complementary degrees of freedom for the optimizer. With our study, we provide insights on the qualitative properties and quantifiable measures on the efficiency of deep neural networks as shape generative models for engineering optimization problems, as well as analyses of geometric representations for engineering optimization with evolutionary algorithms.

In the early design phase of automotive digital development, one of the key challenges for the designer is to consider multiple-criteria like aerodynamics and structural efficiency besides aesthetic aspects for designing a car shape. In our research, we imagine a cooperative design system in the automotive domain which provides guidance to the designer for finding sets of design options or well-performing designs for preferred search areas. In the present paper, we focus on two perspectives for this multi-criteria decision-making problem: First, a scenario without prior information about design preferences, where the designer aims to explore the search space for a diverse set of design alternatives. Second, a scenario where the designer has a prior intuition on preferred solutions of interest. For both scenarios, we assume that historic 3D car shape data exists, which we can utilize to learn a compact low-dimensional design representation based on a variational autoencoder (VAE). In contrast to evolutionary multi-objective optimization approaches where starting populations are randomly initialized, we propose to seed the population more efficiently by exploiting the advantage of linear interpolation in the latent space of the VAE. In our experiments, we demonstrate that the multi-objective optimization converges faster and achieves a diverse set of solutions. For the second scenario, when specifying design preferences by weights, we improve on the weighted-sum method, which simplifies the multi-objective problem and propose a strategy for efficiently adapting the weights towards the preferred design solution.

The imbalanced classification problem is very relevant in both academic and industrial applications. The task of finding the best machine learning model to use for a specific imbalanced dataset is complicated due to a large number of existing algorithms, each with its own hyperparameters. The Combined Algorithm Selection and Hyperparameter optimization (CASH) has been introduced to tackle both aspects at the same time. However, CASH has not been studied in detail in the class imbalance domain, where the best combination of resampling technique and classification algorithm is searched for, together with their optimized hyperparameters. Thus, we target the CASH problem for imbalanced classification. We experiment with a search space of 5 classification algorithms, 21 resampling approaches and 64 relevant hyperparameters in total. Moreover, we investigate performance of 2 well-known optimization approaches: Random search and Tree Parzen Estimators approach which is a kind of Bayesian optimization. For comparison, we also perform grid search on all combinations of resampling techniques and classification algorithms with their default hyperparameters. Our experimental results show that a Bayesian optimization approach outperforms the other approaches for CASH in this application domain.

Recent years have seen the advancement of data-driven paradigms in population-based and evolutionary optimization. This reflects on one hand the mere abundance of available data, but on the other hand also progresses in the refinement of previously available machine learning methods. Surprisingly, deep pattern recognition methods emerging from the studies of neural networks have only been sparingly applied. This comes unexpected, as the complex data generated by evolutionary search algorithms can be considered tedious and intractable for manual analysis with mere practical intuitions. In this work, we therefore explore opportunities to employ deep networks to directly learn problem characteristics of continuous optimization problems. Particularly, with data obtained during initial runs of an optimization algorithm. We find that a graph neural network, trained upon a graph representation of continuous search spaces, shows in comparison to more traditional approaches higher validation accuracy and retrieves characteristics within the latent space which are better at distinguishing different continuous optimization problems. We hope that our study can pave the way towards new approaches which allow us to learn problem-dependent algorithm components and recall these from predictions of inputs generated during the run-time of an optimization algorithm.

Evolutionary algorithms are a class of population-based meta-heuristic methods partially inspired by natural evolution. Specifically, they rely on stochastic variation and selection processes to sequentially find optimal solutions of a function of interest. We attempt in this work to extract preferences in these stochastic evolutionary operators in form of empirical and improved distributions as basis for model-based mutation operators. The latter can be considered as representing problem-tailored search operators which exist independently from the optimisation run and thus can be transferred to similar problem instances. This offline approach is different to existing model-based optimisation techniques, e.g. EDA's, CMA-ES and Bayesian approaches, where adaption happens rather in an online manner without the influence of prior experience. Our approach can be rather considered to follow the recent line of research on knowledge transfer in optimisation, which until now heavily relies upon the transfer of candidate solutions across different optimisation tasks. We investigate in this paper the interplay between algorithm and optimisation task, its influence on the retrieved distributions and explore whether or not these can lead to performance improvements on a selected range of problems, as well as when transferring them across problems. At last, we make a comparison of built distributions in the hope of relating similarity in statistical distances between distributions to possible performance gains.

Transfer learning has been used for solving multiple optimization and dynamic multi-objective optimization problems, since transfer learning is believed to be able to transfer useful information from one problem instance to help solving another related problem instance. This paper aims to study how effective transfer learning is in dynamic multi-objective optimization (DMO). Through computation time analysis of transfer learning, we show that the `inner' optimization problem introduced by transfer learning is very time-consuming. In order to enhance the efficiency, two alternatives are computationally investigated on a number of dynamic bi- and tri-objective test problems. Experimental results have shown that the greatly enhanced efficiency does not result in much degeneration on the performance of transfer learning. Considering the high computational cost of transfer learning, it is likely that the original purpose of using transfer learning in DMO might be negated. In other words, the computation time saved in optimization is eaten up by computationally expensive transfer learning. As a result, there is less gain than expected in the overall computational efficiency. To verify this, experiments have been conducted, regarding using computational cost of transfer learning to optimize randomly generated solutions. The results have demonstrated that the convergence and diversity of final solutions generated from the random solutions are significantly better than those generated from transferred solutions under the same total computational budget.

In order to reduce the dimensionality of 3D point cloud representations, autoencoder architectures generate increasingly abstract, compressed features of the input data. Visualizing these features is central to understanding the learning process, however, while successful visualization techniques exist for neural networks applied to computer vision tasks, similar methods for geometric, especially non-Euclidean, input data are currently lacking. Hence, we propose a first-of-kind method to project the features learned by point cloud autoencoders into a 3D-space augmented with color maps. Our proposal explores the properties of 1D-convolutions, used in state-of-the art point cloud autoencoder architectures to handle the input data, which leads to an intuitive interpretation of the visualized features. Furthermore, we tackle the search for relevant co-activations in the feature space by clustering the input data in the latent space, where we explore the correspondence between network features and geometric characteristics of typical shapes of the clusters. We tested our approach with experiments on a benchmark data set, and with three different configurations of a point cloud autoencoder, where we show that the features learned by the autoencoder correlate with the occupancy of the input space by the training data.

Clinical time series are known for irregular, highly-sporadic and strongly-complex structures and are consequently difficult to model by traditional state-space models. In this paper, we investigate the potential of applying variational recurrent neural networks (VRNNs) for forecasting clinical time series extracted from electronic health records (EHRs) of patients. Variational recurrent neural networks (VRNNs) combine recurrent neural networks (RNNs) and variational inference (VI) and are state-of-the-art methods to model highly-variable sequential data such as text, speech, time series and multimedia signals in a generative fashion. We propose to incorporate multiple correlated time series to improve the forecasting of VRNNs. The selection of these correlated time series is based on the similarity of the supplementary medical information e.g., disease diagnostics, ethnicity and age etc. between the patients. We evaluate the effectiveness of utilizing such supplementary information with root mean square error (RMSE), on clinical benchmark data-set "Medical Information Mart for Intensive Care (MIMIC III)" for multi-step-ahead prediction. We further perform subjective analysis to highlight the effects of the similarity of the supplementary medical information on individual temporal features e.g., Systolic Blood Pressure (SBP), Heart Rate (HR) etc. of the patients from the same data-set. Our results clearly show that incorporating the correlated time series based on the supplementary medical information can help improving the accuracy of the VRNNs for clinical time series forecasting.

The notion of learning from different problem instances, although an old and known one, has in recent years regained popularity within the optimization community. Notable endeavors have been drawing inspiration from machine learning methods as a means for algorithm selection and solution transfer. However, surprisingly approaches which are centered around internal sampling models have not been revisited. Even though notable algorithms have been established in the last decades. In this work, we progress along this direction by investigating a method that allows us to learn an evolutionary search strategy reflecting rough characteristics of a fitness landscape. This latter model of a search strategy is represented through a flexible mixture-based distribution, which can subsequently be transferred and adapted for similar problems of interest. We validate this approach in two series of experiments in which we first demonstrate the efficacy of the recovered distributions and subsequently investigate the transfer with a systematic from the literature to generate benchmarking scenarios.

Engineering designs can involve multiple stages, where at each stage, the design models are incrementally modified and optimized. In contrast to traditional dynamic optimization problems, where the changes are caused by some objective factors, the changes in such incremental optimization problems (IOPs) are usually caused by the modifications made by the decision makers during the design process. While existing work in the literature is mainly focused on traditional dynamic optimization, little research has been dedicated to solving such IOPs. In this paper, we study how to adopt cooperative coevolution to efficiently solve a specific type of IOPs, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of IOPs with increasing decision variables and exploitable modular structure. Then, we propose a contribution-based cooperative coevolutionary framework coupled with an incremental grouping method for dealing with them. On one hand, the benchmark function generator is capable of generating various benchmark functions with various characteristics. On the other hand, the proposed framework is promising in solving such problems in terms of both optimization accuracy and computational efficiency. In addition, the proposed method is further assessed using a real-world application, i.e., the design optimization of a stepped cantilever beam.

The interests in multiobjective and many-objective optimization have been rapidly increasing in the evolutionary computation community. However, most studies on multiobjective and many-objective optimization are limited to small-scale problems, despite the fact that many real-world multiobjective and many-objective optimization problems may involve a large number of decision variables. As has been evident in the history of evolutionary optimization, the development of evolutionary algorithms (EAs) for solving a particular type of optimization problems has undergone a co-evolution with the development of test problems. To promote the research on large-scale multiobjective and many-objective optimization, we propose a set of generic test problems based on design principles widely used in the literature of multiobjective and many-objective optimization. In order for the test problems to be able to reflect challenges in real-world applications, we consider mixed separability between decision variables and nonuniform correlation between decision variables and objective functions. To assess the proposed test problems, six representative evolutionary multiobjective and many-objective EAs are tested on the proposed test problems. Our empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new EAs dedicated to large-scale multiobjective and many-objective optimization.

A steady state analysis of the optimization quality of a classical self-adaptive evolution strategy (ES) on a class of robust optimization problems is presented. A novel technique for calculating progress rates for nonquadratic noisy fitness landscapes is presented. This technique yields asymptotically exact results in the infinite population size limit. This technique is applied to a class of functions with noise-induced multimodality. The resulting progress rate formulas are compared with high-precision experiments. The influence of fitness resampling is considered and the steady state behavior of the ES is derived and compared with simulations. The questions whether one should sample and average fitness values and how to choose the truncation ratio are discussed giving rise to further research perspectives.

The standard covariance matrix adaptation evolution strategy (CMA-ES) comprises two evolution paths, one for the learning of the mutation strength and one for the rank-1 update of the covariance matrix. In this paper, it is shown that one can approximately transform this algorithm in such a manner that one of the evolution paths and the covariance matrix itself disappear. That is, the covariance update and the covariance matrix square root operations are no longer needed in this novel so-called matrix adaptation (MA) ES. The MA-ES performs nearly as well as the original CMA-ES. This is shown by empirical investigations considering the evolution dynamics and the empirical expected runtime on a set of standard test functions. Furthermore, it is shown that the MA-ES can be used as a search engine in a bi-population (BiPop) ES. The resulting BiPop-MA-ES is benchmarked using the BBOB comparing continuous optimizers (COCO) framework and compared with the performance of the CMA-ES-v3.61 production code. It is shown that this new BiPop-MA-ES-while algorithmically simpler-performs nearly equally well as the CMA-ES-v3.61 code.

In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.

To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map all found nondominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.

The focus of most research in evolutionary dynamic optimization has been tracking moving optimum (TMO). Yet, TMO does not capture all the characteristics of real-world dynamic optimization problems (DOPs), especially in situations where a solution's future fitness has to be considered. To account for a solution's future fitness explicitly, we propose to find robust solutions to DOPs, which are formulated as the robust optimization over time (ROOT) problem. In this paper we analyze two robustness definitions in ROOT and then develop two types of benchmark problems for the two robustness definitions in ROOT, respectively. The two types of benchmark problems are motivated by the inappropriateness of existing DOP benchmarks for the study of ROOT. Additionally, we evaluate four representative methods from the literature on our proposed ROOT benchmarks, in order to gain a better understanding of ROOT problems and their relationship to more popular TMO problems. The experimental results are analyzed, which show the strengths and weaknesses of different methods in solving ROOT problems with different dynamics. In particular, the real challenges of ROOT problems have been revealed for the first time by the experimental results on our proposed ROOT benchmarks.

Dynamic Optimization Problems (DOPs) have been widely studied using Evolutionary Algorithms (EAs). Yet, a clear and rigorous definition of DOPs is lacking in the Evolutionary Dynamic Optimization (EDO) community. In this paper, we propose a unified definition of DOPs based on the idea of multiple-decision-making discussed in the Reinforcement Learning (RL) community. We draw a connection between EDO and RL by arguing that both of them are studying DOPs according to our definition of DOPs. We point out that existing EDO or RL research has been mainly focused on some types of DOPs. A conceptualized benchmark problem, which is aimed at the systematic study of various DOPs, is then developed. Some interesting experimental studies on the benchmark reveal that EDO and RL methods are specialized in certain types of DOPs and more importantly new algorithms for DOPs can be developed by combining the strength of both EDO and RL methods.

Although the integration of engineering data within the framework of product data management systems has been successful in the recent years, the holistic analysis (from a systems engineering perspective) of multi-disciplinary data or data based on different representations and tools is still not realized in practice. At the same time, the application of advanced data mining techniques to complete designs is very promising and bears a high potential for synergy between different teams in the development process. In this paper, we propose shape mining as a framework to combine and analyze data from engineering design across different tools and disciplines. In the first part of the paper, we introduce unstructured surface meshes as meta-design representations that enable us to apply sensitivity analysis, design concept retrieval and learning as well as methods for interaction analysis to heterogeneous engineering design data. We propose a new measure of relevance to evaluate the utility of a design concept. In the second part of the paper, we apply the formal methods to passenger car design. We combine data from different representations, design tools and methods for a holistic analysis of the resulting shapes. We visualize sensitivities and sensitive cluster centers (after feature reduction) on the car shape. Furthermore, we are able to identify conceptual design rules using tree induction and to create interaction graphs that illustrate the interrelation between spatially decoupled surface areas. Shape data mining in this paper is studied for a multi-criteria aerodynamic problem, i.e. drag force and rear lift, however, the extension to quality criteria from different disciplines is straightforward as long as the meta-design representation is still applicable.

Measures of novelty and interestingness are frequently encountered in the context of developmental robotics, being derived from human psychology. This work addresses these measures from the viewpoint of enhancing design-space exploration in black-box optimization. We provide a unifying notational and naming scheme with the intent of facilitating comparison, implementation, and application in the domain of design optimization. Initial analysis shows a promising interestingness measure for being tried on real-world design problems.

To deal with complex optimization problems plagued with computationally expensive fitness functions, the use of surrogates to replace the original functions within the evolutionary framework is becoming a common practice. However, the appropriate datacentric approximation methodology to use for the construction of surrogate model would depend largely on the nature of the problem of interest, which varies from fitness landscape and state of the evolutionary search, to the characteristics of search algorithm used. This has given rise to the plethora of surrogate-assisted evolutionary frameworks proposed in the literature with ad hoc approximation/surrogate modeling methodologies considered. Since prior knowledge on the suitability of the data centric approximation methodology to use in surrogate-assisted evolutionary optimization is typically unavailable beforehand, this paper presents a novel evolutionary framework with the evolvability learning of surrogates (EvoLS) operating on multiple diverse approximation methodologies in the search. Further, in contrast to the common use of fitness prediction error as a criterion for the selection of surrogates, the concept of evolvability to indicate the productivity or suitability of an approximation methodology that brings about fitness improvement in the evolutionary search is introduced as the basis for adaptation. The backbone of the proposed EvoLS is a statistical learning scheme to determine the evolvability of each approximation methodology while the search progresses online. For each individual solution, the most productive approximation methodology is inferred, that is, the method with highest evolvability measure. Fitness improving surrogates are subsequently constructed for use within a trust-region enabled local search strategy, leading to the self-configuration of a surrogate-assisted memetic algorithm for solving computationally expensive problems. A numerical study of EvoLS on commonly used benchmark problems and a real-world computationally expensive aerodynamic car rear design problem highlights the efficacy of the proposed EvoLS in attaining reliable, high quality, and efficient performance under a limited computational budget.

Evolutionary dynamic optimization has been drawing more and more research attention, and yet most work in this area is focused on Tracking Moving Optimum (TMO), which is to optimize the current fitness function at any time point. Recently, we proposed a more practical way to solve dynamic optimization problems, which is referred to as Robust Optimization Over Time (ROOT). In ROOT, we are trying to find solutions whose performances are acceptable over more than one environmental state, i.e., fitness functions. Before any development of benchmarks or algorithms for ROOT, it is necessary to have some understanding of what aspects of an environment can change and more importantly how these changes influence the solving of ROOT problems. In this paper, we develop a number of measures which can be used to characterize and analyse the underlying changing environment in the framework of ROOT. We test these measures on several benchmark problem instances, and it is shown that these measures are able to differentiate different dynamics effectively and provide useful information about what kind of algorithms might or might not suit certain dynamic environments.

In this paper, we present a novel cross-surrogate assisted memetic algorithm (CSAMA) as a manifestation of multi co-objective evolutionary computation to enhance the search on computationally expensive problems by means of transferring, sharing and reusing information across objectives. In particular, the construction of surrogate for one objective is augmented with information from other related objectives to improve the prediction quality. The process is termed as a cross-surrogate modelling methodology, which will be used in lieu with the original expensive functions during the evolutionary search. Analyses on the prediction quality of the cross-surrogate modelling and the search performance of the proposed algorithm are conducted on the benchmark problems with assessments made against several state-of-the-art multiobjective evolutionary algorithms. The results obtained highlight the efficacy of the proposed CSAMA in attaining high quality Pareto optimal solutions under limited computational budget.

Redundancy is believed to play a key role in robustness and evolvability of biological systems. This paper investigates the influence of redundancy on the evolutionary performance of a gene regulatory network governing a cellular growth process. Extensive simulation results suggest that, for the developmental model studied in this work, maintaining sufficient redundancy helps to improve the ability of the evolutionary algorithm to achieve better performance. To examine the change of redundancy during the evolutionary process and its relationship to evolutionary performance, we propose a quantitative definition for measuring different aspects of redundancy, namely, structural redundancy, functional redundancy and functional proximity. Our results show that evolution attempts to increase the functional redundancy after pruning of redundant genes if the evolution is under a larger selection pressure. It is also interesting to notice that an increase in functional proximity enhances the evolutionary performance.

A computational model is presented that simulates stable growth of cellular structures that are in some cases capable of regeneration. In the model, cellular growth is governed by a gene regulatory network. By evolving the parameters and structure of the genetic network using a modified evolution strategy, a dynamically stable state can be achieved in the developmental process, where cell proliferation and cell apoptosis reach an equilibrium. The results of evolution with different setups in fitness evaluation during the development are compared with respect to their regeneration capability as well as their gene regulatory network structure. Network motifs responsible for stable growth and regeneration that emerged from the evolution are also analyzed. We expect that our findings can help to gain a better understanding of the process of growth and regeneration inspired by biological systems, in order to solve complex engineering problems, such as the design of self-healing materials.

Most developmental representations for design optimization with evolutionary computation that have been described in the literature are graph-based mimicking the interactions observed in biological gene regulatory networks. Alternative methods that directly manipulate the dynamical control system for developmental processes have been termed Vector Field Embryogeny (VFE) and have been applied successfully to cell differentiation. In this paper, we compare the evolvability of graph-based and vector field representations for controlling developmental processes. Inspired by the notion of strong causality in evolutionary strategies, we measure the covariance between genotype and phenotype changes for both representations. Furthermore, we propose a measure to characterize the representational power of both methods. If we compare VFE and graph-based representations with similar representational power, we notice that the covariance measure and therefore, the expected evolvability of VFE is higher. We also observe that the representational power of both methods decreases with increasing degree of freedom. We speculate that the reason for this could be the increased probability of the occurrence of strong point attractors.

Body morphology is thought to have heavily influenced the evolution of neural architecture. However, the extent of this interaction and its underlying principles are largely unclear. To help us elucidate these principles, we examine the artificial evolution of a hypothetical nervous system embedded in a fish-inspired animat. The aim is to observe the evolution of neural structures in relation to both body morphology and required motor primitives. Our investigations reveal that increasing the pressure to evolve a wider range of movements also results in higher levels of neural symmetry. We further examine how different body shapes affect the evolution of neural structure; we find that, in order to achieve optimal movements, the neural structure integrates and compensates for asymmetrical body morphology. Our study clearly indicates that different parts of the animat - specifically, nervous system and body plan - evolve in concert with and become highly functional with respect to the other parts. The autonomous emergence of morphological and neural computation in this model contributes to unveiling the surprisingly strong coupling of such systems in nature.

We aim to develop a new self-reconfigurable modular robot, Cross-Ball, so that we can apply bio-inspired morphogenesis mechanisms to modular robots to adapt to dynamic environments automatically. To this end, the mechanical design of modular robots has to be flexible and robust enough for various complex configurations. The major contributions of the design of this Cross-Ball robots include: 1) it provides several flexible 3D reconfiguration capabilities, such as rotating, parallel, and diagonal movements; (2) a flexible and robust hardware platform for modular robots using more complex self-reconfiguration algorithms; and (3) the mobility of each individual module. Furthermore, a skeleton-based approach is proposed for the motion control of the modules, where the module movements can be conducted in groups to improve the system reconfiguration efficiency. Some simulation results have demonstrated the feasibility of the proposed module design and the corresponding controller by reconfiguring the robots to various complex configurations.

This paper investigates the influence of redundancy on the evolutionary performance of a gene regulatory network governing a cellular growth process. Redundancy is believed to play a key role in robustness and evolvability of biological systems. We use a cellular model controlled by a gene regulatory network to evolve elongated morphologies. We show that removing the redundancy in the genome during the evolution decreases the performance of the evolution strategy. A comparing run with few parameters and therefore no redundancy performs worst, which supports the hypothesis that redundancy improves evolvability.

Steiner T, Jin Y, Sendhoff B, Pelikan M, Branke J. Evolving heterochrony for cellular differentiation using vector field embryogeny. In: Proceedings of the 12th annual conference on Genetic and evolutionary computation. New York, NY, USA: ACM; 2010: 571-578.

Using surrogate models in evolutionary search provides an efficient means of handling today's complex applications plagued with increasing high-computational needs. Recent surrogate-assisted evolutionary frameworks have relied on the use of a variety of different modeling approaches to approximate the complex problem landscape. From these recent studies, one main research issue is with the choice of modeling scheme used, which has been found to affect the performance of evolutionary search significantly. Given that theoretical knowledge available for making a decision on an approximation modela prioriis very much limited, this paper describes a generalization of surrogate-assisted evolutionary frameworks for optimization of problems with objectives and constraints that are computationally expensive to evaluate. The generalized evolutionary framework unifies diverse surrogate models synergistically in the evolutionary search. In particular, it focuses on attaining reliable search performance in the surrogate-assisted evolutionary framework by working on two major issues: 1) to mitigate the'curse of uncertainty'robustly, and 2) to benefit from the 'bless of uncertainty.' The backbone of the generalized framework is a surrogate-assisted memetic algorithm that conducts simultaneous local searches usingensembleandsmoothingsurrogate models, with the aims of generating reliable fitness prediction and search improvements simultaneously. Empirical study on commonly used optimization benchmark problems indicates that the generalized framework is capable of attaining reliable, high quality, and efficient performance under a limited computational budget.

A new cellular model for evolving stable, lightweight structures is presented in this paper. The focus lies in enhancing the ability of the cellular system to create complex 3D shapes with non self-similar regions. Compared to our previous work, the model proposed in this paper is composed of polarized cells that have directionally differential force functions for cell adhesion and thus are able to follow morphogen gradients (chemotaxis). We investigate the evolution of global information in form of evolving morphogen gradients that are created prior to development, which serve to guide cellular and shape differentiation. Our analysis shows that for a set of Pareto-optimal solutions of lightweight stable structures, no unique gradient can be evolved. Nevertheless, it is revealed that neighboring individuals in the genotype space are also neighbored in the gradient space. By contrast, neighborhood in the fitness space is not maintained in the genotype space. These results suggest that a hierarchical genetic formulation might be better than a 'common predefined spatial pattern' in form of a predefined gradient. In addition, our analysis also implies that some well-known properties in direct-coding evolutionary algorithms may be lost in developmental mappings.

This paper investigates empirically the influence of regulation logic on the dynamics of two computational models of genetic regulatory network motifs. The gene regulatory network motifs considered in this work consist of three genes with both positive and negative feedback loops. Two forms of fuzzy logic, namely, the Zadeh operators and the probabilistic operators, as well as the summation logic have been investigated. We show that the easiness of evolving sustained oscillation, and the stability of the evolved oscillation depend both on the regulation logic and on the consistency of the regulation on the target gene.

The Baldwin effect can be observed if phenotypic learning influences the evolutionary fitness of individuals, which can in turn accelerate or decelerate evolutionary change. Evidence for both learning-induced acceleration and deceleration can be found in the literature. Although the results for both outcomes were supported by specific mathematical or simulation models, no general predictions have been achieved so far. Here we propose a general framework to predict whether evolution benefits from learning or not. It is formulated in terms of the gain function, which quantifies the proportional change of fitness due to learning depending on the genotype value. With an inductive proof we show that a positive gain-function derivative implies that learning accelerates evolution, and a negative one implies deceleration under the condition that the population is distributed on a monotonic part of the fitness landscape. We show that the gain-function framework explains the results of several specific simulation models. We also use the gain-function framework to shed some light on the results of a recent biological experiment with fruit flies.

In the above titled paper (ibid., vol. 38, no. 3, pp. 397-415, May 08), there are three sites where an inequality is put wrongly. The corrections are presented here.

Autoregulation, toggle switch and relaxation oscillators are important regulatory motifs found in biological gene regulatory networks and interesting results have been reported on theoretical analyses of these regulatory units. However, it is so far unclear how evolution has shaped these motifs based on elementary biochemical reactions. This paper presents a method of designing important dynamics such as bistability and oscillation with these network motifs using an artificial evolutionary algorithm. The evolved dynamics of the network motifs are then verified when the initial states and the parameters of the network motifs are perturbed. It has been found that while it is straightforward to evolve the switching behavior, it is difficult to evolve stable oscillatory dynamics. We show that a higher Hill coefficient will facilitate the generation of undamped oscillation, however, an evolutionary path that can lead to a high Hill coefficient remains an open question for future research.

Inspired from bacteria, a gene regulatory network model for signal transduction is presented in this paper. After describing experiments on stabilizing the population size for sustained open-ended evolution, we examine the ability of the model to evolve gradient-following behavior resembling bacterial chemotaxis. Under the conditions defined in this paper, an overwhelming chemotaxis behavior does not seem to emerge. Further experimentation suggests that chemotaxis is selectively favored, however, it is shown that the gradient information, which is critical for evolving chemotaxis, is heavily degraded under the current regime. It is hypothesized that lack of consistent gradient information results in the selection of non chemotaxis behavior. Future work on revising the model as well as the environmental setups is discussed.

The Pareto front (Pareto set) of a continuous optimization problem with m objectives is a (m-1) dimensional piecewise continuous manifold in the objective space (the decision space) under some mild conditions. Based on this regularity property in the objective space, we have recently developed several multiobjective estimation of distribution algorithms (EDAs). However, this property has not been utilized in the decision space. Using the regularity property in both the objective and decision space, this paper proposes a simple EDA for multiobjective optimization. Since the location information has not efficiently used in EDAs, a combination of EDA and differential evolution (DE) is suggested for improving the algorithmic performance. The hybrid method and the pure EDA method proposed in this paper, and a DE based method are compared on several test instances. Experimental results have shown that the algorithm with the proposed strategy is very promising.

We present a model of simulated evolutionary development on the basis of cells as building blocks for growth. In this model, cells grow and interact in a three-dimensional (3D) environment, where development is controlled by a simple genome. Using cell-cell interaction such as differential adhesion, cells sort and form complex arrangements. This developmental process is evolved using a multi-objective evolutionary algorithm to achieve lightweight and stable material with a complex inner structure.

Computational fluid dynamics (CFD) simulations have been extensively used in many aerodynamic design optimization problems, such as wing and turbine blade shape design optimization. However, it normally takes very long time to solve such optimization problems due to the heavy computation load involved in CFD simulations, where a number of differential equations are to be solved. Some efforts have been seen using feedforward neural networks to approximate CFD models. However, feedforward neural network models cannot capture well the dynamics of the differential equations. Thus, training data from a large number of different designs are needed to train feedforward neural network models to achieve reliable generalization. In this work, a technique using differential recurrent neural networks has been proposed to predict the performance of candidate designs before the CFD simulation is fully converged. Compared to existing methods based on feedforward neural networks, this approach does not need a large number of previous designs. Case studies show that the proposed method is very promising.

Machine learning is inherently a multiobjective task. Traditionally, however, either only one of the objectives is adopted as the cost function or multiple objectives are aggregated to a scalar cost function. This can be mainly attributed to the fact that most conventional learning algorithms can only deal with a scalar cost function. Over the last decade, efforts on solving machine learning problems using the Pareto-based multiobjective optimization methodology have gained increasing impetus, particularly due to the great success of multiobjective optimization using evolutionary algorithms and other population-based stochastic search methods. It has been shown that Pareto-based multiobjective learning approaches are more powerful compared to learning algorithms with a scalar cost function in addressing various topics of machine learning, such as clustering, feature selection, improvement of generalization ability, knowledge extraction, and ensemble generation. One common benefit of the different multiobjective learning approaches is that a deeper insight into the learning problem can be gained by analyzing the Pareto front composed of multiple Pareto-optimal solutions. This paper provides an overview of the existing research on multiobjective machine learning, focusing on supervised learning. In addition, a number of case studies are provided to illustrate the major benefits of the Pareto-based approach to machine learning, e.g., how to identify interpretable models and models that can generalize on unseen data from the obtained Pareto-optimal solutions. Three approaches to Pareto-based multiobjective ensemble generation are compared and discussed in detail. Finally, potentially interesting topics in multiobjective machine learning are suggested.

In this paper, we present a model for simulating the evolution of development together with a method for the analysis of emergence of negative feedback inside the regulatory network. In order to record the development of feedback during evolution, we analyze both the static as well as the dynamic interactions between the transcription factors in the regulatory network. When perturbing the gene regulatory network using random mutations, we find that the evolved negative feedback is the main mechanism for robustness against such mutations. We argue that this robustness is the reason for the sustained emergence of negative feedback during evolution.

Target shape design optimization problem (TS-DOP) is a miniature model for real world design optimization problems. It is proposed as a test bed to design and analyze optimization approaches for design optimization with tremendously reducing the running period of optimization process, while, the merit can be only achieved by correctly approximating the real design situation and satisfying the causality of design and evaluation. The representation of the designed object is mostly described by parameterization techniques. To realize the design optimization, is to vary the parameterized object by means of operating the relevant parameters. The solution of design optimization often involved the choice of suitable description for the designed object, which can be obtained by expanding the design freedom. When changing the description length, the original parameters of the designed object will then varied. This bring about the requirements for optimization algorithms to self-adapt their strategy parameters and related variables to perform consistently searching. We first put forwards a revised fitness evaluation mechanism for the TSDOP in order to more reasonably check the designed shape and direct optimization procedures. Based on the revised TSDOP framework, we further discuss the parameter setting problem for algorithms, especially evolution strategies, to adapt and initial their search strategy parameters. A solution method is proposed with solving a linear equations by a recursive way with linear time complexity. All discussions are limited with the B-spline parameterization framework, but may generally suit other parameterization techniques. Experiments are used to verify the causality of the revised fitness evaluation mechanism and to study the significance of the proposed method for suitable parameter settings of optimization algorithms during the adaptation of the description length for design optimization.

The Pareto optimal set of a continuous multiobjective optimization problem is a piecewise continuous manifold under some mild conditions.We have recently developed several multi-objective evolutionary algorithms based on this property. However, the modelling methods used in these algorithms are rather costly. In this paper, a cheap and effective modelling strategy is proposed for building the probabilistic models of promising solutions. A new criterion is proposed for measuring the convergence of the algorithm. The locality degree of each local model is adjusted according to the proposed convergence criterion. Experimental results show that the algorithm with the proposed strategy is very promising.

Surrogate-Assisted Memetic Algorithm (SAMA) is a hybrid evolutionary algorithm, particularly a memetic algorithm that employs surrogate models in the optimization search. Since most of the objective function evaluations in SAMA are approximated, the search performance of SAMA is likely to be affected by the characteristics of the models used. In this paper, we study the search performance of using different meta modeling techniques, ensembles, and multi-surrogates in SAMA. In particular, we consider the SAMA-TRF, a SAMA model management framework that incorporates a trust region scheme for interleaving use of exact objective function with computationally cheap local meta models during local searches. Four different metamodels, namely Gaussian Process (GP), Radial Basis Function (RBF), Polynomial Regression (PR), and Extreme Learning Machine (ELM) neural network are used in the study. Empirical results obtained show that while some metamodeling techniques perform best on particular benchmark problems, ensemble of metamodels and multisurrogates yield robust and improved solution quality on the benchmark problems in general, for the same computational budget.

Multiobjective optimization problems with many local Pareto fronts is a big challenge to evolutionary algorithms. In this paper, two operators, biased initialization and biased crossover, are proposed to improve the global search ability of RM-MEDA, a recently proposed multiobjective estimation of distribution algorithm. Biased initialization inserts several globally Pareto optimal solutions into the initial population; biased crossover combines the location information of some best solutions found so far and globally statistical information extracted from current population. Experiments have been conducted to study the effects of these two operators.

In this paper, we propose two evolutionary strategies for the optimization of problems with actuator noise as encountered in robust optimization, where the design or objective parameters are subject to noise: the ROSAES and the ROCSAES. Both algorithms use a control rule for increasing the population size when the residual error to the optimizer state has been reached. Theoretical analysis has previously shown that the residual error depends among other factors on the population size and on the variance of the noise. Furthermore, ROSAES exploits the similarity of the mutation term in evolutionary strategies and the additive noise term in the case of actuator noise. The population variance is controlled to guarantee that the realized noise level is adjusted correctly. Simulations are carried out on test functions and the results are analyzed with respect to the performance and the dependence of ROSAES and ROCSAES on newly introduced exogenous strategy parameters.

In both numerical and stochastic optimization methods, surrogate models are often employed in lieu of the expensive high-fidelity models to enhance search efficiency. In gradient-based numerical methods, the trustworthiness of the surrogate models in predicting the fitness improvement is often addressed using ad hoc move limits or a trust region framework (TRF). Inspired by the success of TRF in line search, here we present a Trusted Evolutionary Algorithm (TEA) which is a surrogate-assisted evolutionary algorithm that exhibits the concept of surrogate model trustworthiness in its search. Empirical study on benchmark functions reveals that TEA converges to near-optimum solutions more efficiently than the canonical evolutionary algorithm.

In our previous work [1], it has been shown that the performance of multi-objective evolutionary algorithms can be greatly enhanced if the regularity in the distribution of Pareto-optimal solutions is used. This paper suggests a new hybrid multi-objective evolutionary algorithm by introducing a convergence based criterion to determine when the model-based method and when the genetics-based method should be used to generate offspring in each generation. The basic idea is that the genetics-based method, i. e., crossover and mutation, should be used when the population is far away from the Pareto front and no obvious regularity in population distribution can be observed. When the population moves towards the Pareto front, the distribution of the individuals will show increasing regularity and in this case, the model-based method should be used to generate offspring. The proposed hybrid method is verified on widely used test problems and our simulation results show that the method is effective in achieving Pareto-optimal solutions compared to two state-of-the-art evolutionary multi-objective algorithms: NSGA-II and SPEA2, and our pervious method in [1].

Several heuristic methods have been suggested for improving the generalization capability in neural network learning, most of which are concerned with a single-objective (SO) learning tasks. In this work, we discuss generalization improvement in multi-objective learning (MO). As a case study, we investigate the generation of neural network classifiers based on the receiver operating characteristics (ROC) analysis using an evolutionary multi-objective optimization algorithm. We show on a few benchmark problems that for MO learning such as the ROC based classification, the generalization ability can be more efficiently improved within a multi-objective framework than within a single-objective one.

Handling catastrophic forgetting is an interesting and challenging topic in modeling the memory mechanisms of the human brain using machine learning models. From a more general point of view, catastrophic forgetting reflects the stability-plasticity dilemma, which is one of the several dilemmas to be addressed in learning systems: to retain the stored memory while learning new information. Different to the existing approaches, we introduce a Pareto-optimality based multi-objective learning framework for alleviating catastrophic learning. Compared to the single-objective learning methods, multi-objective evolutionary learning with the help of pseudo-rehearsal is shown to be more promising in dealing with the stability-plasticity dilemma.

This paper proposes and analyzes a class of test functions for evolutionary robust optimization, the "functions with noise-induced multimodality" (FNIMs). After a motivational introduction gleaned from a real-world optimization problem, the robust optimizer properties of this test class are investigated with respect to different robustness measures. The steady-state behavior of evolution strategies on FNIMs will be investigated empirically. Being based on the empirical results, a subclass of FNIMs is identified which is amenable to an asymptotical performance analysis. The results of this analysis will be used to derive recommendations for the choice of strategy-specific parameters such as population size and truncation ratio

We present a case study of applying multi-objective optimization techniques to the three dimensional design of a turbine blade in a gas turbine that is designed for use in a small business jet. We illustrate the iterative approach to the formulation of the fitness function that is characteristic for such a practical problem and show how the Pareto front accumulated in this process may serve to represent the knowledge on this problem that was collected in the complete optimization process

Decomposing a complex computational problem into sub-problems, which are computationally simpler to solve individually and which can be combined to produce a solution to the full problem, can efficiently lead to compact and general solutions. Modular neural networks represent one of the ways in which this divide-and-conquer strategy can be implemented. Here we present a co-evolutionary model which is used to design and optimize modular neural networks with task-specific modules. The model consists of two populations. The first population consists of a pool of modules and the second population synthesizes complete systems by drawing elements from the pool of modules. Modules represent a part of the solution, which co-operates with others in the module population to form a complete solution. With the help of two artificial supervised learning tasks created by mixing two sub-tasks we demonstrate that if a particular task decomposition is better in terms of performance on the overall task, it can be evolved using this co-evolutionary model.

Theoretical analysis of the dynamics of evolutionary algorithms is believed to be very important to understand the search behavior of evolutionary algorithms and to develop more efficient algorithms. We investigate the dynamics of a canonical genetic algorithm with one-point crossover and mutation theoretically. To this end, a new theoretical framework has been suggested in which the probability of each chromosome in the offspring population can be calculated from the probability distribution of the parent population after crossover and mutation. Empirical studies are conducted to verify the theoretical analysis. The finite population effect is also discussed. Compared to existing approaches to dynamics analysis, our theoretical framework is able to provide richer information on population dynamics and is computationally more efficient

Genetic algorithms (GAs) and evolution strategies (ESs) are two widely used evolutionary algorithms. The main differences between GAs and ESs lie in their representations and variation operators, which result in very different search dynamics. In this paper, we compare the search dynamics of GAs and ESs theoretically using a theoretical framework for analyzing the search dynamics of evolution strategies proposed in this paper and a framework for genetic algorithms we suggested in (2005). Based on the theoretical analysis, interesting aspects of the search dynamics of GAs and ESs for single objective optimization are revealed. As an extension, preliminary results on the search dynamics of GAs for multi-objective optimization are also presented

In this paper, we present the application of evolutionary optimization methods to a demanding, industrially relevant engineering domain, the three-dimensional optimization of gas turbine stator blades. This optimization problem is high-dimensional search and computationally very expensive. We show that, despite of its difficulty, the problem is feasible. Our approach not only successfully optimizes the aerodynamic design but also yields interesting results from an engineering point of view.

Design optimization is a well established application field of evolutionary computation. However, standard recombination operators acting on the genotypic representation of the design or shape are often too disruptive to be useful during optimization. In this work, we will analyze whether morphing methods between two shapes can be used as recombination operators acting on the phenotype space, thus directly on the shape or design. We introduce three different morphing methods and employ them as recombination operators in a standard evolution strategy (es). We compare their performance with an evolution strategy without any recombination operators on two target shape approximation problem. We can conclude that two of the three morphing methods can be useful during search although all morphing methods still turn out to hinder the self-adaptation of the step sizes of the evolution strategy.

A major problem in designing artificial neural networks is the proper choice of the network architecture. Especially for vision networks classifying three-dimensional (3-D) objects this problem is very challenging, as these networks are necessarily large and therefore the search space for defining the needed networks is of a very high dimensionality. This strongly increases the chances of obtaining only suboptimal structures from standard optimization algorithms. We tackle this problem in two ways. First, we use biologically inspired hierarchical vision models to narrow the space of possible architectures and to reduce the dimensionality of the search space. Second, we employ evolutionary optimization techniques to determine optimal features and nonlinearities of the visual hierarchy. Here, we especially focus on higher order complex features in higher hierarchical stages. We compare two different approaches to perform an evolutionary optimization of these features. In the first setting, we directly code the features into the genome. In the second setting, in analogy to an ontogenetical development process, we suggest the new method of an indirect coding of the features via an unsupervised learning process, which is embedded into the evolutionary optimization. In both cases the processing nonlinearities are encoded directly into the genome and are thus subject to optimization. The fitness of the individuals for the evolutionary selection process is computed by measuring the network classification performance on a benchmark image database. Here, we use a nearest-neighbor classification approach, based on the hierarchical feature output. We compare the found solutions with respect to their ability to generalize. We differentiate between a first- and a second-order generalization. The first-order generalization denotes how well the vision system, after evolutionary optimization of the features and nonlinearities using a database A, can classify previously unseen test views of objects from this database A. As second-order generalization, we denote the ability of the vision system to perform classification on a database B using the features and nonlinearities optimized on database A. We show that the direct feature coding approach leads to networks with a better first-order generalization, whereas the second-order generalization is on an equally high level for both direct and indirect coding. We also compare the second-order generalization results with other state-of-the-art recognition systems and show that both approaches lead to optimized recognition systems, which are highly competitive with recent recognition algorithms.

Regularization is an essential technique to improve generalization of neural networks. Traditionally, regularization is conducted by including an additional term in the cost function of a learning algorithm. One main drawback of these regularization techniques is that a hyperparameter that determines to which extension the regularization influences the learning algorithm must be determined beforehand. This paper addresses the neural network regularization problem from a multi-objective optimization point of view. During the optimization, both structure and parameters of the neural network will be optimized. A slightly modified version of two multi-objective optimization algorithms, the dynamic weighted aggregation (DWA) method and the elitist non-dominated sorting genetic algorithm (NSGA-II) are used and compared. An evolutionary multi-objective approach to neural network regularization has a number of advantages compared to the traditional methods. First, a number of models with a spectrum of model complexity can be obtained in one optimization run instead of only one single solution. Second, an efficient new regularization term can be introduced, which is not applicable to gradient-based learning algorithms. As a natural by-product of the multi-objective optimization approach to neural network regularization, neural network ensembles can be easily constructed using the obtained networks with different levels of model complexity. Thus, the model complexity of the ensemble can be adjusted by adjusting the weight of each member network in the ensemble. Simulations are carried out on a test function to illustrate the feasibility of the proposed ideas.

We introduce a decision making framework that uses evolutionary and learning methods. It is applied to competitive games to learn online the current opponent strategy and to adapt the system counter-strategy appropriately. We compared our system for the iterated prisoner's dilemma and rock-paper-scissors with three other methods against different typical game strategies as opponents. Results show that our system performs best in most cases and is able to adapt its strategy online to the current opponent. Moreover we could show that a good prediction of the opponent is no guaranty for a good payoff, since a good prediction is often the result of a poor opponent strategy which leads to a low payoff for both players.

The distribution of the Pareto-optimal solutions often has a clear structure. To adapt evolutionary algorithms to the structure of a multi-objective optimization problem, either an adaptive representation or adaptive genetic operators should be employed. We suggest an estimation of distribution algorithm for solving multi-objective optimization, which is able to adjust its reproduction process to the problem structure. For this purpose, a new algorithm called Voronoi-based estimation of distribution algorithm (VEDA) is proposed. In VEDA, a Voronoi diagram is used to construct stochastic models, based on which new offspring will be generated. Empirical comparisons of the VEDA with other estimation of distribution algorithms (EDAs) and the popular NSGA-II algorithm are carried out. In addition, representation of Pareto-optimal solutions using a mathematical model rather than a solution set is also discussed.

Target shape design optimization problem is to approximate an unknown shape, when a black-box function provides the fitness of the shape. The framework to solve this problem can be applied to the finding of optimized aerodynamic structures such as airplane wings or gas turbine blades. In order to approximate the two- and three-dimensional closed curve shapes, we use the idea of incremental abstraction, that is to find the best n-point polygon in the beginning and double the number n in the next stage until n reaches the specified limit. This idea is embodied into evolution strategies with a modified 1/5 rule using multiple layers. Furthermore, for the three-dimensional hidden object, the problem was decomposed into several 2D optimization problems. The results show that the suggested method is quite effective to solve the given problems even if the evaluation function has stochastic noise elements. The general strategy can also be applied to other practical applications using evolutionary algorithms.

Local search techniques have proved to be very efficient in evolutionary multi-objective optimization (MOO). However, the reasons behind the success of local search in MOO have not yet been well discussed. This paper attempts to investigate empirically the main factors that may have contributed significantly to the success of local search in MOO. It is found that for many widely used test problems, the Pareto optimal solutions are connected both in objective space and parameter space. Besides, the Pareto-optimal solutions often distribute so regularly in parameter space that they can be defined by piecewise linear functions. By constructing an approximate model using the solutions produced by an optimizer, the quality of the non-dominated solution set can be further improved. The evolutionary dynamic weighted aggregation (EDWA) method has been adopted as a local search technique in finding Pareto-optimal solutions. Its effectiveness for MOO is demonstrated on a number of two or three objective optimization problems.

Although many methods for dealing with multi-objective optimisation (MOO) problems are available as stated in K. Deb (2001) and successful applications have been reported on C.A. Coello et al. (2001), the comparison between MOO methods applied to real-world problem was rarely carried out. This paper reports the comparison between MOO methods applied to a real-world problem, namely, the optimization of a micro heat exchanger (/spl mu/HEX). Two MOO methods, dynamically weighted aggregation (DWA) proposed by Y. Jin et al. (2001) and non-dominated sorting genetic algorithms (NSGA-II) proposed by K. Deb et al. (2000) and K. Deb et al. (2002), were used for the study. The commercial computational fluid dynamics (CFD) solver CFD-ACE+ is used to evaluate fitness. We introduce how to interface the commercial solver with evolutionary computation (EC) and also report the necessary functionalities of the commercial solver to be used for the optimisation.

A large number of methods for solving multiobjective optimisation (MOO) problems have been developed. To compare these methods rigorously, or to measure the performance of a particular MOO algorithm quantitatively, a variety of performance indices (PIs) have been proposed. We provide an overview of the various PIs and attempts to categorise them into a certain number of classes according to their properties. Comparative studies have been conducted using a group of artificial solution sets and a group of solution sets obtained by various MOO solvers to show the advantages and disadvantages of the PIs. The comparative studies show that many PIs may be misleading in that they fail to truly reflect the quality of solution sets. Thus, it may not be a good practice to evaluate the performance of MOO solvers based on PIs only.

For tackling multiobjective optimisation (MOO) problem, many methods are available in the field of evolutionary computation (EC). To use the proposed method(s), the choice of the representation should be considered first. In EC, often binary representation and real-valued representation are used. We propose a hybrid representation, composed of binary and real-valued representations for multi-objective optimisation problems. Several issues such as discretisation error in the binary representation, self-adaptation of strategy parameters and adaptive switching of representations are addressed. Experiments are conducted on five test functions using six different performance indices, which shows that the hybrid representation exhibits better and more stable performance than the single binary or real-valued representation.

Neural networks and Kriging method are compared for constructing fitness approximation models in evolutionary optimization algorithms. The two models are applied in an identical framework to the optimization of a number of well known test functions. In addition, two different ways of training the approximators are evaluated: in one setting the models are built off-line using data from previous optimization runs and in the other setting the models are built online from the data available from the current optimization.

It is not unusual that an approximate model is needed for fitness evaluation in evolutionary computation. In this case, the convergence properties of the evolutionary algorithm are unclear due to the approximation error of the model. In this paper, extensive empirical studies are carried out to investigate the convergence properties of an evolution strategy using an approximate fitness function on two benchmark problems. It is found that incorrect convergence will occur if the approximate model has false optima. To address this problem, individual- and generation-based evolution control are introduced and the resulting effects on the convergence properties are presented. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization, which is able to guarantee the correct convergence of the evolutionary algorithm, as well as to reduce the computation cost as much as possible. Control of the evolution and updating of the approximate models are based on the estimated fidelity of the approximate model. Numerical results are presented for three test problems and for an aerodynamic design example.

Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is time-consuming. Simulations on two benchmark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time.

The evaluation of fluid dynamic properties of various different structures is a computationally very demanding process. This is of particular importance when population based evolutionary algorithms are used for the optimization of aerodynamic structures like wings or turbine blades. Besides choosing algorithms which only need few generations or function evaluations, it is important to reduce the number of object parameters as much as possible. This is usually done by restricting the optimization to certain attributes of the design which are seen as important. By doing so, the freedom for the optimization is restricted to areas of the design space where good solutions are expected. This can be problematic especially if the properties of the design and their interactions are not known sufficiently well like for example for transonic flow conditions. In order to be able to combine the conflicting constraints of a minimal set of parameters and the maximal degree of freedom, we propose an adaptive or growing representation for spline coded structures. In this way, the optimization is started with a simple representation with a minimal description length. The number of describing parameters is adapted during the optimization using a mutation operator working on the structure of the encoding. We compare this method with four different evolution strategies using a spline fitting problem as a test function.

In order to optimise unconstrained, large neural network structures with evolutionary algorithms, indirect encodings have been proposed. However, if the evolutionary process is combined with network learning, which is sensible both with respect to technical applications in dynamical environments and to the biological paragon, a way has to be found to combine learning with the evolutionary optimisation of such large structures. Utilising the development of neural systems during ontogeny seems a logical starting point for the realization of a step by step learning in networks. Furthermore, the combination of network growth during the developmental phase with an incremental problem complexity might allow the optimisation of large network structures together with learning. The author proposes a model to simulate such a combined approach and applies it to the problem of time series modelling. By introducing several measures for the transfer of information from one developmental step to the next, we will be able to quantitatively analyse the behaviour of the proposed model.

The combination of evolutionary algorithms and neural networks for the purpose of structure optimization has frequently been discussed. In this paper we apply an indirect encoding method, the recursive encoding combined with a gradual growth process of the network structure, to the problem of time series prediction and modelling. Modularity of the network structure, the optimization of the encoding parameters on a larger time-scale, i.e., a meta-evolutionary process and the choice of encoding dependent search operators to enhance the strong causality of the search process are discussed.

Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC(3)). Flexibility, and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of the input variables increases. However, the completeness and consistency conditions are often violated if a fuzzy system is generated from data collected from real world applications. A systematic design paradigm is proposed using evolution strategies. The structure of the fuzzy rules, which determines the compactness of the fuzzy systems, is evolved along with the parameters of the fuzzy systems. Special attention has been paid to the completeness and consistency of the rule base. The completeness is guaranteed by checking the completeness of the fuzzy partitioning of input variables and the completeness of the rule structure. An index of inconsistency is suggested with the help of a fuzzy similarity which can prevent the algorithm from generating rules that seriously contradict with each other or with the heuristic knowledge. In addition, soft T-norm and BADD defuzzification are introduced and optimized to increase the flexibility of the fuzzy system. The proposed approach is applied to the design of a distance controller for cars. It is verified that a FC(3) fuzzy system works very well both, for training and test driving situations, especially when the training data are insufficient.

Artificial neural networks have evolved from their biologically inspired roots to a well established means to solve a broad spectrum of engineering problems. Their embedding into modern statistics has provided the necessary theoretical foundation for challenging engineering tasks, such as advanced real time image and signal processing. These are exemplary demonstrations for the applicability of this approach to complex information processing. However, the large number of applications must not obscure the fact that there are some major unsolved problems concerning neural networks. There are still no satisfactorily constructive ways to determine the optimal structure (elements as well as organization) or the learning and evaluation dynamics. Ongoing research addresses these problems. In addition to pursuing this direction, one can ask what other lessons we can learn from biology concerning complex information processing. Our goal is to sketch a possible pathway from neural networks to more comprehensive neural strategies.