The practical deployment of Federated Learning (FL) on resource-constrained devices is fundamentally limited by the high cost of training large models and the instability caused by heterogeneous (non-IID) client data. Conventional pruning methods often treat data heterogeneity as a problem to be mitigated. In this work, we introduce a paradigm shift: we reframe client diversity as a feature to be harnessed. We propose AutoFLIP, a framework that begins not with training, but with a one-time federated loss exploration. During this phase, clients collaboratively build a map of the collective loss landscape, using their diverse data to reveal the problem's essential structure. This shared intelligence then guides an adaptive pruning strategy that is dynamically refined by client agreement throughout training. This approach allows AutoFLIP to identify robust and efficient sub-networks from the outset. Our extensive experiments show that AutoFLIP reduces computational overhead by an average of 52% and communication costs by over 65% while simultaneously achieving state-of-the-art accuracy in challenging non-IID settings.

The rapid advancement of generative AI enables highly realistic synthetic video, posing significant challenges for content authentication and raising urgent concerns about misuse. Existing detection methods often struggle with generalization and capturing subtle temporal inconsistencies. We propose $ReStraV$ ($Re$presentation $Stra$ightening for $V$ideo), a novel approach to distinguish natural from AI-generated videos. Inspired by the ``perceptual straightening'' hypothesis—which suggests real-world video trajectories become more straight in neural representation domain—we analyze deviations from this expected geometric property. Using a pre-trained self-supervised vision transformer (DINOv2), we quantify the temporal curvature and stepwise distance in the model's representation domain. We aggregate statistical and signals descriptors of these measures for each video and train a classifier. Our analysis shows that AI-generated videos exhibit significantly different curvature and distance patterns compared to real videos. A lightweight classifier achieves state-of-the-art detection performance (e.g., $97.17$ % accuracy and $98.63$ % AUROC on the VidProM benchmark, substantially outperforming existing image- and video-based methods. ReStraV is computationally efficient, it is offering a low-cost and effective detection solution. This work provides new insights into using neural representation geometry for AI-generated video detection.

A common aim in real-world optimisation problems is to seek a solution offering highest performance on expected scenarios, but at the same time guaranteeing an at least acceptable performance on worst-case scenarios. Competitive coevolution evolves a population of solutions alongside a population of difficult scenarios in order to find so-called robust solutions. However, solutions with maximal worst-case performance often exhibit poor performance on more typical scenarios. Existing coevolutionary approaches generally favour such solutions over ones which sacrifice only a small amount of average performance for an almost as large gain in worst-case performance, despite the latter being favourable in most practical applications. We present a new coevolutionary algorithm which treats average performance and worst-case performance as two objectives of a bicriteria optimisation problem and seeks the corresponding Pareto front. Such an algorithm enables the discovery of solutions with strong performance in both of these metrics, which would otherwise be rejected if optimising for only one. Our algorithm constitutes the first coevolutionary approach to this solution concept. We also provide experimental results on the performance of this algorithm on the design of smart controllers for the management of energy flow between buildings, renewable energy sources, and electric vehicles.

Automated machine learning (AutoML) has emerged as a pivotal tool for applying machine learning (ML) models to real-world problems. Tree-based pipeline optimization tool (TPOT) is an AutoML framework known for effectively solving complex tasks. TPOT's search involves two fundamental objectives: finding optimal pipeline structures (i.e., combinations of ML operators) and identifying suitable hyperparameters for these structures. While its use of genetic programming enables TPOT to excel in structural search, its hyperparameter search, involving discretization and random selection from extensive potential value ranges, can be computationally inefficient. This paper presents a novel methodology that heavily restricts the initial hyperparameter search space, directing TPOT's focus towards structural exploration. As the search evolves, Bayesian optimization (BO) is used to refine the hyperparameter space based on data from previous pipeline evaluations. This method leads to a more targeted search, crucial in situations with limited computational resources. Two variants of this approach are proposed and compared with standard TPOT across six datasets, with up to 20 features and 20,000 samples. The results show the proposed method is competitive with canonical TPOT, and outperforms it in some cases. The study also provides new insights into the dynamics of pipeline structure and hyperparameter search within TPOT.

Federated learning (FL) has emerged as a ground-breaking paradigm in machine learning (ML), offering privacy-preserving collaborative model training across diverse datasets. Despite its promise, FL faces significant hurdles in non-identically and independently distributed (non-IID) data scenarios, where most existing methods often struggle with data heterogeneity and lack robustness in performance. This paper introduces Federated Loss Exploration (FedLEx), an innovative approach specifically designed to tackle these challenges. FedLEx distinctively addresses the shortcomings of existing FL methods in non-IID settings by optimizing its learning behavior for scenarios in which assumptions about data heterogeneity are impractical or unknown. It employs a federated loss exploration technique, where clients contribute to a global guidance matrix by calculating gradient deviations for model parameters. This matrix serves as a strategic compass to guide clients’ gradient updates in subsequent FL rounds, thereby fostering optimal parameter updates for the global model. FedLEx effectively navigates the complex loss surfaces inherent in non-IID data, enhancing knowledge transfer in an efficient manner, since only a small number of epochs and small amount of data are required to build a strong global guidance matrix that can achieve model convergence without the need for additional data sharing or data distribution statics in a large client scenario. Our extensive experiments with state-of-the art FL algorithms demonstrate significant improvements in performance, particularly under realistic non-IID conditions, thus highlighting FedLEx’s potential to overcome critical barriers in diverse FL applications.

Multiobjective optimization problems whose objectives have different evaluation costs are commonly seen in the real world. Such problems are now known as multiobjective optimization problems with heterogeneous objectives (HE-MOPs). So far, however, only a few studies have been reported on addressing HE-MOPs, and most of them focus on biobjective problems with one fast objective and one slow objective. In this work, we aim to deal with HE-MOPs having more than two black-box and heterogeneous objectives. To this end, we develop a multiobjective Bayesian evolutionary optimization (BEO) approach to HE-MOPs that can alleviate search biases resulting from the different numbers of function evaluations allowed for the cheap and expensive objectives, which is achieved by designing a new acquisition function that penalizes the search bias toward the fast objectives, thereby achieving a balance between convergence and diversity. In addition, to make the best use of the different amounts of training data while avoiding increasing the computational cost, an ensemble consisting of two Gaussian processes is constructed for each cheap objective, one trained on the data collected before the Bayesian optimization starts, and the other on those evaluated during the BEO. Empirical studies on widely used multi-/many-objective benchmark problems whose objectives are assumed to be heterogeneously expensive demonstrate that the proposed algorithm is able to find high-quality solutions for HE-MOPs compared with the state-of-the-art methods.

Tree-based pipeline optimization tool (TPOT) is used to automatically construct and optimize machine learning pipelines for classification or regression tasks. The pipelines are represented as trees comprising multiple data transformation and machine learning operators --- each using discrete hyper-parameter spaces --- and optimized with genetic programming. During the evolution process, TPOT evaluates numerous pipelines which can be challenging when computing budget is limited. In this study, we integrate TPOT with Bayesian Optimization (BO) to extend its ability to search across continuous hyper-parameter spaces, and attempt to improve its performance when there is a limited computational budget. Multiple hybrid variants are proposed and systematically evaluated, including (a) sequential/periodic use of BO and (b) use of discrete/continuous search spaces for BO. The performance of these variants is assessed using 6 data sets with up to 20 features and 20,000 samples. Furthermore, an adaptive variant was designed where the choice of whether to apply TPOT or BO is made automatically in each generation. While the variants did not produce results that are significantly better than "standard" TPOT, the study uncovered important insights into the behavior and limitations of TPOT itself which is valuable in designing improved variants.

Abstract In the early stages of engineering design, multitudes of feasible designs can be generated using structural optimization methods by varying the design requirements or user preferences for different performance objectives. Data mining such potentially large datasets is a challenging task. An unsupervised data-centric approach for exploring designs is to find clusters of similar designs and recommend only the cluster representatives for review. Design similarity can be defined not only on a purely functional level but also based on geometric properties, such as size, shape, and topology. While metrics such as chamfer distance measure the geometrical differences intuitively, it is more useful for design exploration to use metrics based on geometric features, which are extracted from high-dimensional 3D geometric data using dimensionality reduction techniques. If the Euclidean distance in the geometric features is meaningful, the features can be combined with performance attributes resulting in an aggregate feature vector that can potentially be useful in design exploration based on both geometry and performance. We propose a novel approach to evaluate such derived metrics by measuring their similarity with the metrics commonly used in 3D object classification. Furthermore, we measure clustering accuracy, which is a state-of-the-art unsupervised approach to evaluate metrics. For this purpose, we use a labeled, synthetic dataset with topologically complex designs. From our results, we conclude that Pointcloud Autoencoder is promising in encoding geometric features and developing a comprehensive design exploration method.

In multiobjective decision making, most knee identification algorithms implicitly assume that the given solutions are well distributed and can provide sufficient information for identifying knee solutions. However, this assumption may fail to hold when the number of objectives is large or when the shape of the Pareto front is complex. To address the above issues, we propose a knee-oriented solution augmentation (KSA) framework that converts the Pareto front into a multimodal auxiliary function whose basins correspond to the knee regions of the Pareto front. The auxiliary function is then approximated using a surrogate and its basins are identified by a peak detection method. Additional solutions are then generated in the detected basins in the objective space and mapped to the decision space with the help of an inverse model. These solutions are evaluated by the original objective functions and added to the given solution set. To assess the quality of the augmented solution set, a measurement is proposed for the verification of knee solutions when the true Pareto front is unknown. The effectiveness of KSA is verified on widely used benchmark problems and successfully applied to a hybrid electric vehicle controller design problem.

Topology optimization optimizes material layout in a design space for a given objective, such as crash energy absorption, and a set of boundary conditions. In industrial applications, multi-objective topology optimization requires expensive simulations to evaluate the objectives and generate multiple Pareto-optimal solutions. So, it is more economical to identify preferred regions on the Pareto front and generate only the desired solutions. Clustering methods, a widely used subclass of machine learning methods, provide an unsupervised approach to summarize the dataset, which eases the identification of the preferred set of designs. However, generating solutions similar to the preferred designs based on different metrics is a challenging task. In this paper, we present an interactive method to generate designs similar to a preferred set using one of the state-of-the-art weighted-sum approaches called scaled energy weighting - hybrid cellular automata (SEW-HCA). To avoid unnecessary computations, metamodels are used to predict the desired weight vectors needed by SEW-HCA. We evaluate an application of our method for cooperative topology optimization using a cantilever multi-load-case problem and a crashworthiness optimization problem. Using the proposed method, we could successfully generate designs that are similar to preferred solutions based on geometry and performance. We believe that this is a crucial component that will improve the usefulness of multi-objective topology optimization in real-world applications.

In the context of real-world path planning applications for Unmanned Aerial Vehicles (UAVs), aspects such as handling of multiple objectives (e.g., minimizing risk, path length, travel time, energy consumption, or noise pollution), generation of smooth trajectories in 3D space, and the ability to deal with urban environments have to be taken into account jointly by an optimization algorithm to provide practically feasible solutions. Since the currently available methods do not allow for that, in this paper, we propose a holistic approach for solving a Multi-Objective Path Planning (MOPP) problem for UAVs in a three-dimensional, large-scale urban environment. For the tackled optimization problem, we propose an energy model and a noise model for a UAV, following a smooth 3D path. We utilize a path representation based on 3D Non-Uniform Rational B-Splines (NURBS). As optimizers, we use a conventional version of an Evolution Strategy (ES), two standard Multi-Objective Evolutionary Algorithms (MOEAs) - NSGA2 and MO-CMA-ES, and a gradient-based L-BFGS-B approach. To guide the optimization, we propose hybrid versions of the mentioned algorithms by applying an advanced initialization scheme that is based on the exact bidirectional Dijkstra algorithm. We compare the different algorithms with and without hybrid initialization in a statistical analysis, which considers the number of function evaluations and quality features of the obtained Pareto fronts indicating convergence and diversity of the solutions. We evaluate the methods on a realistic 3D urban path planning scenario in New York City, based on real-world data exported from OpenStreetMap. The examination's results indicate that hybrid initialization is the main factor for the efficient identification of near-optimal solutions.

Most existing multiobjective evolutionary algorithms (MOEAs) implicitly assume that each objective function can be evaluated within the same period of time. Typically. this is untenable in many real-world optimization scenarios where evaluation of different objectives involves different computer simulations or physical experiments with distinct time complexity. To address this issue, a transfer learning scheme based on surrogate-assisted evolutionary algorithms (SAEAs) is proposed, in which a co-surrogate is adopted to model the functional relationship between the fast and slow objective functions and a transferable instance selection method is introduced to acquire useful knowledge from the search process of the fast objective. Our experimental results on DTLZ and UF test suites demonstrate that the proposed algorithm is competitive for solving bi-objective optimization where objectives have non-uniform evaluation times.

In preference-based optimization, knee points are considered the naturally preferred tradeoff solutions, especially when the decision maker has little a priori knowledge about the problem to be solved. However, identifying all convex knee regions of a Pareto front remains extremely challenging, in particular in a high-dimensional objective space. This article presents a new evolutionary multiobjective algorithm for locating knee regions using two localized dominance relationships. In the environmental selection, the α-dominance is applied to each subpopulation partitioned by a set of predefined reference vectors, thereby guiding the search toward different potential knee regions while removing possible dominance resistant solutions. A knee-oriented-dominance measure making use of the extreme points is then proposed to detect knee solutions in convex knee regions and discard solutions in concave knee regions. Our experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art knee identification algorithms on a majority of multiobjective optimization test problems having up to eight objectives and a hybrid electric vehicle controller design problem with seven objectives.

In practical multi/many-objective optimization problems, a decision maker is often only interested in a handful of solutions of interest (SOI) instead of the entire Pareto Front (PF). It is therefore of significant research interest to design algorithms that can automatically detect SOIs and search around them instead of attempting to find the entire PF. However, this is challenging for a number of reasons. First and foremost, the interpretation of the underlying measures in terms of quantifying trade-off information for SOIs is not straightforward. Scalability is also an issue for most of such existing measures. Additionally, for many-objective algorithms that rely on decomposition, adaptation of reference directions and appropriate means to scale the objectives to maintain solution density around SOIs is not trivial. Lastly, constraints and decision-space are often overlooked in the existing studies but are important for practical applications. In this work, we present a simple approach to identify SOIs, using normalized net gain over nadir point and angle of influence. We illustrate the utility of the measure for offline and online identification of SOIs using a range of unconstrained and constrained benchmarks and practical design problems spanning up to 5 objectives. We also show further analysis in decision-space for an application problem to aid decision-making in practical scenarios.

Despite the success of evolutionary algorithms (EAs) for solving multi-objective problems, most of them are based on the assumption that all objectives can be evaluated within the same period of time. However, in many real-world applications, such an assumption is unrealistic since different objectives must be evaluated using different computer simulations or physical experiments with various time complexities. To address this issue, a surrogate assisted evolutionary algorithm along with a parameter-based transfer learning (T-SAEA) is proposed in this work. While the surrogate for the cheap objective can be updated on sufficient training data, the surrogate for the expensive one is updated by either the training data set or a transfer learning approach. To find out the transferable knowledge, a filter-based feature selection algorithm is used to capture the pivotal features of each objective, and then use the common important features as a carrier for knowledge transfer between the cheap and expensive objectives. Then, the corresponding parameters in the surrogate models are adaptively shared to enhance the quality of the surrogate models. The experimental results demonstrate that the proposed algorithm outperforms the compared algorithms on the bi-objective optimization problems whose objectives have a large difference in computational complexities.

In multiobjective optimization, it is nontrivial for decision makers to articulate preferences without a priori knowledge, which is particularly true when the number of objectives becomes large. Depending on the shape of the Pareto front, optimal solutions such as knee points may be of interest. Although several multi- and many-objective optimization test suites have been proposed, little work has been reported focusing on designing multiobjective problems whose Pareto front contains complex knee regions. Likewise, few performance indicators dedicated to evaluate an algorithm's ability of accurately locating all knee points in high-dimensional objective space have been suggested. This paper proposes a set of multiobjective optimization test problems whose Pareto front consists of complex knee regions, aiming to assess the capability of evolutionary algorithms to accurately identify all knee points. Various features related to knee points have been taken into account in designing the test problems, including symmetry, differentiability, and degeneration. These features are also combined with other challenges in solving the optimization problems, such as multimodality, linkage between decision variables, nonuniformity, and scalability of the Pareto front. The proposed test problems are scalable to both decision and objective spaces. Accordingly, new performance indicators are suggested for evaluating the capability of optimization algorithms in locating the knee points. The proposed test problems, together with the performance indicators, offer a new means to develop and assess preference-based evolutionary algorithms for solving multi- and many-objective optimization problems.

Black-box topology optimization (BBTO) uses evolutionary algorithms and other soft computing techniques to generate near-optimal topologies of mechanical structures. Although evolutionary algorithms are widely used to compensate the limited applicability of conventional gradient optimization techniques, methods based on BBTO have been criticized due to numerous drawbacks. In this article, we discuss topology optimization as a black-box optimization problem. We review the main BBTO methods, discuss their challenges and present approaches to relax them. Dealing with those challenges effectively can lead to wider applicability of topology optimization, as well as the ability to tackle industrial, highly constrained, nonlinear, many-objective, and multimodal problems. Consequently, future research in this area may open the door for innovating new applications in science and engineering that may go beyond solving classical optimization problems of mechanical structures. Furthermore, algorithms designed for BBTO can be added to existing software toolboxes and packages of topology optimization.

In this paper, a new real-world application problem, i.e., the vehicle fleet maintenance scheduling optimization problem, is defined and a specialized multi-objective evolutionary algorithm framework (grouping strategy, three vector chromosome and corresponding genetic operators) is proposed to solve the problem. State-of-the-art multi-objective evolutionary algorithms such as NSGA-III, SMS-EMOA, DI-MOEA are employed in the proposed algorithm framework to solve the problem, and their behavior is investigated. Although DI-MOEA is used the first time for a real-world application problem, its performance is better than other algorithms for some instances.

Past decades have witnessed a rapid development in research on multi- and many-objective evolutionary optimization. Reference-based and preference-based strategies are both widely used in dealing with the multi- and many-objective optimization problems. However, little effort has been devoted to a critical analysis of similarities and differences between the two approaches. This paper revisits the methodologies, compares the similarities and differences, and discusses the limitations of reference-based and preference-based many-objective evolutionary algorithms. Our analyses reveal that preference information may be embedded into reference-based methods in dealing with irregular problems so that the objective space can be better explored and a solution set of interest to the user will be obtained. Meanwhile, it is far from trivial for a decision-maker to provide informed preferences without sufficient a priori knowledge of the problem in the preference-based optimization. Therefore, this paper suggests a new approach to many-objective optimization problems that integrates preference-based and reference-based methodologies, where the solutions of natural interest such as the knee regions are identified at first and then the acquired knowledge of the knee regions can be used in reference-based methods. This way, accurate, diverse and preferred solutions can be obtained, and a deeper insight into the problem can be gained.

This work presents a hybrid optimization approach that couples Efficient Global Optimization (EGO) and Co-variance Matrix Adaptation Evolution Strategy (CMA-ES) in the Topology Optimization (TO) of mechanical structures. Both of these methods are regarded as good optimization strategies for continuous global optimization of expensive and multimodal problems, e.g. associated with vehicle crashworthiness. CMA-ES is flexible and robust to changing circumstances. Moreover, by taking advantage of a low-dimensional parametrization introduced by the Evolutionary Level Set Method (EA-LSM) for structural Topology Optimization, such Evolution Strategy allows for dealing with costly problems even more efficiently. However, it is characterized by high computational costs, which can be mitigated by using the EGO algorithm at the early stages of the optimization process. By means of surrogate models, EGO allows for the construction of cheap-to-evaluate approximations of the objective functions, leading to an initial fast convergence towards the optimum in opposition to a poor exploitive behavior. The approach presented here - the Hybrid Kriging-assisted Level Set Method (HKG-LSM) - first uses the Kriging-based method for Level Set Topology Optimization (KG-LSM) to converge fast at the beginning of the optimization process and explore the design space to find promising regions. Afterwards, the algorithm switches to the EA-LSM using CMA-ES, whose parameters are initialized based on the previous model. A static benchmark test case is used to assess the proposed methodology in terms of convergence speed. The obtained results show that the HKG-LSM represents a valuable option for speeding up the optimization process in real-world applications with limited computational resources. As such, the proposed methodology exhibits a much more general potential, e.g. when dealing with high-fidelity crash simulations.

Many evolutionary algorithms have been proposed and demonstrated to have excellent performance in striking a balance between convergence and diversity in dealing with multiobjective optimization problems. However, little attention has been paid to the decision making stage where a small number of solutions are selected to be presented to the user. It is believed that knee points are considered to be the naturally preferred solutions when no specific preferences are available, because knee solutions incur a large loss in at least one objective to gain a small amount in other objectives. One common issue in the identification of knee points is that some knee points are easily ignored and knees in concave regions are hard to be identified. To resolve these issues, this paper proposes a novel method for knee identification, which first maps the non-dominated solutions to a constructed hyperplane and then divides them into groups, each representing a candidate knee region, based on the density of the solutions projected on the hyperplane. Finally, the convexity and curvature of the candidate knee groups are determined and only those having a strong curvature are kept. The proposed method is empirically demonstrated to be effective in identifying knee points located in both convex and concave regions on three existing test problems and one newly proposed test problem.

The main goal in structural Topology Optimization is to find an optimal distribution of material within a defined design domain, under specified boundary conditions. This task is frequently solved with gradient-based methods, but for some problems, e.g. in the domain of crash Topology Optimization, analytical sensitivity information is not available. The recent Evolutionary Level Set Method (EA-LSM) uses Evolutionary Strategies and a representation based on geometric Level Set Functions to solve such problems. However, computational costs associated with Evolutionary Algorithms are relatively high and grow significantly with rising dimensionality of the optimization problem. In this paper, we propose an improved version of EA-LSM, exploiting an adaptive representation, where the number of structural components increases during the optimization. We employ a learning-based approach, where a pre-trained neural network model predicts favorable topological changes, based on the structural state of the design. The proposed algorithm converges quickly at the beginning, determining good designs in low-dimensional search spaces, and the representation is gradually extended by increasing structural complexity. The approach is evaluated on a standard minimum compliance design problem and its superiority with respect to a random adaptive method is demonstrated.

Computational Fluid Dynamics (CFD) simulations are able to produce complex and large outputs that accurately describe the physical properties of fluids and gases in various domains, such as air flow around a car, or the multi-phase flow inside an internal combustion engine. The simulation results, i.e. the flow fields, are often too complex to be analyzed directly. With the increasing number of simulations as well as their complexity, there is a need of automated processes that can analyze these complex outputs. In this paper, inspired by the success of convolutional neural networks (CNNs) in Computer Vision, we apply for the first time CNNs on CFD output. We show their capabilities in capturing and processing flow patterns. Furthermore, we design a novel CNN architecture tailored to the data produced by CFD simulations, as well as two conventional architectures and compare them. We propose and construct a new dataset of turbulent flow, within the application domain of steady flow around passenger cars. We use that dataset to evaluate and compare the proposed methods, on different tasks that depend on flow patterns. Finally, we compare our methods with a baseline k-nearest neighbor approach, tuned to be comparable to the state-of-the-art.

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.

Structural topology optimization addresses the problem of providing designers and engineers with concepts of mechanical structures. Evolutionary optimization algorithms are suitable for practical domains, such as crashworthiness problems, that are characterized by strong non-linearities and black box simulations. However, due to the high computational cost of the structural analysis, their application requires a representation, that avoids excessive computational cost. In this work, we propose an algorithm based on two main concepts. Firstly, we propose a novel, adaptive and low dimensional representation of the discretized structural design space. It is based on a clustering of design space elements, which show similar Local State Features such as energies or displacements and is dynamically updated during the optimization. Secondly, instead of directly modifying the structure, an evolutionary optimization provides update signals, that determine the decrease or increase of the amount of material for each of the distinct clusters of elements. The de-randomized Evolution Strategy with Covariance Matrix Adaptation is used to optimize the vector of update signals, hence optimizing the change of the material distribution. The feasibility of the method is at first demonstrated on a compliance minimization reference problem and subsequently applied to a problem from the field of crashworthiness topology optimization, for which standard gradient-based methods are not feasible. The novel method achieves remarkably better performance, when compared to a baseline obtained by a uniform energy heuristics for crashworthiness topology optimization.

During the past decade, continuum topology optimization became an important industrial tool for the conceptual design of mechanical structures. The field of evolutionary computation provides suitable stochastic optimization algorithms for problems involving strong non-linearities or black-box simulations, for which existing gradient-based methods are not feasible. Due to the high design freedom of the phenotypic space, the encoding of the structural design is a critical aspect when applying evolutionary algorithms. Currently, the encoding approaches are scattered throughout different literature fields. This paper gathers them and provides a contemporary overview on the various structural representations used in conjunction with evolutionary computation for topology optimization. The important influence of the representation on the scalability of the approaches motivates the proposed categorization in three groups: Grid, Geometric and Indirect Representations. The existing representations are described and discussed on a conceptual level and chances and challenges are outlined.

Although Topology Optimization is widely used in many industrial applications, it is still in the initial phase of development for highly nonlinear, multimodal and noisy problems, where the analytical sensitivity information is either not available or difficult to obtain. For these problems, including the highly relevant crashworthiness optimization, alternative approaches, relying not solely on the gradient, are necessary. One option are Evolutionary Algorithms, which are well-suited for this type of problems, but with the drawback of considerable computational costs. In this paper we propose a hybrid evolutionary optimization method using a geometric Level-Set Method for an implicit representation of mechanical structures. Hybrid optimization approach integrates gradient information in stochastic search to improve convergence behavior and global search properties. Gradient information can be obtained from structural state as well as approximated via equivalent state or any known heuristics. In order to evaluate the proposed methods, a minimum compliance problem for a standard cantilever beam benchmark case is considered. These results show that the hybridization is very beneficial in terms of convergence speed and performance of the optimized designs.

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.

Multiobjective evolutionary algorithms (MOEAs) usually achieve a set of nondominated solutions as the approximation of the Pareto front. In order to utilize the solutions, a final decision making process is indispensable in most cases in which a small number of solutions have to be selected. In this process a decision maker selects the solutions according to his or her preferences or based on the knowledge acquired by observing the approximated Pareto front. Due to the limited number of solutions an algorithm can obtain, in particular when the number of objectives is large, a decision maker may be interested in sampling additional solutions in some preferred regions. This paper proposes to use a reference vector based preference articulation (RVPA) method to obtain such additional solutions in preferred regions. After describing the proposed method in detail, experiments are conducted on six benchmark MOPs to assess the performance of the proposed RVPA method. Our empirical results show that, by setting reference vectors in the objective space, the proposed RVPA is able to obtain corresponding solutions in the preferred regions at a much lower cost compared to e.g. a re-start strategy. In addition, by setting the reference vectors in a uniform way, the proposed RVPA method is also able to improve the general quality (convergence and distribution) of the solutions obtained by an MOEA.

In this paper we propose a novel method for the topology optimization of mechanical structures, based on a hybrid combination of a neuro-evolution with a gradient-based optimizer. Conventional gradient-based topology optimization requires problem-specific sensitivity information, however this is not available in the general case. The proposed method substitutes the analytical gradient by an artificial neural network approximation model, whose parameters are learned by an evolutionary algorithm. Advantageous is that the number of parameters in the evolutionary search is not directly coupled to the mesh of the discretized design, potentially enabling the optimization of fine discretizations. Concretely, the network maps features, obtained for each element of the discretized design, to an update signal, that is used to determine a new design. A new network is learned for every iteration of the topology optimization. The proposed method is evaluated on the minimum compliance design problem, with two different sets of features. Feasible designs are obtained, showing that the neural network is able to successfully replace analytical sensitivity information. In concluding remarks, we discuss the significant improvement that is achieved when including the strain energy as feature.

The development of adaptive systems, which react autonomously to changes in their environment, require the coordinated generation of sensors, providing information about the environment and signal processing structures, which generate suitable reactions to changed conditions. In this work we demonstrate the applicability of a concurrent evolutionary design of the optimal sensory and controller parts of a system for the example of an adaptive wing design. The focus of the work is twofold. First on the realization of developmental stages of the sensory and controlling systems design, defined as a growth process, and second on the comparison of the differences in structures of the systems developed through the presented evolutionary growth method and of evolved systems, having fixed set of sensory elements. We ascertained that the success of the realized growth process depends among others on the relation between the triggering methods and timing of the system enlargement and on parameter settings of the optimization strategy after a growth phase.

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.

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.

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.

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.

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.