Many real-world optimization problems exhibit dynamic characteristics, posing significant challenges for traditional optimization methods. Evolutionary Dynamic Optimization Algorithms (EDOAs) have been developed to address these challenges by adapting to changing environments over time. However, the reproducibility and consistency of experimental results in the literature remain limited due to the lack of publicly available source codes and the complexity of accurately re-implementing algorithms and performance evaluation protocols. To support the community, we introduce E volutionary D ynamic O ptimization LAB oratory (EDOLAB), an open source MATLAB platform designed for both research and educational purposes. EDOLAB includes 27 EDOAs, four highly configurable benchmark generators, and a growing suite of performance indicators. The platform supports full parameter tuning, batch experiment management, parallel execution, and automated statistical comparisons—including rankings, significance testing, box plots, and performance trend visualizations over time. An educational application allows users to observe: (a) dynamic changes in a 2D problem landscape, (b) the movement of individuals in response to these changes, and (c) the ability of an algorithm to track moving optima. By providing an integrated environment for experimentation, benchmarking, and instructional use, EDOLAB promotes reproducibility, comparative analysis, and a deeper understanding of EDOAs in dynamic environments.

Simulated annealing is a well-established general purpose optimiser that is often used for simulation optimisation. Parallelising it is non-trivial, as the algorithm is inherently sequential. This paper revisits the idea of speculative computation, in which several iterations of simulated annealing are executed in parallel, each based on speculation on the outcome of the previous iterations, and backtracking if the speculation was wrong. The paper extends the idea to the case of stochastic problems, for which several replications of the simulation have to be run to obtain a reliable estimate of a solution’s quality. We show how to find optimal speculation policies via dynamic programming, and that the optimal policies can be different from those found with the typically used greedy heuristic. We also examine how the results depend on correctly estimating the acceptance probability. Empirical results demonstrate the speed-up that can be gained via speculative execution in different settings.

We study payoff manipulation in repeated multi-objective Stackelberg games, where a leader may strategically influence a follower’s deterministic best response, e.g., by offering a share of their own payoff. We assume that the follower’s utility function, representing preferences over multiple objectives, is unknown but linear, and its weight parameter must be inferred through interaction. This introduces a sequential decision-making challenge for the leader, who must balance preference elicitation with immediate utility maximisation. We formalise this problem and propose manipulation policies based on expected utility (EU) and long-term expected utility (longEU), which guide the leader in selecting actions and offering incentives that trade off short-term gains with long-term impact. We prove that under infinite repeated interactions, longEU converges to the optimal manipulation. Empirical results across benchmark environments demonstrate that our approach improves cumulative leader utility while promoting mutually beneficial outcomes, all without requiring explicit negotiation or prior knowledge of the follower’s utility function.

Abstract Multi-objective Bayesian optimization aims to find the Pareto front of trade-offs between a set of expensive objectives while collecting as few samples as possible. In some cases, it is possible to evaluate the objectives separately, and a different latency or evaluation cost can be associated with each objective. This decoupling of the objectives presents an opportunity to learn the Pareto front faster by avoiding unnecessary, expensive evaluations. We propose a scalarization based knowledge gradient acquisition function which accounts for the different evaluation costs of the objectives. We prove asymptotic consistency of the estimator of the optimum for an arbitrary, D-dimensional, real, compact search space and show empirically that the algorithm performs comparably with the state of the art and significantly outperforms versions which always evaluate both objectives.

Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning, i.e., optimization with a decision maker in the loop, allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and allows to learn the decision maker's preferences from pairwise comparisons. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.

This article discusses the challenge when evaluating multiobjective optimization algorithms under noise. It argues that it is important to take into account possible selection errors by a decision maker, due to inaccurate estimates of a solution’s true objective values. It demonstrates that commonly used performance metrics do not properly account for such errors, and proposes two alternative performance metrics that do account for such errors by adapting the popular R2 and${\mathrm { IGD}}^{+}$metrics.

Real-world problems often consist of multiple conflicting objectives to be optimized simultaneously, featuring a set of Pareto-optimal solutions. Estimating the entire Pareto front can be computationally expensive, and is not always necessary, as decision makers (DMs) will likely be interested only in specific regions of the Pareto front. In the absence of knowledge about the DM preferences, the so-called knees in the Pareto front are considered to be particularly attractive. In this article, we propose using Thompson sampling in the Bayesian optimization framework to estimate the location of the knee regions in a data-efficient manner. Our experimental results show that the proposed methods accurately locate the knee regions after a very small number of evaluations, providing a computationally efficient approach to single- and multiknee detection in multiobjective optimization.

Quality Diversity (QD) algorithms such as MAP-Elites are a class of optimisation techniques that attempt to find many high performing points that all behave differently according to a user-defined behavioural metric. In this paper we propose the Bayesian Optimisation of Elites (BOP-Elites) algorithm. Designed for problems with expensive black-box objective and behaviour functions, it is able to return a QD solution-set after a relatively small number of samples. BOP-Elites models both objective and behavioural descriptors with Gaussian Process surrogate models and uses Bayesian Optimisation strategies for choosing points to evaluate in order to solve the quality-diversity problem. In addition, BOP-Elites produces high quality surrogate models which can be used after convergence to predict solutions with any behaviour in a continuous range. An empirical comparison shows that BOP-Elites significantly outperforms other state-of-the-art algorithms without the need for problem-specific parameter tuning.

This paper formulates a new Best-Arm Identification problem in the non-stationary stochastic bandits setting, where the means of all arms are shifted in the same way due to a global influence of the environment. The aim is to identify the unique best arm across environmental change given a fixed total budget. While this setting can be regarded as a special case of Adversarial Bandits or Corrupted Bandits, we demonstrate that existing solutions tailored to those settings do not fully utilise the nature of this global influence, and thus, do not work well in practice (despite their theoretical guarantees). To overcome this issue, in this paper we develop a novel selection policy that is consistent and robust in dealing with global environmental shifts. We then propose an allocation policy, LinLUCB, which exploits information about global shifts across all arms in each environment. Empirical tests depict a significant improvement in our policies against other existing methods.

Clustering in dynamic environments is of increasing importance, with broad applications ranging from real-time data analysis and online unsupervised learning to dynamic facility location problems. While meta-heuristics have shown promising effectiveness in static clustering tasks, their application for tracking optimal clustering solutions or robust clustering over time in dynamic environments remains largely underexplored. This is partly due to a lack of dynamic datasets with diverse, controllable, and realistic dynamic characteristics, hindering systematic performance evaluations of clustering algorithms in various dynamic scenarios. This deficiency leads to a gap in our understanding and capability to effectively design algorithms for clustering in dynamic environments. To bridge this gap, this paper introduces the Dynamic Dataset Generator (DDG). DDG features multiple dynamic Gaussian components integrated with a range of heterogeneous, local, and global changes. These changes vary in spatial and temporal severity, patterns, and domain of influence, providing a comprehensive tool for simulating a wide range of dynamic scenarios.

Robust optimization over time (ROOT) is the combination of robust optimization and dynamic optimization. In ROOT, frequent changes to deployed solutions are undesirable, which can be due to the high cost of switching between deployed solutions, limitations on the resources required to deploy new solutions, and/or the system’s inability to tolerate frequent changes in the deployed solutions. ROOT is dedicated to the study and development of algorithms capable of dealing with the implications of deploying or maintaining solutions over longer time horizons involving multiple environmental changes. This paper presents an in-depth review of the research on ROOT. The overarching aim of this survey is to help researchers gain a broad perspective on the current state of the field, what has been achieved so far, and the existing challenges and pitfalls. This survey also aims to improve accessibility and clarity by standardizing terminology and unifying mathematical notions used across the field, providing explicit mathematical formulations of definitions, and improving many existing mathematical descriptions. Moreover, we classify ROOT problems based on two ROOT-specific criteria: the requirements for changing or keeping deployed solutions and the number of deployed solutions. This classification helps researchers gain a better understanding of the characteristics and requirements of ROOT problems, which is crucial to systematic algorithm design and benchmarking. Additionally, we classify ROOT methods based on the approach they use for finding robust solutions and provide a comprehensive review of them. This survey also reviews ROOT benchmarks and performance indicators. Finally, we identify several future research directions.

This paper presents a novel way for interactively identifying a most preferable solution based on quality and behavioural characteristics. Our algorithm combines the principles of Quality-Diversity Search and Bayesian Optimization to create Gaussian Process surrogate models of the behaviour and fitness space. Unlike traditional Quality-Diversity methods which aim to find good solutions with different behavioural characteristics, we propose a three-step interactive approach that allows a decision maker to efficiently identify the most preferred solution(s). In the first stage, it uses an entropy-based acquisition function to generate an illumination model, followed by an interactive phase where the decision maker can specify regions of interest and a target behaviour. These preferences are then utilized by an improvement greedy acquisition function to guide the optimization process and quickly identify a solution close to the user-specified target. In a case study, with a simulated decision maker, we demonstrate that our approach can find better solutions much more quickly than by selecting the most preferred solution from an archive generated with MAP-Elites.

Many real-world optimization problems are dynamic. The field of robust optimization over time (ROOT) deals with dynamic optimization problems in which frequent changes of the deployed solution are undesirable. This can be due to the high cost of switching the deployed solutions, the limitation of the needed resources to deploy such new solutions, and/or the system being intolerant towards frequent changes of the deployed solution. In the considered ROOT problems in this article, the main goal is to find solutions that maximize the average number of environments where they remain acceptable. In the state-of-the-art methods developed to tackle these problems, the decision makers/metrics used to select solutions for deployment mostly make simplifying assumptions about the problem instances. Besides, the current methods all use the population control components which have been originally designed for tracking the global optimum over time without taking any robustness considerations into account. In this paper, a multi-population ROOT method is proposed with two novel components: a robustness estimation component that estimates robustness of the promising regions, and a dual-mode computational resource allocation component to manage sub-populations by taking several factors, including robustness, into account. Our experimental results demonstrate the superiority of the proposed method over other state-of-the-art approaches.

Hyperparameter optimization constitutes a large part of typical modern machine learning (ML) workflows. This arises from the fact that ML methods and corresponding preprocessing steps often only yield optimal performance when hyperparameters are properly tuned. But in many applications, we are not only interested in optimizing ML pipelines solely for predictive accuracy; additional metrics or constraints must be considered when determining an optimal configuration, resulting in a multi-objective optimization problem. This is often neglected in practice, due to a lack of knowledge and readily available software implementations for multi-objective hyperparameter optimization. In this work, we introduce the reader to the basics of multi-objective hyperparameter optimization and motivate its usefulness in applied ML. Furthermore, we provide an extensive survey of existing optimization strategies from the domains of evolutionary algorithms and Bayesian optimization. We illustrate the utility of multi-objective optimization in several specific ML applications, considering objectives such as operating conditions, prediction time, sparseness, fairness, interpretability, and robustness.

Multipopulation methods are highly effective in solving dynamic optimization problems. Three factors affect this significantly: 1) the exclusion mechanisms to avoid the convergence to the same peak by multiple subpopulations; 2) the resource allocation mechanism that assigns the computational resources to the subpopulations; and 3) the control mechanisms to adaptively adjust the number of subpopulations by considering the number of optima and available computational resources. In the existing exclusion mechanisms, when the distance (i.e., the distance between their best found positions) between two subpopulations becomes less than a predefined threshold, the inferior one will be removed/reinitialized. However, this leads to incapability of algorithms in covering peaks/optima that are closer than the threshold. Moreover, despite the importance of resource allocation due to the limited available computational resources between environmental changes, it has not been well studied in the literature. Finally, the number of subpopulations should be adapted to the number of optima. However, in most existing adaptive multipopulation methods, there is no predefined upper bound for generating subpopulations. Consequently, in problems with large numbers of peaks, they can generate too many subpopulations sharing limited computational resources. In this article, a multipopulation framework is proposed to address the aforementioned issues by using three adaptive approaches: 1) subpopulation generation; 2) double-layer exclusion; and 3) computational resource allocation. The experimental results demonstrate the superiority of the proposed framework over several peer approaches in solving various benchmark problems.

Dynamic changes are an important and inescapable aspect of many real-world optimization problems. Designing algorithms to find and track desirable solutions while facing challenges of dynamic optimization problems is an active research topic in the field of swarm and evolutionary computation. To evaluate and compare the performance of algorithms, it is imperative to use a suitable benchmark that generates problem instances with different controllable characteristics. In this article, we give a comprehensive review of existing benchmarks and investigate their shortcomings in capturing different problem features. We then propose a highly configurable benchmark suite, the generalized moving peaks benchmark, capable of generating problem instances whose components have a variety of properties, such as different levels of ill-conditioning, variable interactions, shape, and complexity. Moreover, components generated by the proposed benchmark can be highly dynamic with respect to the gradients, heights, optimum locations, condition numbers, shapes, complexities, and variable interactions. Finally, several well-known optimizers and dynamic optimization algorithms are chosen to solve generated problems by the proposed benchmark. The experimental results show the poor performance of the existing methods in facing new challenges posed by the addition of new properties.

Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part article, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms (DOAs), namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multipopulation methods, which are underrepresented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an in-depth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the DOAs, and dynamic real-world applications. Finally, several opportunities for future work are pointed out.

This article presents the second Part of a two-Part survey that reviews evolutionary dynamic optimization (EDO) for single-objective unconstrained continuous problems over the last two decades. While in the first part, we reviewed the components of dynamic optimization algorithms (DOAs); in this part, we present an in-depth review of the most commonly used benchmark problems, performance analysis methods, static optimization methods used in the framework of DOAs, and real-world applications. Compared to the previous works, this article provides a new taxonomy for the benchmark problems used in the field based on their baseline functions and dynamics. In addition, this survey classifies the commonly used performance indicators into fitness/error-based and efficiency-based ones. Different types of plots used in the literature for analyzing the performance and behavior of algorithms are also reviewed. Furthermore, the static optimization algorithms that are modified and utilized in the framework of DOAs as the optimization components are covered. We then comprehensively review some real-world dynamic problems that are optimized by EDO methods. Finally, some challenges and opportunities are pointed out for future directions.

Experimental studies are prevalent in Evolutionary Computation (EC), and concerns about the reproducibility and replicability of such studies have increased in recent times, reflecting similar concerns in other scientific fields. In this article, we discuss, within the context of EC, the different types of reproducibility and suggest a classification that refines the badge system of the Association of Computing Machinery (ACM) adopted by ACM Transactions on Evolutionary Learning and Optimization (https://dlnext.acm.org/journal/telo). We identify cultural and technical obstacles to reproducibility in the EC field. Finally, we provide guidelines and suggest tools that may help to overcome some of these reproducibility obstacles.

Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity ( route failure), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm.

Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark (MPB) and show its nonseparable nature irrespective of its number of peaks. We then propose a composite MPB suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower-dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200-D, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems.

Many real-world optimization problems involve uncertainties, and in such situations it is often desirable to identify robust solutions that perform well over the possible future scenarios. In this paper, we focus on input uncertainty, such as in manufacturing, where the actual manufactured product may differ from the specified design but should still function well. Estimating a solution's expected fitness in such a case is challenging, especially if the fitness function is expensive to evaluate, and its analytic form is unknown. One option is to average over a number of scenarios, but this is computationally expensive. The archive sample approximation method reduces the required number of fitness evaluations by reusing previous evaluations stored in an archive. The main challenge in the application of this method lies in determining the locations of additional samples drawn in each generation to enrich the information in the archive and reduce the estimation error. In this paper, we use the Wasserstein distance metric to approximate the possible benefit of a potential sample location on the estimation error, and propose new sampling strategies based on this metric. Contrary to previous studies, we consider a sample's contribution for the entire population, rather than inspecting each individual separately. This also allows us to dynamically adjust the number of samples to be collected in each generation. An empirical comparison with several previously proposed archive-based sample approximation methods demonstrates the superiority of our approaches.

Robust optimization over time is a new way to tackle dynamic optimization problems where the goal is to find solutions that remain acceptable over an extended period of time. The state-of-the-art methods in this domain try to identify robust solutions based on their future predicted fitness values. However, predicting future fitness values is difficult and error prone. In this paper, we propose a new framework based on a multipopulation method in which subpopulations are responsible for tracking peaks and also gathering characteristic information about them. When the quality of the current robust solution falls below the acceptance threshold, the algorithm chooses the next robust solution based on the collected information. We propose four different strategies to select the next solution. The experimental results on benchmark problems show that our newly proposed methods perform significantly better than existing algorithms.

This paper proposes a novel sequential sampling scheme to allocate samples to individuals in order to maximally inform the selection step in Covariance Matrix Adaptation Evolution Strategies (CMA-ES) for noisy function optimisation. More specifically we adopt the well-known Knowledge Gradient (KG) method to minimise the Kullback-Leibler divergence (relative entropy) between the distribution used for generating the next offspring population based on the μ selected individuals, and the distribution based on the true μ best individuals that would have been chosen in the absence of noise. Empirical tests demonstrate the benefit of integrating sequential sampling into CMA-ES, and that the proposed KG technique specifically adapted to the needs of CMA-ES indeed outperforms a more straightforward application of KG.

Dynamic optimization problems (DOPs) are problems that change over time. However, most investigations in this domain are focused on tracking moving optima (TMO) without considering the cost of switching from one solution to another when the environment changes. Robust optimization over time (ROOT) tries to address this shortcoming by finding solutions which remain acceptable for several environments. However, ROOT methods change solutions only when they become unacceptable. Indeed, TMO and ROOT are two extreme cases in the sense that in the former, the switching cost is considered zero and in the latter, it is considered very large. In this paper, we propose a new semi ROOT algorithm based on a new approach to switching cost. This algorithm changes solutions when: 1) the current solution is not acceptable and 2) the current solution is still acceptable but algorithm has found a better solution and switching is preferable despite the cost. The main objective of the proposed algorithm is to maximize the performance based on the fitness of solutions and their switching cost. The experiments are done on modified moving peaks benchmark (mMPB) and the performance of the proposed algorithm alongside state-of-the-art ROOT and TMO methods is investigated.

This paper proposes a simulated annealing variant for optimization problems in which the solution quality can only be estimated by sampling from a random distribution. The aim is to find the solution with the best expected performance, as, e.g., is typical for problems where solutions are evaluated using a stochastic simulation. Assuming Gaussian noise with known standard deviation, we derive a fully sequential sampling procedure and decision rule. The procedure starts with a single sample of the value of a proposed move to a neighboring solution and then continues to draw more samples until it is able to make a decision to accept or reject the move. Under constraints of equilibrium detailed balance at each draw, we find a decoupling between the acceptance criterion and the choice of the rejection criterion. We derive a universally optimal acceptance criterion in the sense of maximizing the acceptance probability per sample and thus the efficiency of the optimization process. We show that the choice of the move rejection criterion depends on expectations of possible alternative moves and propose a simple and practical (albeit more empirical) solution that preserves detailed balance. An empirical evaluation shows that the resulting approach is indeed more efficient than several previously proposed simulated annealing variants.

Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d ≤ 4 from the G-function suite [16] and on an airfoil shape example.

For many real-world optimization problems, evaluating a solution involves running a computationally expensive simulation model. This makes it challenging to use evolutionary algorithms that usually have to evaluate thousands of solutions before converging. On the other hand, in many cases, even a prematurely stopped run of the simulation may serve as a cheaper, albeit less accurate (low fidelity), estimate of the true fitness value. For evolutionary optimization, this opens up the opportunity to decide about the simulation run length for each individual. In this paper, we propose a mechanism that is capable of learning the appropriate simulation run length for each solution. To test our approach, we propose two new benchmark problems, one simple artificial benchmark function and one benchmark based on a computational fluid dynamics (CFDs) simulation scenario to design a toy submarine. As we demonstrate, our proposed algorithm finds good solutions much more quickly than always using the full CFDs simulation and provides much better solution quality than a strategy of progressively increasing the fidelity level over the course of optimization.

In multiobjective engineering design, evaluation of a single design (solution) often requires running one or more computationally expensive simulation models. Surrogate assisted optimization (SAO) approaches have long been used for solving such problems, in which approximations/surrogates are used in lieu of computationally expensive simulations during the course of search. Existing SAO approaches use a variety of surrogate models and model management strategies, and the best choice is still a matter under investigation. Our current proposal is an attempt to exploit the best features of several strategies, and in particular compares two possible versions of pre-selection in multiobjective optimization. The proposed algorithm is based on the non-dominated sorting genetic algorithm (NSGA-II) but, instead of evaluating the potential offspring solutions directly, a surrogate assisted evolutionary search is conducted in the neighborhood of every offspring solution using the best local surrogate model (among Kriging, Radial basis function (RBF), Polynomial response surface method (RSM) of order 1 and 2 and Multilayer perceptrons (MLP)). Out of the combined set of candidate solutions generated using the above step, the most promising offspring solutions are pre-selected, and we examine and compare two versions of pre-selection, one ignoring the parents and one taking the parents into account. The performance of the proposed approach is studied using a number of well known numerical benchmarks and engineering design optimization problems.

Hyper-heuristics have recently emerged as a powerful approach to automate the design of heuristics for a number of different problems. Production scheduling is a particularly popular application area for which a number of different hyper-heuristics have been developed and are shown to be effective, efficient, easy to implement, and reusable in different shop conditions. In particular, they seem to be a promising way to tackle highly dynamic and stochastic scheduling problems, an aspect that is specifically emphasized in this survey. Despite their success and the substantial number of papers in this area, there is currently no systematic discussion of the design choices and critical issues involved in the process of developing such approaches. This paper strives to fill this gap by summarizing the state-of-the-art approaches, suggesting a taxonomy, and providing the interested researchers and practitioners with guidelines for the design of hyper-heuristics in production scheduling. This paper also identifies challenges and open questions and highlights various directions for future work.

Many real-world problems are subject to uncertainty, and often solutions should not only be good, but also robust against environmental disturbances or deviations from the decision variables. While most papers dealing with robustness aim at finding solutions with a high expected performance given a distribution of the uncertainty, we examine the trade-off between the allowed deviations from the decision variables (tolerance level), and the worst case performance given the allowed deviations. A possible application are manufacturing tolerances, where an engineer can specify an allowed tolerance for manufacturing, but a low tolerance requirement incurs substantially higher manufacturing cost, whereas a high tolerance requirement usually means having to accept a lower worst-case quality of the solution.

Dispatching rules are frequently used for real-time, online scheduling in complex manufacturing systems. Design of such rules is usually done by experts in a time consuming trial-and-error process. Recently, evolutionary algorithms have been proposed to automate the design process. There are several possibilities to represent rules for this hyper-heuristic search. Because the representation determines the search neighborhood and the complexity of the rules that can be evolved, a suitable choice of representation is key for a successful evolutionary algorithm. In this paper we empirically compare three different representations, both numeric and symbolic, for automated rule design: A linear combination of attributes, a representation based on artificial neural networks, and a tree representation. Using appropriate evolutionary algorithms (CMA-ES for the neural network and linear representations, genetic programming for the tree representation), we empirically investigate the suitability of each representation in a dynamic stochastic job shop scenario. We also examine the robustness of the evolved dispatching rules against variations in the underlying job shop scenario, and visualize what the rules do, in order to get an intuitive understanding of their inner workings. Results indicate that the tree representation using an improved version of genetic programming gives the best results if many candidate rules can be evaluated, closely followed by the neural network representation that already leads to good results for small to moderate computational budgets. The linear representation is found to be competitive only for extremely small computational budgets.

One way to accelerate evolutionary algorithms with expensive fitness evaluations is to combine them with surrogate models. Surrogate models are efficiently computable approximations of the fitness function, derived by means of statistical or machine learning techniques from samples of fully evaluated solutions. But these models usually require a numerical representation, and therefore cannot be used with the tree representation of genetic programming (GP). In this paper, we present a new way to use surrogate models with GP. Rather than using the genotype directly as input to the surrogate model, we propose using a phenotypic characterization. This phenotypic characterization can be computed efficiently and allows us to define approximate measures of equivalence and similarity. Using a stochastic, dynamic job shop scenario as an example of simulation-based GP with an expensive fitness evaluation, we show how these ideas can be used to construct surrogate models and improve the convergence speed and solution quality of GP.

Adaptive population sizing aims at improving the overall progress of an evolution strategy. At each generation, it determines the parental population size that promises the largest fitness gain, based on the information collected during the evolutionary process. In this paper, we develop an adaptive variant of a (μ/μ, λ) evolution strategy. Based on considerations on the sphere, we derive two approaches for adaptive population sizing. We then test these approaches empirically on the sphere model using a normalized mutation strength and cumulative mutation strength adaption. Finally, we compare the methodology on more general functions with a fixed population, covariance matrix adaption evolution strategy (CMA-ES). The results confirm that our adaptive population sizing methods yield better results than even the best fixed population size.

This paper proposes an interactive multiobjective evolutionary algorithm (MOEA) that attempts to learn a value function capturing the users' true preferences. At regular intervals, the user is asked to rank a single pair of solutions. This information is used to update the algorithm's internal value function model, and the model is used in subsequent generations to rank solutions incomparable according to dominance. This speeds up evolution toward the region of the Pareto front that is most desirable to the user. We take into account the most general additive value function as a preference model and we empirically compare different ways to identify the value function that seems to be the most representative with respect to the given preference information, different types of user preferences, and different ways to use the learned value function in the MOEA. Results on a number of different scenarios suggest that the proposed algorithm works well over a range of benchmark problems and types of user preferences.

Many practical optimization problems are constrained and have a bounded search space. In this paper, we propose and compare a wide variety of bound handling techniques for particle swarm optimization. By examining their performance on flat landscapes, we show that many bound handling techniques introduce significant search bias. Furthermore, we compare the performance of many bound handling techniques on a variety of test problems, demonstrating that the bound handling technique can have a major impact on the algorithm performance, and that the method recently proposed as the standard does not, in general, perform well.

Meta-optimization techniques for tuning algorithm parameters usually try to find optimal parameter settings for a given computational budget allocated to the lower-level algorithm. If the available computational budget changes, parameters have to be optimized again from scratch, as they usually depend on the available time. For example, a small computational budget requires a focus on exploitation, while a larger budget allows more exploration. In situations where the optimization problem is expected to be solved for various computational budgets, meta-optimization is very time consuming. The method proposed in this paper can, in a single run, identify the best parameter settings for all possible computational budgets up to a specified maximum, hence saving a lot of time.

Due to steadily increasing mobility and the resulting rising traffic demands, serious congestion problems can be observed in many cities. One promising approach to alleviate the congestion effects is the coordination of the network's traffic signals in response to the traffic flow. The recently introduced Decentralised Progressive Signal Systems approach is an adaptive coordination mechanism for traffic signals in urban road networks that relies on local traffic data only. Since the decentralised process cannot lead to optimal results in some special cases, it is extended with an optional hierarchical component introduced in this paper. Based on a broader view on the current network traffic, this Regional Manager is responsible for determining which intersections are coordinated. The efficiency of the coordination determined by the Regional Manager is demonstrated in a simulation-based evaluation that considers the decentralised mechanism and an uncoordinated system for comparison.

Statistical selection procedures are used to select the best of a finite set of alternatives, where “best” is defined in terms of each alternative's unknown expected value, and the expected values are inferred through statistical sampling. One effective approach, which is based on a Bayesian probability model for the unknown mean performance of each alternative, allocates samples based on maximizing an approximation to the expected value of information (EVI) from those samples. The approximations include asymptotic and probabilistic approximations. This paper derives sampling allocations that avoid most of those approximations to the EVI but entails sequential myopic sampling from a single alternative per stage of sampling. We demonstrate empirically that the benefits of reducing the number of approximations in the previous algorithms are typically outweighed by the deleterious effects of a sequential one-step myopic allocation when more than a few dozen samples are allocated. Theory clarifies the derivation of selection procedures that are based on the EVI.

In this paper, we review several proposals for guide selection in Multi-Objective Particle Swarm Optimization (MOPSO) and compare them with each other in terms of convergence, diversity and computational times. The new proposals made for guide selection, both personal best (dasiapbestpsila) and global best (dasiagbestpsila), are found to be extremely effective and perform well compared to the already existing methods. The combination of selection methods for choosing dasiagbestpsila and dasiapbestpsila is also studied and it turns out that there exist certain combinations which yield an overall superior performance outperforming the others on the tested benchmark problems. Furthermore, two new proposals namely velocity trigger (as a substitute for ldquoturbulence operatorrdquo) and a new scheme of boundary handling is made.

This paper studies the multi-objectivization of single-objective optimization problems (SOOP) using evolutionary multi-objective algorithms (EMOAs). In contrast to the single-objective case, diversity can be introduced by the multi-objective view of the algorithm and the dynamic use of objectives. Using the travelling salesman problem as an example we illustrate that two basic approaches, a) the addition of new objectives to the existing problem and b) the decomposition of the primary objective into sub-objectives, can improve performance compared to a single-objective genetic algorithm when objectives are used dynamically. Based on decomposition we propose the concept "Multi-Objectivization via Segmentation" (MOS), at which the original problem is reassembled. Experiments reveal that this new strategy clearly outperforms both the traditional genetic algorithm (GA) and the algorithms based on existing multiobjective approaches even without changing objectives.

The problem of finding entities with the best worst-case performance across multiple scenarios arises in domains ranging from job shop scheduling to designing physical artifacts. In spite of previous successful applications of evolutionary computation techniques, particularly coevolution, to such domains, little work has examined utilizing coevolution for optimizing worst-case behavior. Previous work assesses certain algorithm mechanisms using aggregate performance on test problems. We examine fitness and population trajectories of individual algorithm runs, making two observations: first, that aggregate plots wash out important effects that call into question what these algorithms can produce; and second, that none of the mechanisms is generally better than the rest. More importantly, our dynamics analysis explains how the interplay of algorithm properties and problem properties influences performance. These contributions argue in favor of a reassessment of what makes for a good worst-case coevolutionary algorithm and suggest how to design one.

Uncertainties in design variables and problem parameters are often inevitable and must be considered in an optimization task if reliable optimal solutions are sought. Besides a number of sampling techniques, there exist several mathematical approximations of a solution's reliability. These techniques are coupled in various ways with optimization in the classical reliability-based optimization field. This paper demonstrates how classical reliability-based concepts can be borrowed and modified and, with integrated single and multiobjective evolutionary algorithms, used to enhance their scope in handling uncertainties involved among decision variables and problem parameters. Three different optimization tasks are discussed in which classical reliability-based optimization procedures usually have difficulties, namely (1) reliability-based optimization problems having multiple local optima, (2) finding and revealing reliable solutions for different reliability indices simultaneously by means of a bi-criterion optimization approach, and (3) multiobjective optimization with uncertainty and specified system or component reliability values. Each of these optimization tasks is illustrated by solving a number of test problems and a well-studied automobile design problem. Results are also compared with a classical reliability-based methodology.

In this paper, we study parallelization of multi-objective optimization algorithms on a set of heterogeneous resources based on the Master-Slave model. The Master-Slave model is known to be the simplest parallelization paradigm, where a master processor sends function evaluations to several slave processors. The critical issue when using the standard methods on heterogeneous resources is that in every iteration of the optimization, the master processor has to wait for all of the computing resources (including the slow ones) to deliver the evaluations. In this paper, we study a new algorithm where all of the available computing resources are efficiently utilized to perform the multi-objective optimization task independent of the speed (fast or slow) of the computing processors. For this we propose a hybrid method using Multi-objective Particle Swarm optimization and Binary search methods. The new algorithm has been tested on a scenario containing heterogeneous resources and the results show that not only does the new algorithm perform well for parallel resources, but also when compared to a normal serial run on one computer.

This paper examines the performance characteristics of both asynchronous and synchronous parallel particle swarm optimisation algorithms in heterogeneous, fault-prone environments. Algorithm convergence is measured as a function of both iterations completed and time elapsed, allowing the two particle update mechanisms to be comprehensively evaluated and compared in such an environment. Asynchronous particle updates are shown to negatively impact the convergence speed in regards to iterations completed, however the increased parallel efficiency of the asynchronous model appears to counter this performance reduction, ensuring the asynchronous update mechanism performs comparably to the synchronous mechanism in fault-free environments. When faults are introduced, the synchronous update method is shown to suffer significant performance drops, suggesting that at least partly asynchronous algorithms should be used in real-world environments where faults can regularly occur.

In Multi-Objective Problems (MOPs) involving uncertainty, each solution might be associated with a cluster of performances in the objective space depending on the possible scenarios. Therefore, in MOPs, the worst case might not be a single scenario but rather a set of such worst case scenarios, depending on the user preferences. The evolution of solutions based on their related sets of worst case scenarios has been recently introduced. It has been termed: "worst case evolutionary multi-objective optimization." In the current paper the worst case evolutionary multi-objective optimization is further developed. In contrast to the former work where the number of possible scenarios is small and the set of worst cases can thus be easily determined, here, the number of scenarios is assumed to be large, and the worst cases are searched for by means of an embedded evolutionary search. This means that for each nominal solution, a worst set of scenarios has to be found. In the current study, the resulting front, consisting of sets of solutions' worst cases, is formally defined, and a new approach to support decision making based on it, is suggested. The new decision support poses the selection as an auxiliary MOP, highlighting the tradeoff which might result from the worst being a set and not a single point. An academic example and an engineering design problem are given in order to explain the methodology and to demonstrate its applicability to real life problems.

In this paper, we combine reliability-based optimization with a multi-objective evolutionary algorithm for handling uncertainty in decision variables and parameters. This work is an extension to a previous study by the second author and his research group to more accurately compute a multi-constraint reliability. This means that the overall reliability of a solution regarding all constraints is examined, instead of a reliability computation of only one critical constraint. First, we present a brief introduction into this so-called 'structural reliability' aspects. Thereafter, we introduce a method for identifying inactive constraints according to the reliability evaluation. With this method, we show that with less number of constraint evaluations, an identical solution can be achieved. Furthermore, we apply our approach to a number of problems including a real-world car side impact design problem to illustrate our method.

This paper describes two performance measures for measuring an EMO (evolutionary multiobjective optimization) algorithm's ability to track a time-varying Pareto-front in a dynamic environment. These measures are evaluated using a dynamic multiobjective test function and a dynamic multiobjective PSO,maximinPSOD, which is capable of handling dynamic multiobjective optimization problems.maximinPSODis an extension from a previously proposed multiobjective PSO,maximinPSO. Our results suggest that these performance measures can be used to provide useful information about how well a dynamic EMO algorithm performs in tracking a time-varying Pareto-front. The results also show thatmaximinPSODcan be made self-adaptive, tracking effectively the dynamically changing Pareto-front.

Estimation of distribution algorithms replace the typical crossover and mutation operators by constructing a probabilistic model and generating offspring according to this model. In previous studies, it has been shown that this generally leads to diversity loss due to sampling errors. In this paper, for the case of the simple Univariate Marginal Distribution Algorithm (UMDA), we propose and test several methods for counteracting diversity loss. The diversity loss can come in two phases: sampling from the probability model (offspring generation) and selection. We show that it is possible to completely remove the sampling error during offspring generation. Furthermore, we examine several plausible model construction variants which counteract diversity loss during selection and demonstrate that these update rules work better than the standard update on a variety of simple test problems.

Introduction: Multiobjective optimization represents an important class of optimization techniques which have a direct implication for solving many real-world problems. In recent years, using evolutionary algorithms to solve multiobjective optimization problems, commonly known as EMO (Evolutionary Multi-objective Optimization), has gained rapid popularity. Since Evolutionary Algorithms (EAs) make use of a population of candidate solutions, a diverse set of optimal solutions so called Pareto-optimal solutions can be found within a single run. EAs offer a distinct advantage over many traditional optimization methods where multiple solutions must be found in multiple separate runs.

Abstract. In recent years, a number of authors have successfully extended particle swarm optimization to problem domains with multiple objectives. This paper addresses the issue of parallelizing multi-objective particle swarms. We propose and empirically compare two parallel versions which differ in the way they divide the swarm into subswarms that can be processed independently on different processors. One of the variants works asynchronously and is thus particularly suitable for heterogeneous computer clusters as occurring e.g. in modern grid computing platforms. 1

This paper describes an extension to a speciation-based particle swarm optimizer (SPSO) to improve performance in dynamic environments. The improved SPSO has adopted several proven useful techniques. In particular, SPSO is shown to be able to adapt to a series of dynamic test cases with varying number of peaks (assuming maximization). Inspired by the concept of quantum swarms, this paper also proposes a particle diversification method that promotes particle diversity within each converged species. Our results over the moving peaks benchmark test functions suggest that SPSO incorporating this particle diversification method can greatly improve its adaptability hence optima tracking performance.

In the past, the focus of the computer industry has been to improve hardware performance and add more and more features to the software. As a result, more and more appliances surrounding us are equipped with embedded computational power and wireless communication. As such, they become ever more flexible and multifunctional, and almost indispensable in daily life. On the other hand, the resulting systems become increasingly complex and unreliable, posing new challenges to designer and user. Organic Computing (OC) has the vision to address the challenges of complex distributed systems by making them more life-like (organic), i.e. endowing them with abilities such as self-organization, self-configuration, self-repair, or adaptation. The designer's task is simplified, because it is no longer necessary to exactly specify the low-level system behavior in all possible situations that might occur, but instead leaving the system with a certain degree of freedom which allows it to react in an intelligent way to new situations. Also, use ofsuch systems is simplified, as they can be controlled by setting few high-level goals, rather than having to manipulate many low-level parameters with unclear influence. In this paper, we give a general introduction to OC, and propose a generic observer-controller architecture as a framework for designing OC systems. Then, it is shown how to use this architecture at the example of a traffic light controller. The paper concludes with a summary and a discussion of future challenges.

Many real-world problems are dynamic, requiring an optimization algorithm which is able to continuously track a changing optimum over time. In this paper, we explore new variants of particle swarm optimization (PSO) specifically designed to work well in dynamic environments. The main idea is to split the population of particles into a set of interacting swarms. These swarms interact locally by an exclusion parameter and globally through a new anti-convergence operator. In addition, each swarm maintains diversity either by using charged or quantum particles. This paper derives guidelines for setting the involved parameters and evaluates the multiswarm algorithms on a variety of instances of the multimodal dynamic moving peaks benchmark. Results are also compared with other PSO and evolutionary algorithm approaches from the literature, showing that the new multiswarm optimizer significantly outperforms previous approaches

For many real-world optimization problems, the robustness of a solution is of great importance in addition to the solution's quality. By robustness, we mean that small deviations from the original design, e.g., due to manufacturing tolerances, should be tolerated without a severe loss of quality. One way to achieve that goal is to evaluate each solution under a number of different scenarios and use the average solution quality as fitness. However, this approach is often impractical, because the cost for evaluating each individual several times is unacceptable. In this paper, we present a new and efficient approach to estimating a solution's expected quality and variance. We propose to construct local approximate models of the fitness function and then use these approximate models to estimate expected fitness and variance. Based on a variety of test functions, we demonstrate empirically that our approach significantly outperforms the implicit averaging approach, as well as the explicit averaging approaches using existing estimation techniques reported in the literature.

This paper investigates the use of evolutionary multi-objective optimization methods (EMOs) for solving single-objective optimization problems in dynamic environments. A number of authors proposed the use of EMOs for maintaining diversity in a single objective optimization task, where they transform the single objective optimization problem into a multi-objective optimization problem by adding an artificial objective function. We extend this work by looking at the dynamic single objective task and examine a number of different possibilities for the artificial objective function. We adopt the non-dominated sorting genetic algorithm version 2 (NSGA2). The results show that the resultant formulations are promising and competitive to other methods for handling dynamic environments.

Although the interest in nature-inspired optimization of dynamic problems has been growing constantly over the past decade, very little has been done to analyze and characterize a changing fitness landscape. However, it would be very helpful for algorithm development to have a better understanding of the nature of fitness changes in dynamic real-world problems. In this paper, we propose a number of measures that can be used to analyze and characterize the dynamism in a problem changing over time. Additionally, we introduce a new dynamic multi-dimensional knapsack problem as a close-to-real-world test problem.

Evolutionary algorithms (EAs) are widely used to deal with optimization problems in dynamic environments (DE) [3]. When using EAs to solve DE problems, we are usually interested in the algorithm's ability to adapt and recover from the changes. One of the main problems facing an evolutionary method when solving DE problems is the loss of genetic diversity.In this paper, we investigate the use of evolutionary multi-objective optimization methods (EMOs) for single-objective DE problems. For that purpose, we introduce an artificial second objective with the aim to maintain useful diversity in the population. Six different artificial objectives are examined and compared.All the results will be compared against a traditional GA and the random immigrants algorithm[4]. NSGA2 is employed as the evolutionary multi-objective technique.

Evolutionary algorithms often have to solve optimization problems in the presence of a wide range of uncertainties. Generally, uncertainties in evolutionary computation can be divided into the following four categories. First, the fitness function is noisy. Second, the design variables and/or the environmental parameters may change after optimization, and the quality of the obtained optimal solution should be robust against environmental changes or deviations from the optimal point. Third, the fitness function is approximated, which means that the fitness function suffers from approximation errors. Fourth, the optimum of the problem to be solved changes over time and, thus, the optimizer should be able to track the optimum continuously. In all these cases, additional measures must be taken so that evolutionary algorithms are still able to work satisfactorily. This paper attempts to provide a comprehensive overview of the related work within a unified framework, which has been scattered in a variety of research areas. Existing approaches to addressing different uncertainties are presented and discussed, and the relationship between the different categories of uncertainties are investigated. Finally, topics for future research are suggested.

Evolutionary multi-objective optimization (EMO) may be computationally quite demanding, because instead of searching for a single optimum, one generally wishes to find the whole front of Pareto-optimal solutions. For that reason, parallelizing EMO is an important issue. Since we are looking for a number of Pareto-optimal solutions with different tradeoffs between the objectives, it seems natural to assign different parts of the search space to different processors. We propose the idea of cone separation which is used to divide up the search space by adding explicit constraints for each process. We show that the approach is more efficient than simple parallelization schemes, and that it also works on problems with a non-convex Pareto-optimal front.

Recently, there has been increased interest in evolutionary computation applied to changing optimization problems. The paper surveys a number of approaches that extend the evolutionary algorithm with implicit or explicit memory, suggests a new benchmark problem and examines under which circumstances a memory may be helpful. From these observations, we derive a new way to explore the benefits of a memory while minimizing its negative side effects.