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.

In dynamic optimization problems where optimal solutions change over time, traditional ant colony optimization (ACO) algorithms face limitations. This study explores the adaptation of multi-colony ACO algorithms, known for their enhanced search capabilities in stationary problems, to tackle optimization problems in dynamic environments. Various strategies for exchanging information between colonies, which is a critical factor influencing algorithm performance, are investigated. Using the dynamic traveling salesman problem as a foundation, we generate test cases to reflect real-world complexities. Our results on a set of problem instances reveal that the choice of communication strategy between colonies significantly impacts the adaptability and efficiency of multi-colony ACO algorithms in tracking moving optimum.

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.

Genetic programming (GP), as a predictive data analytic tool, has difficulties dealing with high-dimensional problems. Therefore, some GP variants have been proposed for this type of problem, such as multi-stage GP (MSGP). Filter-based feature selection is commonly used in the literature for various machine learning purposes. However, its application for GP is overlooked due to GP's capability to operate as a wrapper-based feature selection while trying to find an optimal expression of the target variable via a functional combination of predictors. The effectiveness of wrapper- and filer-based feature selection approaches in machine learning has been the subject of a long-standing debate in the literature. This study aims to introduce an efficient feature selection approach and couple it with MSGP in order to handle high-dimensional problems. In addition, the stages of the GP are systematically ordered based on the variables' information. The proposed approach is tested against five real high-dimensional datasets. The results show that GP's inherent wrapper feature selection ability can be advanced further by using a filter-based feature selection approach to shrink the search space, which results in improving computational costs, expression complexity and the accuracy of MSGP.

Variable grouping provides an efficient approach to large-scale optimization, and multipopulation strategies are effective for both large-scale optimization and dynamic optimization. However, variable grouping is not well studied in large-scale dynamic optimization when cooperating with multipopulation strategies. Specifically, when the numbers/sizes of the variable subcomponents are large, the performance of the algorithms will be substantially degraded. To address this issue, we propose a bilevel variable grouping (BLVG)-based framework. First, the primary grouping applies a state-of-the-art variable grouping method based on variable interaction analysis to group the variables into subcomponents. Second, the secondary grouping further groups the subcomponents into variable cells, that is, combination variable cells and decomposition variable cells. We then tailor a multipopulation strategy to process the two types of variable cells efficiently in a cooperative coevolutionary (CC) way. As indicated by the empirical study on large-scale dynamic optimization problems (DOPs) of up to 300 dimensions, the proposed framework outperforms several state-of-the-art frameworks for large-scale dynamic optimization.

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.

Population clustering methods, which consider the position and fitness of individuals to form sub-populations in multi-population algorithms, have shown high efficiency in tracking the moving global optimum in dynamic optimization problems. However, most of these methods use a fixed population size, making them inflexible and inefficient when the number of promising regions is unknown. The lack of a functional relationship between the population size and the number of promising regions significantly degrades performance and limits an algorithm’s agility to respond to dynamic changes. To address this issue, we propose a new species-based particle swarm optimization with adaptive population size and number of sub-populations for solving dynamic optimization problems. The proposed algorithm also benefits from a novel systematic adaptive deactivation component that, unlike the previous deactivation components, adapts the computational resource allocation to the sub-populations by considering various characteristics of both the problem and the sub-populations. We evaluate the performance of our proposed algorithm for the Generalized Moving Peaks Benchmark and compare the results with several peer approaches. The results indicate the superiority of the proposed method.

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.

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

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.

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.

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.

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.

Swarm intelligence algorithms are amongst the most efficient approaches toward solving optimization problems. Up to now, most of swarm intelligence approaches have been proposed for optimization in static environments. However, numerous real-world problems are dynamic which could not be solved using static approaches. In this paper, a novel approach based on artificial fish swarm algorithm (AFSA) has been proposed for optimization in dynamic environments in which changes in the problem space occur in discrete intervals. The proposed algorithm can quickly find the peaks in the problem space and track them after an environment change. In this algorithm, artificial fish swarms are responsible for finding and tracking peaks and several behaviors and mechanisms are employed to cope with the dynamic environment. Extensive experiments show that the proposed algorithm significantly outperforms previous algorithms in most of tested dynamic environments modeled by moving peaks benchmark.

Artificial fish swarm algorithm is one of the swarm intelligence algorithms which performs based on population and stochastic search contributed to solve optimization problems. This algorithm has been applied in various applications e.g. data clustering, neural networks learning, nonlinear function optimization, etc. Several problems in real world are dynamic and uncertain, which could not be solved in a similar manner of static problems. In this paper, for the first time, a modified artificial fish swarm algorithm is proposed in consideration of dynamic environments optimization. The results of the proposed approach were evaluated using moving peak benchmarks, which are known as the best metric for evaluating dynamic environments, and also were compared with results of several state-of-the-art approaches. The experimental results show that the performance of the proposed method outperforms that of other algorithms in this domain.

Objective function or the constraints and consequently the optimal value of the problem can be changed during time in Dynamic optimization problems. There are several challenges in dynamic environments, so that algorithms designed for optimization in these environments would utilize several mechanisms in order to conquer the challenges. In this paper, a novel hybrid algorithm for optimization in dynamic environments, called HPSOLS, is proposed based on particle swarm optimization and local search approaches. In this approach, it aims to increase the ability of local search around optimum with focusing on best found peak in each environment. The results of the proposed approach are evaluated using moving peak benchmark, which is currently the most well-known benchmark for evaluating dynamic environments, and are compared with results of several state-of-the-art algorithms in this domain. Experimental results show that the efficiency of the proposed method outperforms that of other algorithms in this domain.

Swarm intelligence algorithms have been extensively used in clustering based applications e.g. image segmentation which is one of the fundamental components in image analysis and pattern recognition domains. Particle swarm optimization is amongst swarm intelligence algorithms that performs based on population and random search. In this paper, a hybrid algorithm based on PSO, k-means and learning automata is proposed for image segmentation. In the proposed algorithm, learning automata is responsible for activating and deactivating PSO and k-means methods based on current conditions of the segmentation problem. The proposed approach along with other comparative studies has been applied for segmenting benchmark images. Efficiency of the proposed method has been compared with that of other methods and experimental results show the superiority proposed algorithm.