A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

W. Hong K. Tang Peng Yang

5 Januari 2021

Large-scale multi-objective optimization problems (MOPs) that involve a large number of decision variables, have emerged from many real-world applications. While evolutionary algorithms (EAs) have been widely acknowledged as a mainstream method for MOPs, most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables. More recently, it has been reported that traditional multi-objective EAs (MOEAs) suffer severe deterioration with the increase of decision variables. As a result, and motivated by the emergence of real-world large-scale MOPs, investigation of MOEAs in this aspect has attracted much more attention in the past decade. This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles. From the key difficulties of the large-scale MOPs, the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables. From the perspective of methodology, the large-scale MOEAs are categorized into three classes and introduced respectively: divide and conquer based, dimensionality reduction based and enhanced search-based approaches. Several future research directions are also discussed.

Xiaodong Li Yutao Qi Xiaoliang Ma + 3 lainnya

22 Desember 2021

Multiobjectivization has emerged as a new promising paradigm to solve single-objective optimization problems (SOPs) in evolutionary computation, where an SOP is transformed into a multiobjective optimization problem (MOP) and solved by an evolutionary algorithm to find the optimal solutions of the original SOP. The transformation of an SOP into an MOP can be done by adding helper-objective(s) into the original objective, decomposing the original objective into multiple subobjectives, or aggregating subobjectives of the original objective into multiple scalar objectives. Multiobjectivization bridges the gap between SOPs and MOPs by transforming an SOP into the counterpart MOP, through which multiobjective optimization methods manage to attain superior solutions of the original SOP. Particularly, using multiobjectivization to solve SOPs can reduce the number of local optima, create new search paths from local optima to global optima, attain more incomparability solutions, and/or improve solution diversity. Since the term “multiobjectivization” was coined by Knowles et al. in 2001, this subject has accumulated plenty of works in the last two decades, yet there is a lack of systematic and comprehensive survey of these efforts. This article presents a comprehensive multifacet survey of the state-of-the-art multiobjectivization methods. Particularly, a new taxonomy of the methods is provided in this article and the advantages, limitations, challenges, theoretical analyses, benchmarks, applications, as well as future directions of the multiobjectivization methods are discussed.

Kangjia Qiao Jing J. Liang B. Qu + 5 lainnya

1 April 2023

Handling constrained multiobjective optimization problems (CMOPs) is extremely challenging, since multiple conflicting objectives subject to various constraints require to be simultaneously optimized. To deal with CMOPs, numerous constrained multiobjective evolutionary algorithms (CMOEAs) have been proposed in recent years, and they have achieved promising performance. However, there has been few literature on the systematic review of the related studies currently. This article provides a comprehensive survey for evolutionary constrained multiobjective optimization. We first review a large number of CMOEAs through categorization and analyze their advantages and drawbacks in each category. Then, we summarize the benchmark test problems and investigate the performance of different constraint handling techniques (CHTs) and different algorithms, followed by some emerging and representative applications of CMOEAs. Finally, we discuss some new challenges and point out some directions of the future research in the field of evolutionary constrained multiobjective optimization.

Jing Liang Dunwei Gong Yinan Guo + 3 lainnya

1 Oktober 2024

Dynamic constrained multiobjective optimization problems (DCMOPs) abound in real-world applications and gain increasing attention in the evolutionary computation community. To evaluate the capability of an algorithm in solving dynamic constrained multiobjective optimization problems (DCMOPs), artificial test problems play a fundamental role. Nevertheless, some characteristics of real-world scenarios are not fully considered in the previous test suites, such as time-varying size, location, and shape of feasible regions, the controllable change severity, as well as small feasible regions. Therefore, we develop the generators of objective functions and constraints to facilitate the systematic design of DCMOPs, and then a novel test suite consisting of nine benchmarks, termed as DCP, is put forward. To solve these problems, a dynamic constrained multiobjective evolutionary algorithm (DCMOEA) with a two-stage diversity compensation strategy (TDCEA) is proposed. Some initial individuals are randomly generated to replace historical ones in the first stage, improving the global diversity. In the second stage, the increment between center points of Pareto sets in the past two environments is calculated and employed to adaptively disturb solutions, forming an initial population with good diversity for the new environment. Intensive experiments show that the proposed test problems enable a good understanding of strengths and weaknesses of algorithms, and TDCEA outperforms other state-of-the-art comparative ones, achieving promising performance in tackling DCMOPs.

Lin Shi Zhi-hui Zhan K. Tan + 1 lainnya

27 Juli 2021

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.