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Characterization of constrained Continuous multiobjective optimization Problems: A Performance Space Perspective

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2025年第1期29卷 275-285页

作者： Vodopija, Aljosa Tusar, Tea Filipic, Bogdan Jozef Stefan Inst Dept Intelligent Syst Ljubljana 1000 Slovenia Jozef Stefan Int Postgrad Sch Ljubljana 1000 Slovenia

constrained multiobjective optimization has gained much interest in the past few years. However, constrained multiobjective optimization problems (CMOPs) are still unsatisfactorily understood. Consequently, the choice of adequate CMOPs for benchmarking is difficult and lacks a formal background. This article takes a step toward addressing this issue by exploring CMOPs from a performance space perspective. First, it presents a novel performance assessment approach designed explicitly for constrained multiobjective optimization. This methodology offers a first attempt at simultaneously measuring the performance in approximating the Pareto front and constraint satisfaction. Second, it proposes an approach to measure the capability of the given optimization problem to differentiate among algorithm performances. Finally, this approach is used to compare eight frequently used artificial test suites of CMOPs. The experimental results reveal which suites are more efficient in discerning between four well-known multiobjective optimization algorithms.

关键词： optimization Evolutionary computation Benchmark testing Linear programming Convergence Behavioral sciences Runtime Benchmarking constrained multiobjective optimization constraint violation hypervolume multiobjective evolutionary algorithm (MOEA) performance measurement test problem

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constrained multiobjective optimization immune algorithm: Convergence and application

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2006年第5期52卷 791-808页

作者： Zhang, Zhuhong Univ Guizhou Dept Math Guiyang 550025 Guizhou Peoples R China

A new optimization technique, multiobjective optimization immune algorithm for constrained nonlinear multiobjective optimization problems is designed based on immune metaphors of humoral immune and Pareto optimality, especially, some interactive metaphors between antigen population and antibody population. It includes four main mechanisms: (1) constraint-handling operation that provides an alternative feasible solution set for rapidly finding Pareto optimal solutions;(2) antibody evolution associated with clonal selection principle and ideas of immune regulation;(3) competition and update of antigens that induces evolution of antibody populations;(4) memory pool used for collecting the best solutions of evolving antibody populations. Convergence is proven through Markov theory as well as demonstrated by the experiment results. Comparative analysis and applications illustrate that it is effective and valuable. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： constrained multiobjective optimization humoral immune immune optimization algorithm Pareto optimality convergence

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constrained multiobjective optimization for IoT-Enabled Computation Offloading in Collaborative Edge and Cloud Computing

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IEEE INTERNET OF THINGS JOURNAL 2021年第17期8卷 13723-13736页

作者： Peng, Guang Wu, Huaming Wu, Han Wolter, Katinka Free Univ Berlin Inst Informat D-14195 Berlin Germany Tianjin Univ Ctr Appl Math Tianjin 300072 Peoples R China

Internet-of-Things (IoT) applications are becoming more resource-hungry and latency-sensitive, which are severely constrained by limited resources of current mobile hardware. Mobile cloud computing (MCC) can provide abundant computation resources, while mobile-edge computing (MEC) aims to reduce the transmission latency by offloading complex tasks from IoT devices to nearby edge servers. It is still challenging to satisfy the quality of service with different constraints of IoT devices in a collaborative MCC and MEC environment. In this article, we propose three constrained multiobjective evolutionary algorithms (CMOEAs) for solving IoT-enabled computation offloading problems in collaborative edge and cloud computing networks. First of all, a constrained multiobjective computation offloading model considering time and energy consumption is established in the mobile environment. Inspired by the push and pull search framework, three CMOEAs are developed by combing the advantages of population-based search algorithms with flexible constraint handling mechanisms. On one hand, three popular and challenging constrained benchmark suites are selected to test the performance of the proposed algorithms by comparing them to the other seven state-of-the-art CMOEAs. On the other hand, a multiserver multiuser multitask computation offloading experimental scenario with a different number of IoT devices is used to evaluate the performance of three proposed algorithms and other compared algorithms as well as representative offloading schemes. The experimental results of the benchmark suites and computation offloading problems demonstrate the effectiveness and superiority of the proposed algorithms.

关键词： Internet of Things Cloud computing Task analysis optimization Servers Edge computing Collaboration Computation offloading constrained multiobjective optimization Internet of Things (IoT) mobile cloud computing (MCC) mobile-edge computing (MEC)

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constrained multiobjective optimization via Multitasking and Knowledge Transfer

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2024年第1期28卷 77-89页

作者： Ming, Fei Gong, Wenyin Wang, Ling Gao, Liang China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

Solving constrained multiobjective optimization problems (CMOPs) with various features and challenges via evolutionary algorithms is very popular. Existing methods usually adopt an additional helper problem to simplify and solve them by divide and conquer. This article proposes a new multitasking framework for CMOPs, borrowing the idea of evolutionary multitasking optimization. The main contributions are: 1) a multitasking framework is proposed, where a CMOP is modeled as a multitasking optimization problem with three tasks. Then, it is solved by constraint-first, constraint-ignored, and constraint-relaxed multiobjective evolutionary algorithms;2) a knowledge expression and a transfer strategy are devised to transfer the knowledge among the tasks;and 3) based on the proposed framework, a new two-stage algorithm is presented to solve CMOPs. The effectiveness of our approach is validated through experiments on four CMOP benchmark suites and 19 real-world CMOPs.

关键词： Task analysis optimization Statistics Sociology Multitasking Convergence Knowledge transfer constrained multiobjective optimization evolutionary algorithm evolutionary transfer optimization (ETO) knowledge transfer multitasking

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Evolutionary constrained multiobjective optimization: Test Suite Construction and Performance Comparisons

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2019年第6期23卷 972-986页

作者： Ma, Zhongwei Wang, Yong Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

For solving constrained multiobjective optimization problems (CMOPs), many algorithms have been proposed in the evolutionary computation research community for the past two decades. Generally, the effectiveness of an algorithm for CMOPs is evaluated by artificial test problems. However, after a brief review of current artificial test problems, we have found that they are not well-designed and fail to reflect the characteristics of real-world applications (e.g., small feasibility ratio). Thus, in this paper, we first propose a new constraint construction method to facilitate the systematic design of test problems. Then, on the basis of this method, we design a new test suite consisting of 14 instances, which covers diverse characteristics extracted from real-world CMOPs and can be divided into four types. Considering that the comprehensive performance comparisons among the constraint-handling techniques (CHTs) remain scarce, we choose several representative CHTs and compare their performance on our test suite. The performance comparisons identify the strengths and weaknesses of different CHTs on different types of CMOPs and provide guidelines on how to select/design a CHT in a specific scenario.

关键词： Pareto optimization Geometry Convergence Evolutionary computation Systematics Indexes constrained multiobjective optimization constraint-handling techniques (CHTs) evolutionary algorithms (EAs) performance comparisons test suite

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Dynamic Auxiliary Task-Based Evolutionary Multitasking for constrained multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2023年第3期27卷 642-656页

作者： Qiao, Kangjia Yu, Kunjie Qu, Boyang Liang, Jing Song, Hui Yue, Caitong Lin, Hongyu Tan, Kay Chen Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Zhongyuan Univ Technol Sch Elect & Informat Engn Zhengzhou 450007 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3000 Australia Hong Kong Polytech Univ Dept Comp Hong Kong Peoples R China

When solving constrained multiobjective optimization problems (CMOPs), the utilization of infeasible solutions significantly affects algorithm's performance because they not only maintain diversity but also provide promising search directions. In light of this situation, this article proposes a new multitasking-constrained multiobjective optimization (MTCMO) framework, in which a dynamic auxiliary task is created to assist in solving a complex CMOP (the main task) via the knowledge transfer. Moreover, the constraint boundary of the auxiliary task reduces dynamically, so that it keeps a high relatedness with the main task to continuously provide supplementary evolutionary directions. Furthermore, an improved e method is designed for the auxiliary task to utilize diverse high-quality infeasible solutions for breaking through infeasible obstacles in the early stage and approaching the feasible boundary from infeasible regions in the later stage. Besides, a new test function with decision space constraints is designed, where one parameter can be adjusted to control the overlap degree between the constrained Pareto front and the unconstrained Pareto front. This function and the other two modified existing functions are used to analyze the characteristics of MTCMO. Finally, compared with 11 state-of-the-art peer methods, the superior or competitive performance of MTCMO is demonstrated on 54 benchmark functions and two real-world applications.

关键词： Task analysis optimization Statistics Sociology Multitasking Search problems Convergence Auxiliary task constrained multiobjective optimization evolutionary multitasking (EMT) improved epsilon method knowledge transfer

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An Evolutionary Multitasking optimization Framework for constrained multiobjective optimization Problems

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2022年第2期26卷 263-277页

作者： Qiao, Kangjia Yu, Kunjie Qu, Boyang Liang, Jing Song, Hui Yue, Caitong Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Zhongyuan Univ Technol Sch Elect & Informat Engn Zhengzhou 450007 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3000 Australia

When addressing constrained multiobjective optimization problems (CMOPs) via evolutionary algorithms, various constraints and multiple objectives need to be satisfied and optimized simultaneously, which causes difficulties for the solver. In this article, an evolutionary multitasking (EMT)-based constrained multiobjective optimization (EMCMO) framework is developed to solve CMOPs. In EMCMO, the optimization of a CMOP is transformed into two related tasks: one task is for the original CMOP, and the other task is only for the objectives by ignoring all constraints. The main purpose of the second task is to continuously provide useful knowledge of objectives to the first task, thus facilitating solving the CMOP. Specially, the genes carried by parent individuals or offspring individuals are dynamically regarded as useful knowledge due to the different complementarities of the two tasks. Moreover, the useful knowledge is found by the designed tentative method and transferred to improve the performance of the two tasks. To the best of our knowledge, this is the first attempt to use EMT to solve CMOPs. To verify the performance of EMCMO, an instance of EMCMO is obtained by employing a genetic algorithm as the optimizer. Comprehensive experiments are conducted on four benchmark test suites to verify the effectiveness of knowledge transfer. Furthermore, compared with other state-of-the-art constrained multiobjective optimization algorithms, EMCMO can produce better or at least comparable performance.

关键词： Task analysis optimization Statistics Sociology Knowledge transfer Multitasking Numerical models constrained multiobjective optimization evolutionary multitasking (EMT) knowledge transfer multitasking optimization problem

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A Dual-Population-Based Evolutionary Algorithm for constrained multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2021年第4期25卷 739-753页

作者： Ming, Mengjun Trivedi, Anupam Wang, Rui Srinivasan, Dipti Zhang, Tao Natl Univ Def Technol Coll Syst Engn Changsha 410073 Peoples R China Natl Univ Def Technol Hunan Key Lab Multienergy Syst Intelligent Interc Changsha 410073 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117581 Singapore

The main challenge in constrained multiobjective optimization problems (CMOPs) is to appropriately balance convergence, diversity and feasibility. Their imbalance can easily cause the failure of a constrained multiobjective evolutionary algorithm (CMOEA) in converging to the Pareto-optimal front with diverse feasible solutions. To address this challenge, we propose a dual-population-based evolutionary algorithm, named c-DPEA, for CMOPs. c-DPEA is a cooperative coevolutionary algorithm which maintains two collaborative and complementary populations, termed Population1 and Population2. In c-DPEA, a novel self-adaptive penalty function, termed saPF, is designed to preserve competitive infeasible solutions in Population1. On the other hand, infeasible solutions in Population2 are handled using a feasibility-oriented approach. To maintain an appropriate balance between convergence and diversity in c-DPEA, a new adaptive fitness function, named bCAD, is developed. Extensive experiments on three popular test suites comprehensively validate the design components of c-DPEA. Comparison against six state-of-the-art CMOEAs demonstrates that c-DPEA is significantly superior or comparable to the contender algorithms on most of the test problems.

关键词： Statistics Sociology Convergence optimization Evolutionary computation Collaboration Space exploration Coevolutionary dual populations constrained multiobjective optimization convergence diversity feasibility

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A coevolutionary algorithm based on reference line guided archive for constrained multiobjective optimization

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APPLIED SOFT COMPUTING 2023年 142卷

作者： Wang, Pengbo Xiao, Houxiu Han, Xiaotao Yang, Fan Li, Liang Chongqing Univ Sch Elect Engn Chongqing Peoples R China Huazhong Univ Sci & Technol Wuhan Natl High Magnet Field Ctr Wuhan Peoples R China

The objective space of the constrained multiobjective optimization problem (CMOP) is constantly torn by the applied constraints. This makes evolutionary algorithms, which are driven by objectives, face greater difficulties in feasibility, convergence, and diversity. Most evolutionary algorithms will be trapped in local optimums such as a fake Pareto-optimal front or a mutilated Pareto-optimal front. To address this issue, this paper proposes an archive-assisted evolutionary framework with a novel archive structure and cooperative mechanism. A reference line guided archive (RA) is established to record the evolution of the unconstrained solutions. The updated criteria of RA are based on the distance from the individual to the reference line and the unconstrained dominance relation. A specially designed adaptive mating selection operator will select mating parents from RA and the main population according to the convergence of the main population and RA, respectively. The participation of RA in offspring reproduction is conducive to skipping infeasible regions for extensive searches. The performance of the archive-assisted nondominated sorting genetic algorithm (AA-NSGA), which embeds the proposed archive strategy into the nondominated sorting genetic algorithm II, is compared with four state-of-the-art constrained multiobjective evolutionary algorithms (MOEAs). The experimental results on 38 benchmark CMOPs and a reactor network design problem show that the proposed AA-NSGA has a high performance among the existing MOEAs in terms of feasibility, convergence, and diversity. (c) 2023 Published by Elsevier B.V.

关键词： Evolutionary algorithm Nondominated sorting constrained multiobjective optimization Archive strategy Cooperative mechanism

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Utilizing the Relationship Between Unconstrained and constrained Pareto Fronts for constrained multiobjective optimization

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第6期53卷 3873-3886页

作者： Liang, Jing Qiao, Kangjia Yu, Kunjie Qu, Boyang Yue, Caitong Guo, Weifeng Wang, Ling Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Zhongyuan Univ Technol Sch Elect & Informat Engn Zhengzhou 450007 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

constrained multiobjective optimization problems (CMOPs) involve multiple objectives to be optimized and various constraints to be satisfied, which challenges the evolutionary algorithms in balancing the objectives and constraints. This article attempts to explore and utilize the relationship between constrained Pareto front (CPF) and unconstrained Pareto front (UPF) to solve CMOPs. Especially, for a given CMOP, the evolutionary process is divided into the learning stage and the evolving stage. The purpose of the learning stage is to measure the relationship between CPF and UPF. To this end, we first create two populations and evolve them by specific learning strategies to approach the CPF and UPF, respectively. Then, the feasibility information and dominance relationship of the two populations are used to determine the relationship. Based on the learned relationship, specific evolving strategies are designed in the evolving stage to improve the utilization efficiency of objective information, so as to better solve this CMOP. By the above process, a new constrained multiobjective evolutionary algorithm (CMOEA) is presented. Comprehensive experimental results on 65 benchmark functions and ten real-world CMOPs show that the proposed method has a better or very competitive performance in comparison with several state-of-the-art CMOEAs. Moreover, this article demonstrates that using the relationship between CPF and UPF to guide the utilization of objective information is promising in solving CMOPs.

关键词： Statistics Sociology optimization Linear programming Search problems Evolutionary computation Shape constrained multiobjective optimization evolutionary algorithm objective function relationship

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