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A tri-stage competitive swarm optimizer for constrained multi-objective optimization

APPLIED INTELLIGENCE 2023年第7期53卷 7892-7916页

作者： Dong, Jun Gong, Wenyin Ming, Fei China Univ Geosci Sch Comp Sci Wuhan 430074 Hubei Peoples R China

objective optimization and constraint satisfaction should be considered simultaneously when dealing with constrained multi-objective optimization problems (CMOPs). But it is difficult for existing constraint multi-objective evolutionary algorithms (CMOEAs) to strike a good balance between them, especially for CMOPs with complex constraints. To address this issue, this paper proposes a tri-stage competitive swarm optimizer (CSO), namely TSCSO, where objective optimization and constraint satisfaction receive different attention in different stages. In Stage-I, the population converges to the vicinity of the unconstrained Pareto front (PF) without considering any constraints. In Stage-II, a balance strategy and ranking approach based on convergence, diversity, and feasibility are proposed to enhance the diversity of the population and explore more feasible regions. An external archive is used to store the feasible solutions explored during the evolutionary process. In Stage-III, the population is first initialized by the feasible solutions in the archive, and the CSO operator with efficient search is used to search for the feasible regions omitted in Stage-II. Statistical results on two benchmark suites with twenty-eight problems and five real-world problems indicate that the proposed algorithm performs better than other state-of-the-art CMOEAs overall.

关键词： constrained multi-objective optimization Evolutionary algorithm Competitive swarm optimizer Tri-stage

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BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

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COMPUTERS & OPERATIONS RESEARCH 2013年第1期40卷 282-302页

作者： Li, Xiang Du, Gang Tianjin Univ Sch Management Tianjin 300072 Peoples R China

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： multi-objective optimization constrained multi-objective optimization Inequality constraint Constraint handling Genetic algorithms Boundary simulation method Binary search method Population diversity Pareto optimum Pareto set Pareto front Trie-tree Rtrie-tree Atrie-tree

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A multi-objective differential evolutionary algorithm for constrained multi-objective optimization problems with low feasible ratio

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APPLIED SOFT COMPUTING 2019年 80卷 42-56页

作者： Yang, Yongkuan Liu, Jianchang Tan, Shubin Wang, Honghai Northeastern Univ Dept Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Liaoning Peoples R China

Most current evolutionary multi-objective optimization (EMO) algorithms perform well on multi-objective optimization problems without constraints, but they encounter difficulties in their ability for constrained multi-objective optimization problems (CMOPs) with low feasible ratio. To tackle this problem, this paper proposes a multi-objective differential evolutionary algorithm named MODE-SaE based on an improved epsilon constraint-handling method. Firstly, MODE-SaE self-adaptively adjusts the epsilon level in line with the maximum and minimum constraint violation values of infeasible individuals. It can prevent epsilon level setting from being unreasonable. Then, the feasible solutions are saved to the external archive and take part in the population evolution by a co-evolution strategy. Finally, MODE-SaE switches the global search and local search by self-switching parameters of search engine to balance the convergence and distribution. With the aim of evaluating the performance of MODE-SaE, a real-world problem with low feasible ratio in decision space and fourteen bench-mark test problems, are used to test MODE-SaE and five other state-of-the-art constrained multi-objective evolution algorithms. The experimental results fully demonstrate the superiority of MODE-SaE on all mentioned test problems, which indicates the effectiveness of the proposed algorithm for CMOPs which have low feasible ratio in search space. (C) 2019 Elsevier B.V. All rights reserved.

关键词： constrained multi-objective optimization Epsilon constraint handling method Different evolution

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An Adaptive Two-Population Evolutionary Algorithm for constrained multi-objective optimization Problems

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IEEE ACCESS 2023年 11卷 82118-82131页

作者： Zhao, Kaiwen Wang, Peng Tong, Xiangrong Yantai Univ Sch Comp & Control Engn Yantai 264005 Peoples R China

Striking a balance between objective optimization and constraint satisfaction is essential for solving constrained multi-objective optimization problems (CMOPs). Nevertheless, most existing evolutionary algorithms face significant challenges on CMOPs with intricate infeasible regions. To tackle these challenges, this paper proposes an adaptive two-population evolutionary algorithm, named ATEA, which dynamically exploits promising information under infeasible solutions to facilitate objective optimization and constraint satisfaction. Specifically, a two-population collaboration mechanism is designed to balance the unconstrained Pareto front search and constrained Pareto front search. Moreover, an adaptive constraint handling strategy is presented to reasonably deploy search resources. Furthermore, a promising infeasibility-based environmental selection and an elitist feasibility-based environmental selection are developed for the two populations to break through complex infeasible barriers and enhance selection pressure, respectively. Comparison experimental results of ATEA with five state-of-the-art algorithms on 33 benchmark test problems and 4 real-word CMOPs demonstrate that ATEA performs competitively with the chosen designs.

关键词： constrained multi-objective optimization evolutionary algorithm two-population collaboration mechanism multi-state objective optimization constraint satisfaction

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A self-organizing assisted multi-task algorithm for constrained multi-objective optimization problems

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INFORMATION SCIENCES 2024年 664卷

作者： Ye, Qianlin Wang, Wanliang Li, Guoqing Dai, Rui Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Peoples R China Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315211 Peoples R China

constrained multi-objective optimization problems (CMOPs) require a delicate balance between satisfying constraints and optimizing objectives. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often struggle to balance convergence, diversity, and feasibility, especially when dealing with CMOPs that have complex feasible regions. This paper proposes a multi-task-based self-organizing mapping evolutionary algorithm (MTSOM) to tackle this challenge, which includes a main and auxiliary task. Two populations independently optimize two tasks without considering constraints in the early stage. Subsequently, in the middle stage, both tasks explore the distribution structure of the population in parallel by employing a novel constraint-to-constraint self-organizing mapping (SOM) approach. In the late stage, the main task fully considers feasibility, while the auxiliary task focuses solely on the highest priority constraints. This approach enables rapid convergence toward feasible regions. To evaluate MTSOM's effectiveness, we conducted a series of experiments on five benchmark suites. Results indicate that MTSOM is competitive when compared to other state-of-the-art CMOEAs. Additionally, our proposed constraint-to-constraint SOM is superior in handling complex CMOPs.

关键词： constrained multi-objective optimization Self-organizing mapping multi-task Constraint-to-constraint

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Joint Energy and Completion Time Difference Minimization for UAV-Enabled Intelligent Transportation Systems: A constrained multi-objective optimization Approach

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2024年第10期25卷 14040-14053页

作者： Peng, Chaoda Wu, Zexiong Huang, Xumin Wu, Yuan Kang, Jiawen Huang, Qiong Xie, Shengli South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Univ Macau State Key Lab Internet Things Smart City Taipa Macau Peoples R China Univ Macau Dept Comp & Informat Sci Taipa Macau Peoples R China

An unmanned aerial vehicle (UAV)-enabled intelligent transportation system utilizes a set of UAVs to collect and process surveillance data for transportation management. Subsequently, the processing results of the UAVs are transmitted to a control center that makes a centralized transportation management decision based on the fusion of all processing results. When performing the monitoring tasks, the UAVs can access to an edge server for offloading. To reduce the energy consumption and improve the fusion performance, the control center schedules the UAVs to perform the tasks in an energy-efficient manner while synchronizing the completion time of the UAVs. As a result, the control center studies a constrained multi-objective optimization problem (CMOP), in which two objectives, i.e., the total energy consumption of the UAVs and total completion time difference among the UAVs, are simultaneously considered. To tackle the CMOP, we develop an improved constrained multi-objective evolutionary algorithm. Particularly, we design an improved genetic operator and repairing constraint-handling technique to improve the overall performance of the proposed algorithm in seeking Pareto optimal solutions for the CMOP. Numerical results demonstrate that compared with the baseline algorithms, the proposed algorithm has great advantages in finding better solutions with the enhanced diversity and convergence for the CMOP.

关键词： Task analysis Autonomous aerial vehicles optimization Servers Internet of Things Evolutionary computation Transportation UAV-enabled intelligent transportation system energy optimization time difference minimization constrained multi-objective optimization evolutionary algorithm

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Co-design of an unmanned cable shovel for structural and control integrated optimization: A highly heterogeneous constrained multi-objective optimization algorithm

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APPLIED ENERGY 2024年第PartB期376卷

作者： Pang, Yong Hu, Zhengguo Zhang, Shuai Guo, Guanchen Song, Xueguan Kan, Ziyun Dalian Univ Technol Sch Mech Engn State Key Lab High Performance Precis Mfg Dalian 116024 Peoples R China

Unmanned cable shovel is an intelligence-based large machine used for excavating in open-pit coal mines, with significant implications for the security and development of energy resources. The co-design of unmanned cable shovels, considering elements from both structural and control systems, has demonstrated superior performance in obtaining optimal solutions compared to the traditional approaches that focus on individual systems. However, the inherent complexities of diverse systems often lead to heterogeneous function evaluations, posing challenges for the existing optimization algorithms. To address highly heterogeneous multi-objective optimization problems characterized by surrogate-approximated expensive functions and explicit inexpensive functions, this study proposes a highly heterogeneous constrained multi-objective optimization (HHCMO) algorithm. Leveraging NSGA-III as an evolutionary optimizer and the Kriging model for approximating expensive functions, HHCMO strategically addresses the challenges posed by highly heterogeneous objective evaluations. A Monte Carlo sampling-based expected hypervolume improvement (EHVI) criterion, employing a new nearest point approximation method in a unified sampling space, effectively handles the impact of heterogeneous objective evaluations on the sequential infill of the Kriging model. Thorough evaluations on both unconstrained and constrained multi-objective benchmark problems validate the correctness of HHCMO and its superiority relative to state-of-the-art algorithms. Finally, the effectiveness of the proposed method is successfully demonstrated in an engineering scenario of an unmanned cable shovel, where it adeptly handles expensive functions from the structural system and inexpensive functions from the control system.

关键词： Unmanned cable shovel Co-design Heterogeneous evaluations constrained multi-objective optimization Expected hypervolume improvement Kriging surrogate model

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A coevolutionary algorithm assisted by two archives for constrained multi-objective optimization problems

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SWARM AND EVOLUTIONARY COMPUTATION 2023年 82卷

作者： Zeng, Yong Cheng, Yuansheng Liu, Jun Huazhong Univ Sci & Technol Sch Naval Architecture & Ocean Engn Wuhan 430074 Peoples R China Deep Sea Explorat CISSE Innovat Ctr Adv Ship Shanghai 200240 Peoples R China

Coevolutionary algorithms have demonstrated high performance on many constrained multi-objective prob-lems. However, on some problems with fraudulent constraints or small feasible regions, they may fail to converge to the Pareto front (PF) or even fail to find a feasible solution. To search for feasible solutions robustly for various problems and obtain solutions approaching the PF as possible, this paper proposes a coevolutionary algorithm assisted by two archives. To be specific, a population for minimizing constraint violation and a population for optimizing objectives without constraints coevolve to find a feasible solution first. Then, the feasible solutions are improved by the population with constrained dominance principle and an archive consisting of inversely-updated infeasible solutions. In addition to searching in the feasible regions found so far, the unconstrained population continues searching the objectives without constraints, expecting that new feasible regions can be spotted in the promising regions. To mitigate the issues that small feasible regions may be missed by the unconstrained population, a diversity archive is updated in a larger objective space than the unconstrained population to enhance exploration. In the experiments, the proposed method is compared with 11 state-of-the-art algorithms on 67 problems to demonstrate its effectiveness. The results show that the proposed method is very robust in finding feasible solutions and obtains better or competitive performance on most problems.

关键词： constrained multi-objective optimization Coevolutionary algorithms Archive assisting

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A dynamic resource allocation strategy for collaborative constrained multi-objective optimization algorithm

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APPLIED INTELLIGENCE 2023年第9期53卷 10176-10201页

作者： Pan, Xiaotian Wang, Liping Zhang, Menghui Qiu, Qicang Zhejiang Univ Finance & Econ Sch Informat Management & Artificial Intelligence Hangzhou 310018 Peoples R China Zhejiang Univ Technol Coll Comp Sci & Technol Coll Software Hangzhou 310023 Peoples R China Zhejiang Lab Hangzhou 310023 Peoples R China

Infeasible solutions are helpful for finding the feasible regions, but how many feasible and infeasible solutions should be invested to achieve the optimal search efficiency remains to be further studied. Combined with the recently proposed collaborative constrained multi-objective framework, the contributions of the helper population and original population in different types of CMOPs are discussed. It is unreasonable to assign equal resources to these two populations in different CMOPs and different searching stages. This paper aims to investigate resource allocation in a constraint environment to efficiently utilize the limited resources and obtain a better performance. Therefore, the concept of return on investment (ROI) is first introduced to measure the contributions of two populations, and then guide the population size allocation (APS). To prevent the ROI from continuously declining as the population size decreases, an evolutionary resource allocation strategy (AER) is proposed to adjust their evolutionary state according to the cooperative relationship, and to further increase their ROI and again compete for population size, to maximize the evolutionary efficiency of the two populations in competition and cooperation. The proposed CCMODRA is compared with seven popular algorithms that cover three types of CMOEAs and test them on three benchmarks that cover four types of CMOPs. The comprehensive performance of CCMODRA is better than the other seven CMOEAs on 71% of the 3-objective CDTLZs, 57% of the 5-objective CDTLZs and 46% of the MWs. The effectiveness of the APS and AER strategies are verified on generating contribution solutions and DOC test problems. In addition, the total profit obtained by CCMODRA in the knapsack problem with capacity constraints is improved by 0.2% to 216% compared with the other seven algorithms.

关键词： Dynamic resource allocation constrained multi-objective optimization Cooperation framework Population size Evolutionary resources

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A modified objective function method with feasible-guiding strategy to solve constrained multi-objective optimization problems

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APPLIED SOFT COMPUTING 2014年第PartC期14卷 363-380页

作者： Jiao, Licheng Luo, Juanjuan Shang, Ronghua Liu, Fang Xidian Univ Minist Educ China Key Lab Intelligent Percept & Image Understanding Xian 710071 Peoples R China

For constrained multi-objective optimization problems (CMOPs), how to preserve infeasible individuals and make use of them is a problem to be solved. In this case, a modified objective function method with feasible-guiding strategy on the basis of NSGA-II is proposed to handle CMOPs in this paper. The main idea of proposed algorithm is to modify the objective function values of an individual with its constraint violation values and true objective function values, of which a feasibility ratio fed back from current population is used to keep the balance, and then the feasible-guiding strategy is adopted to make use of preserved infeasible individuals. In this way, non-dominated solutions, obtained from proposed algorithm, show superiority on convergence and diversity of distribution, which can be confirmed by the comparison experiment results with other two CMOEAs on commonly used constrained test problems. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.

关键词： constrained multi-objective optimization Constraint handling Modified objective function method Feasible-guiding strategy

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