Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization

In practical applications, constrained multi-objective optimization problems (CMOPs) often fail to achieve the desired results when dealing with CMOPs with different characteristics. Therefore, to address this drawback, we designed a constraint multi-objective evolutionary algorithm based on feedbac...

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Main Authors: Yuling Lai, Junming Chen, Yile Chen, Hui Zeng, Jialin Cai
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/4/629
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author Yuling Lai
Junming Chen
Yile Chen
Hui Zeng
Jialin Cai
author_facet Yuling Lai
Junming Chen
Yile Chen
Hui Zeng
Jialin Cai
author_sort Yuling Lai
collection DOAJ
description In practical applications, constrained multi-objective optimization problems (CMOPs) often fail to achieve the desired results when dealing with CMOPs with different characteristics. Therefore, to address this drawback, we designed a constraint multi-objective evolutionary algorithm based on feedback tracking constraint relaxation, referred to as CMOEA-FTR. The entire search process of the algorithm is divided into two stages: In the first stage, the constraint boundaries are adaptively adjusted based on the feedback information from the population solutions, guiding the boundary solutions towards neighboring solutions and tracking high-quality solutions to obtain the complete feasible region, thereby promoting the population to approach the unconstrained Pareto front (UPF). The obtained feasible solutions are stored in an archive and continuously updated to promote the diversity and convergence of the population. In the second stage, the scaling of constraint boundaries is stopped, and a new dominance criterion is established to obtain high-quality parents, thereby achieving the complete constrained Pareto front (CPF). Additionally, we customized an elite mating pool selection, an archive updating strategy, and an elite environmental selection truncation mechanism to maintain a balance between diversity and convergence. To validate the performance of CMOEA-FTR, we conducted comparative experiments on 44 benchmark test problems and 16 real-world application cases. The statistical IGD and HV metrics indicate that CMOEA-FTR outperforms seven other CMOEAs.
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spelling doaj-art-14c26ef3473645699e877ca628ee221b2025-08-20T03:12:09ZengMDPI AGMathematics2227-73902025-02-0113462910.3390/math13040629Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective OptimizationYuling Lai0Junming Chen1Yile Chen2Hui Zeng3Jialin Cai4School of Art and Design, Guangzhou University, Guangzhou 510006, ChinaFaculty of Humanities and Arts, Macau University of Science and Technology, Macao 999078, ChinaFaculty of Humanities and Arts, Macau University of Science and Technology, Macao 999078, ChinaSchool of Design, Jiangnan University, Wuxi 214122, ChinaSchool of Art and Design, Guangzhou University, Guangzhou 510006, ChinaIn practical applications, constrained multi-objective optimization problems (CMOPs) often fail to achieve the desired results when dealing with CMOPs with different characteristics. Therefore, to address this drawback, we designed a constraint multi-objective evolutionary algorithm based on feedback tracking constraint relaxation, referred to as CMOEA-FTR. The entire search process of the algorithm is divided into two stages: In the first stage, the constraint boundaries are adaptively adjusted based on the feedback information from the population solutions, guiding the boundary solutions towards neighboring solutions and tracking high-quality solutions to obtain the complete feasible region, thereby promoting the population to approach the unconstrained Pareto front (UPF). The obtained feasible solutions are stored in an archive and continuously updated to promote the diversity and convergence of the population. In the second stage, the scaling of constraint boundaries is stopped, and a new dominance criterion is established to obtain high-quality parents, thereby achieving the complete constrained Pareto front (CPF). Additionally, we customized an elite mating pool selection, an archive updating strategy, and an elite environmental selection truncation mechanism to maintain a balance between diversity and convergence. To validate the performance of CMOEA-FTR, we conducted comparative experiments on 44 benchmark test problems and 16 real-world application cases. The statistical IGD and HV metrics indicate that CMOEA-FTR outperforms seven other CMOEAs.https://www.mdpi.com/2227-7390/13/4/629constrained multi-objective optimizationevolutionary algorithmfeedback trackingarchive
spellingShingle Yuling Lai
Junming Chen
Yile Chen
Hui Zeng
Jialin Cai
Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization
Mathematics
constrained multi-objective optimization
evolutionary algorithm
feedback tracking
archive
title Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization
title_full Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization
title_fullStr Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization
title_full_unstemmed Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization
title_short Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization
title_sort feedback tracking constraint relaxation algorithm for constrained multi objective optimization
topic constrained multi-objective optimization
evolutionary algorithm
feedback tracking
archive
url https://www.mdpi.com/2227-7390/13/4/629
work_keys_str_mv AT yulinglai feedbacktrackingconstraintrelaxationalgorithmforconstrainedmultiobjectiveoptimization
AT junmingchen feedbacktrackingconstraintrelaxationalgorithmforconstrainedmultiobjectiveoptimization
AT yilechen feedbacktrackingconstraintrelaxationalgorithmforconstrainedmultiobjectiveoptimization
AT huizeng feedbacktrackingconstraintrelaxationalgorithmforconstrainedmultiobjectiveoptimization
AT jialincai feedbacktrackingconstraintrelaxationalgorithmforconstrainedmultiobjectiveoptimization