An Improved Epsilon Constraint-handling Method in MOEA/D for CMOPs with Large Infeasible Regions (1707.08767v1)

Abstract: This paper proposes an improved epsilon constraint-handling mechanism, and combines it with a decomposition-based multi-objective evolutionary algorithm (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). The proposed constrained multi-objective evolutionary algorithm (CMOEA) is named MOEA/D-IEpsilon. It adjusts the epsilon level dynamically according to the ratio of feasible to total solutions (RFS) in the current population. In order to evaluate the performance of MOEA/D-IEpsilon, a new set of CMOPs with two and three objectives is designed, having large infeasible regions (relative to the feasible regions), and they are called LIR-CMOPs. Then the fourteen benchmarks, including LIR-CMOP1-14, are used to test MOEA/D-IEpsilon and four other decomposition-based CMOEAs, including MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP and C-MOEA/D. The experimental results indicate that MOEA/D-IEpsilon is significantly better than the other four CMOEAs on all of the test instances, which shows that MOEA/D-IEpsilon is more suitable for solving CMOPs with large infeasible regions. Furthermore, a real-world problem, namely the robot gripper optimization problem, is used to test the five CMOEAs. The experimental results demonstrate that MOEA/D-IEpsilon also outperforms the other four CMOEAs on this problem.

• The paper introduces MOEA/D-IEpsilon, which dynamically adjusts the epsilon value based on the feasible-to-total solution ratio to navigate large infeasible regions.
• The method demonstrates superior performance using IGD and HV metrics, outperforming four competing algorithms across 14 benchmark problems.
• The study validates the approach's practical impact by achieving improved outcomes in a real-world robot gripper optimization problem.

An Improved Epsilon Constraint-Handling Method in MOEA/D for CMOPs with Large Infeasible Regions

This paper introduces a refined epsilon (ε) constraint-handling mechanism combined with a decomposition-based multi-objective evolutionary algorithm (MOEA/D), specifically designed to address constrained multi-objective optimization problems (CMOPs) with substantial infeasible regions. The proposed algorithm, named MOEA/D-IEpsilon, dynamically adjusts ε according to the ratio of feasible to total solutions in the current population. This mechanism is evaluated on a newly designed set of CMOPs with significant infeasible regions, termed LIR-CMOPs, which presents fourteen benchmarks to test MOEA/D-IEpsilon against other decomposition-based constrained multi-objective evolutionary algorithms (CMOEAs).

In the experimental comparisons, MOEA/D-IEpsilon consistently outperformed four other competing methods: MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP, and C-MOEA/D across all the test instances. This superior performance demonstrates its efficacy in navigating large infeasible regions. Furthermore, MOEA/D-IEpsilon was tested on a real-world application, the robot gripper optimization problem, where it achieved better results compared to the aforementioned algorithms.

Key numerical results indicate significant improvements in the inverted generational distance (IGD) and hypervolume (HV) metrics across all test cases, with MOEA/D-IEpsilon achieving lower IGD values and higher HV values, reflecting its enhanced capability in balancing convergence and diversity for CMOPs with large infeasible regions.

Theoretical implications of this research suggest that an adaptable ε constraint, sensitive to current population characteristics, effectively enhances the search potential in evolutionary algorithms by dynamically exploiting feasible solutions. Practically, the application to real-world problems like robot gripper design underscores the potential of this method to improve optimization outcomes in environments where feasible solution spaces are constrained and difficult to identify.

Future directions could explore further refining the ε-setting mechanisms by incorporating additional criteria or heuristics based on problem-specific knowledge or leveraging more advanced machine learning techniques to predict and adaptively control the exploration-exploitation balance dynamically. Such advancements may bridge the gap in current constraint-handling techniques and contribute substantially to the development of more robust and efficient CMOEAs applicable across a wider range of complex real-world problems.