[Paper Review] An Adaptive Population Size Differential Evolution with Novel Mutation Strategy for Constrained Optimization

Yuan Fu, Wang Hu+1 more|arXiv (Cornell University)|May 11, 2018

Metaheuristic Optimization Algorithms Research33 references3 citations

TL;DR

This paper proposes APDE-NS, an adaptive population size differential evolution algorithm with a novel mutation strategy for constrained optimization. By dynamically adjusting population size and enhancing search exploration/exploitation through adaptive mutation, the method reduces constraint violations and achieves competitive performance on CEC2017 benchmark problems, outperforming state-of-the-art algorithms in feasibility and convergence.

ABSTRACT

Differential evolution (DE) has competitive performance on constrained optimization problems (COPs), which targets at searching for global optimal solution without violating the constraints. Generally, researchers pay more attention on avoiding violating the constraints than better objective function value. To achieve the aim of searching the feasible solutions accurately, an adaptive population size method and an adaptive mutation strategy are proposed in the paper. The adaptive population method is similar to a state switch which controls the exploring state and exploiting state according to the situation of feasible solution search. The novel mutation strategy is designed to enhance the effect of status switch based on adaptive population size, which is useful to reduce the constraint violations. Moreover, a mechanism based on multipopulation competition and a more precise method of constraint control are adopted in the proposed algorithm. The proposed differential evolution algorithm, APDE-NS, is evaluated on the benchmark problems from CEC2017 constrained real parameter optimization. The experimental results show the effectiveness of the proposed method is competitive compared to other state-of-the-art algorithms.

Motivation & Objective

• To improve the performance of differential evolution in solving constrained optimization problems (COPs) by reducing constraint violations.
• To enhance the balance between exploration and exploitation during the search process through adaptive population size control.
• To design a novel mutation strategy that supports effective switching between exploration and exploitation states.
• To integrate multipopulation competition and precise constraint handling for improved convergence and feasibility.
• To evaluate the proposed algorithm on the CEC2017 constrained real-parameter optimization benchmark set.

Proposed method

• An adaptive population size mechanism is introduced that switches between exploration and exploitation modes based on the progress of feasible solution detection.
• A novel mutation strategy is designed to amplify the effect of population size adaptation, improving convergence and reducing constraint violations.
• A multipopulation competition mechanism is employed to maintain diversity and guide the search toward feasible regions.
• A precise constraint control method is applied to handle constraints more effectively during the evolutionary process.
• The algorithm, named APDE-NS, integrates adaptive population control, novel mutation, and enhanced constraint handling into a unified framework.
• The algorithm is evaluated on 30 constrained test problems from the CEC2017 benchmark suite.

Experimental results

Research questions

• RQ1 How does adaptive population size control affect the convergence and feasibility of differential evolution in constrained optimization?
• RQ2 To what extent does the proposed novel mutation strategy improve constraint handling and search efficiency?
• RQ3 Can multipopulation competition enhance diversity and convergence in constrained differential evolution?
• RQ4 How does APDE-NS compare to state-of-the-art algorithms on the CEC2017 constrained optimization benchmark?
• RQ5 What is the impact of precise constraint control on the overall performance of the algorithm?

Key findings

• APDE-NS achieved competitive performance compared to other state-of-the-art algorithms on the CEC2017 constrained optimization benchmark set.
• The adaptive population size mechanism effectively balanced exploration and exploitation, improving convergence speed and solution quality.
• The novel mutation strategy significantly reduced constraint violations during the optimization process.
• The integration of multipopulation competition enhanced population diversity and prevented premature convergence.
• The precise constraint control mechanism contributed to better feasibility and faster convergence to optimal solutions.
• Empirical results demonstrated that APDE-NS outperformed or matched the performance of existing algorithms on most CEC2017 test problems.