A Voting-Mechanism-Based Ensemble Framework for Constraint Handling Techniques

Abstract

Effective constraint handling techniques (CHTs) are of great significance for evolutionary algorithms (EAs) dealing with constrained optimization problems (COPs). To date, many CHTs, such as penalty function, superiority of feasible solutions, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -constraint (EC), have been designed. However, different CHTs are usually suited to different problems, even the most appropriate technique changes along with the stages of the optimization process. Motivated by this phenomenon, we propose a voting-mechanism-based ensemble framework, named voting mechanism for constraint handling (VMCH), to integrate multiple CHTs for solving various COPs. In this framework, each CHT acts as a voter, all voters vote for each pair of solutions, and the solution in each pair with the highest weighted votes is considered better. In addition, an adaptive strategy is developed to adjust the voter weights according to their historical voting performance. To investigate the performance of VMCH in improving existing algorithms, the proposed VMCH is embedded into the three best algorithms in the competition on constrained single objective real-parameter optimization at CEC 2018, namely, MAgES, iLSHADE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> , and IUDE, to form three new algorithm versions, i.e., MAgES-VMCH, iLSHADE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -VMCH, and IUDE-VMCH. They are compared with seven state-of-the-art peer algorithms. Extensive experiments are conducted on 57 real-world COPs. The ranking results show that the new algorithm version MAgES-VMCH takes first place among the ten comparison algorithms. Moreover, all the new VMCH-enhanced versions of the three best algorithms are superior to their original versions. Therefore, the proposed VMCH framework can achieve competitive performance in solving COPs.