On the Efficacy of Ensemble of Constraint Handling Techniques in Self-Adaptive Differential Evolution

Hassan Javed,Muhammad Sulaiman,Rashida Adeeb Khanum,Wali Khan Mashwani,Muhammad Asif Jan,Hidayat Ullah Khan,Nasser Tairan,Habib Shah

doi:10.3390/math7070635

Abstract

Self-adaptive variants of evolutionary algorithms (EAs) tune their parameters on the go by learning from the search history. Adaptive differential evolution with optional external archive (JADE) and self-adaptive differential evolution (SaDE) are two well-known self-adaptive versions of differential evolution (DE). They are both unconstrained search and optimization algorithms. However, if some constraint handling techniques (CHTs) are incorporated in their frameworks, then they can be used to solve constrained optimization problems (COPs). In an early work, an ensemble of constraint handling techniques (ECHT) is probabilistically hybridized with the basic version of DE. The ECHT consists of four different CHTs: superiority of feasible solutions, self-adaptive penalty, ε -constraint handling technique and stochastic ranking. This paper employs ECHT in the selection schemes, where offspring competes with their parents for survival to the next generation, of JADE and SaDE. As a result, JADE-ECHT and SaDE-ECHT are developed, which are the constrained variants of JADE and SaDE. Both algorithms are tested on 24 COPs and the experimental results are collected and compared according to algorithms’ evaluation criteria of CEC’06. Their comparison, in terms of feasibility rate (FR) and success rate (SR), shows that SaDE-ECHT surpasses JADE-ECHT in terms of FR, while JADE-ECHT outperforms SaDE-ECHT in terms of SR.

Highlights

Evolutionary algorithms (EAs) are nature inspired population-based stochastic search and optimization methods
In EAs, selected population members based on a fitness/selection scheme, the so called parents, undergo perturbation by applying genetic operators, mutation and crossover, to produce offspring
A solution is ranked based on its cost value, if it is feasible or if a randomly generated number is smaller than a probability factor p f ; otherwise, it is ranked on the constraints’ violation

Summary

Introduction

Evolutionary algorithms (EAs) are nature inspired population-based stochastic search and optimization methods. SaDE automatically adapts the learning strategies and the parameters’ settings during evolution It probabilistically selects one of the four mutation strategies: DE/rand/1, DE/current to best/2, DE/rand/2, DE/current-to-rand/1 for each individual in the current population. They are not capable to directly solve COPs having constraints of any kind (e.g., equality, inequality, linear and non-linear etc.). SaDE and JADE, being advanced self-adaptive variants, are both unconstrained search and optimization algorithms. The performance of JADE-ECHT and SaDE-ECHT is tested and compared based on feasibility rate (FR) and success rate (SR) on 24 COPs according to algorithms’ evaluation criteria of CEC’06. This rest of this paper is ordered as follows.

Constrained Optimization Problem and ECHT

JADE-ECHT

Result Achieved

Conclusions and Future Work