Extending unified differential evolution with a new ensemble of constraint handling techniques

Abstract

In the constrained optimization competition held in CEC 2017, a unified differential evolution algorithm, named UDE, secured 2nd rank. The UDE algorithm is inspired from some popular DE variants existing in the literature such as CoDE, JADE, SaDE, and ranking-based mutation operator. The primary feature of UDE lies in unifying the main idea of CoDE, JADE, SaDE, ranking-based mutation, and incorporating a DE mutation strategy based local search operation. In UDE, the constraint handling strategy adopted is the static penalty method. However, it is well known that a single constraint handling strategy cannot perform robustly across a variety of constraint optimization problems. This problem can be overcome by incorporating an ensemble of constraint handling techniques in the algorithm. However, in the literature, ensemble of constraint handling strategies has been designed and investigated only in a single study so far for constrained single-objective optimization. In this paper, we present a novel ensemble of the penalty method and the superiority of feasible (SOF) solutions method. In the proposed ensemble technique, the penalty method is adopted for the first 50% of maximum allowed function evaluations, while the SOF method is adopted for remaining function evaluations. The ensemble technique promotes exploration in the first half of the search stage by adopting the penalty method while focusing on exploitation in the last half of the search stage by using the SOF method. The proposed ensemble of constraint handling techniques is integrated in the UDE algorithm, and compared with the penalty method and the SOF method on the 28 benchmark problems of CEC 2017 competition on constrained real parameter optimization. The experimental results demonstrate that the proposed ensemble technique based on sequential operation of penalty method and SOF method is highly promising.