Combined fitness–violation epsilon constraint handling for differential evolution

Over recent decades, several efficient constraint-handling methods have been proposed in the area of evolutionary computation, and the $$\varepsilon $$ ε constraint method is considered as a state-of-the-art method for both single and multiobjective optimization. Still, very few attempts have been made to improve this method when applied to the differential evolution algorithm. This study proposes several novel constraint-handling methods following similar ideas, where the $$\varepsilon $$ ε level is defined based on the current violation in the population, individual $$\varepsilon $$ ε levels are maintained for every constraint, and a combination of fitness and constraint violation is used for determining infeasible solutions. The proposed approaches demonstrate superior performance compared to other approaches in terms of the feasibility rate in high-dimensional search spaces, as well as convergence to global optima. The experiments are performed using the CEC’2017 constrained suite benchmark functions and a set of Economic Load Dispatch problems.