Bound constraints handling in Differential Evolution: An experimental study

Bound constraints are lower and upper limits for coordinate values of feasible solutions. This paper is devoted to the issue of handling bound constraints in Differential Evolution (DE). We overview the majority of popular Bound Constraint Handling Methods (BCHMs), which can be classified as penalty function methods, repair methods and specialized mutation methods. We discuss and empirically verify how BCHMs influence the pattern of individuals generated by DE. We take 7 different DE algorithms and 17 different BCHMs, and perform experimental analysis of their combinations to characterize their efficiency in exploitation and exploration. As a basis for the experiments, we take a 10-dimensional quadratic function with various locations of the minimum and CEC'2017 benchmark set, which defines 30 optimization problems in 10, 30, 50 and 100 dimensions. We observe that DE algorithms differ significantly in the degree to which their efficiency depends on the choice of particular BCHMs. We identify which BCHMs usually lead to efficient optimization for the majority of DE algorithms. Similarly, we identify BCHMs which should definitely be avoided.