Differential evolution outside the box

Consequently, any optimisation algorithm, including nonlinear optimisation heuristics, should be able to deal with such constraints by means of a constraint handling method. Such a method deals with infeasible solution (IS) candidates x R D by means of a suitable approach, involving concepts such as, e.g., ignoring or repairing them. In nonlinear optimisation heuristics inspired by nature, the infeasible components of a solution are generated by the mutation operator, which is expected to help explore regions of the search space outside the scope of the crossover operator and then converge towards solution candidates for which f is minimised or maximised. Intuitively, this search process is disrupted and thus lacks the ability to adapt itself to the properties of the objective function f when it generates many infeasible solutions during the course of the search. In this paper, we present an empirical investigation of the proportion of infeasible solutions generated for various variants and parameter settings of Differential Evolution. The algorithm variants under consideration are introduced in Section 2 while the adopted methods of dealing with generated infeasible solutions, as well as the experimental setup, are introduced in Section 3. The results are discussed in Section 4 and conclusions are drawn in Section 5. 2. Differential evolution Originally intended for a simple fitting problem [36, 31], Differential Evolution (DE) has soon become an established metaheuristic method for general-purpose real-valued optimisation, finding its place among other optimisation methods for real-world applications in engineering, robotics and other fields [35, 30, 41]. Besides the effectiveness of the DE optimisation framework, its success is attributed to the simplicity of its algorithmic structure. As can be seen from the pseudocode in Algorithm 1, it requires tuning only three parameters: the population size N (i.e., number of candidate solutions), the scaling factor F (i.e., a prefixed scalar multiplier in the range p0,2s involved in the mutation process) and the crossover rate C