Mixed-variable engineering optimization based on evolutionary and social metaphors

The co-existence of discrete and continuous independent variables in an engineering optimization problem with a multimodal objective function makes many methods incapable of solving the problem. Four methods are tested here: (a) a Simple Genetic Algorithm (SGA), (b) a Struggle Genetic Algorithm (StrGA), (c) a Particle Swarm Optimization Algorithm (PSOA), and (d) a Particle Swarm Optimization Algorithm with Struggle Selection (PSOStr). The last one has been developed by the author, and it is a hybrid of the evolutionary StrGA and the socially inspired PSOA. They are tested in four purely mathematical and three engineering optimization problems of the aforementioned type. All of the methods solved successfully all the problems and located the global optimum. The PSOStr, however, outperformed the other methods in terms of both solution accuracy and computational cost (i.e. function evaluations).