Probabilistic constraint handling in the framework of joint evolutionary-classical optimization with engineering applications

Optimization for single main objective with multi constraints is considered using a probabilistic approach coupled to evolutionary search. In this approach the problem is converted into a bi-objective problem, treating the constraint ensemble as a second objective subjected to multi-objective optimization for the formation of a Pareto front, and this is followed by a local search for the optimization of the main objective function. In this process a novel probabilistic modeling is applied to the constraint ensemble, so that the stiff constraints are effectively taken care of, while the model parameter is adaptively determined during the evolutionary search. In this way the convergence to the solution is significantly accelerated and an accurate solution is established. The improvements are demonstrated by means of example problems including comparisons with the standard benchmark problems, the solutions of which are reported in the literature.