A nonlinear transformation based hybrid evolutionary method for MINLP solution

In the recent past, some of the population based stochastic direct search methods, like genetic algorithms and differential evolution (DE), have been increasingly applied for solving complex optimization problems in diverse applications. Most of the times, though global optimal solutions are obtained, these stochastic methods have slow convergence and take long computational times. The handling of discrete variables has been quite ad hoc; for instance in DE, the algorithm works assuming them as continuous variables during all the steps but only for the objective function evaluation, a truncation operation is used for forcing the integrality requirements. In this paper, we address both, the convergence issues and improved ways of handling discrete variables. A nonlinear transformation proposed in the literature for representing the discrete variables as continuous variables has been explored for alternate ways of solving MINLP problems to global optimality through conversion of MINLP problems into equivalent NLPs. For finding global optimal solutions to the resulting nonconvex NLP and to improve the convergence rate of DE closer to the optimum, in this work a hybrid method combining stochastic and deterministic approaches has been proposed, which seems to be promising within the scope of the case studies considered, though guarantee of the global optimality still remains an issue.