A metaheuristic penalty approach for the starting point in nonlinear programming

Abstract

Solving nonlinear programming problems usually involve difficulties to obtain a starting point that produces convergence to a local feasible solution, for which the objective function value is sufficiently good. A novel approach is proposed, combining metaheuristic techniques with modern deterministic optimization schemes, with the aim to solve a sequence of penalized related problems to generate convenient starting points. The metaheuristic ideas are used to choose the penalty parameters associated with the constraints, and for each set of penalty parameters a deterministic scheme is used to evaluate a properly chosen metaheuristic merit function. Based on this starting-point approach, we describe two different strategies for solving the nonlinear programming problem. We illustrate the properties of the combined schemes on three nonlinear programming benchmark-test problems, and also on the well-known and hard-to-solve disk-packing problem, that possesses a huge amount of local-nonglobal solutions, obtaining encouraging results both in terms of optimality and feasibility.