Hybrid approach for constraint handling in MINLP optimization

Abstract

Abstract. Stochastic techniques have demonstrated rewarding performance in global optimization of highly multimodal unconstrained models. However, the formulation of a general framework for constraint handling in stochastic optimization is still an open issue. In this work a novel approach to address MINLP models is proposed whose rationale is to convert the constraint verification issue into the identification of the local optima of an unconstrained model. For this purpose the optimality conditions of the original problem, namely its Karush-Kuhn-Tucker system, are solved as an unconstrained optimization model, which minimizes the sum of the equation residuals. The resulting multi-modal unconstrained problem can be efficiently addressed with standard stochastic algorithms. In particular, a sequential niche strategy, which makes use of a genetic algorithm, is adopted in this work to solve the problem. The proposed approach combines the strengths of the deterministic optimality theory together with the ability of stochastic techniques as function optimizers.