Stochastic MINLP optimization using simplicial approximation

Abstract

Mathematical programming has long been recognized as a promising direction to the efficient solution of design, synthesis and operation problems that can gain industry the competitive advantage required to survive in today's difficult economic environment. Most of the engineering design problems can be modelled as MINLP problems with stochastic parameters. In this paper a decomposition algorithm is presented to solve convex stochastic MINLP problems. The proposed approach is an extension of the simplicial approximation approach proposed by Goyal and Ierapetritou [Goyal, V., & Ierapetritou, M. G. (2004a). MINLP optimization using simplicial approx imation method for classes of non-convex problems. In C. A. Floudas, & P. M. Pardalos (Eds.), Frontiers in Global Optimization (p. 165). Goyal, V., & Ierapetritou, M. G. (2004b). Computational studies using a novel simplicial-approximation based algorithm for MINLP optimisation. Computers and Chemical Engineering, 28, 1771], for solving deterministic MINLP problems and is based on the idea of representing the feasible region by a close approximation of its convex hull. Two case studies are presented illustrating the applicability and efficiency of the proposed approach.