A combined penalty function and outer-approximation method for MINLP optimization

An improved outer-approximation algorithm for MINLP optimization is proposed in this paper which is aimed at the solution of problems where convexity conditions may not hold. The proposed algorithm starts by solving the NLP relaxation. If an integer solution is not found, a sequence of iterations consisting of NLP subproblems and MILP master problems is solved. The proposed MILP master problem is based on the outer-approximation/equality-relaxation algorithm and features an exact penalty function that allows violations of linearizations of nonconvex constraints. The search proceeds until no improvement is found in the NLP subproblems. Computational experience is presented on a set of 20 test problems. Included are problems for optimum feed tray location and number of plates for distillation columns which are described in detail. The results show that although no theoretical guarantee can be given, the proposed method has a high degree of reliability for finding the global optimum in nonconvex problems.