Solution of a mixed integer-nonlinear and non-convex optimization problem by convexification methods based on special ordered sets

Document Type : Research Article

Authors

1 Assistant Professor, Faculty of Electrical Engineering, University of Shahreza

2 PhD Candidate, Department of Water Science and Engineering, Ferdowsi University of Mashhad

Abstract

This paper presents a convexification method for mixed integer-nonlinear problems (MINLP) that used mathematic approximations based on special ordered sets (SOS) to solve optimization problems. Many of the engineering problems contain binary variables and nonlinear constraints which leading to a MINLP problems. In addition, the objective function and the constraints some of these MINLP problems include non-convex functions. Solving non-convex MINLP problems is challenging and difficult for many algorithms and optimization methods. Economic dispatch with considering alternative current power flow equations (ACED problem) in electrical engineering is One of these problems. The proposed ACED problem in this paper includes both nonlinear and non-convex practical constraints as well as binary variables. As a result, this problem is a complex and non-convex MINLP problem. To solve this problem, a new solution method based on SOS approximation is presented.  This method relaxes the nonlinear constraints of the model using a convex linear outer approximation based on the concept of special ordered sets (SOS). To show the effectiveness of the proposed solution method, it is tested on the well-known test systems and compared with several other recently published solution methods. These comparisons confirm the validity of the developed approach.

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