Finding all solution sets of piecewise-linear interval equations using an integer programming solver

Abstract

This paper presents an efficient and easily implementable method for finding all solution sets of piecewise-linear interval equations using integer programming. In this method, the problem of finding all solution sets is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that all solution sets are obtained by solving a single mixed integer programming problem and related linear programming problems. Numerical examples are given to confirm the effectiveness of the proposed method.