An improved framework for solving NLIPs with signomial terms in the objective or constraints to global optimality

Abstract

Real application problems are often formulated as nonlinear integer programming problems or as discrete global optimization problems with signomial terms in the objective or constraints. Although various approaches have been proposed to solve the problems, they either utilize numerous extra binary variables and constraints to reconstruct the problems for finding a global solution or are unable to obtain globally optimized solutions. This study proposes a novel linearization method that employs a logarithmic number of extra binary variables and constraints to reformulate a signomial term with discrete variables. The original nonlinear integer program is therefore converted into a mixed-integer linear program solvable to obtain a global optimum. Several numerical experiments are presented to demonstrate the computational efficiency of the proposed methods in solving nonlinear integer problems, especially for treating signomial functions with large-interval variables or multiple variables.