An approximate method for nonlinear integer programming problems

Abstract

In this paper we propose an approximate method for nonlinear integer programming problems. A nonlinear integer programming problem is written as a multidimensional nonlinear knapsack problem. The multidimensional nonlinear knapsack problem can be solved even if the objective and constraint functions of the original nonlinear integer programming problems are nonconvex and undifferentiable. It is difficult to solve large-scale multidimensional nonlinear knapsack problems exactly. Therefore, it is important to develop an effective approximate method for such problems. We propose an approximate method to solve the multidimensional nonlinear knapsack problems using the surrogate constraints method and use the method to solve nonlinear integer programming problems. The proposed approximate method provides an upper bound and an approximate solution that provides a lower bound. We can evaluate the quality of the approximate solution to compare the lower bound with the upper bound. Computational experiments show that the proposed method provides high-quality approximate solutions. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 64–70, 1999