Local search algorithms for the problem of competitive location of enterprises

Abstract

This article deals with the mathematical model that generalizes the known problem of location of enterprises and is represented in the form of the problem of bilevel mathematical programming. In this model two competitive sides sequentially locate enterprises, and each of the sides strives to maximize its profit. As optimal solutions of the investigated problem, optimal cooperative and optimal noncooperative solutions are considered. The method is suggested for calculating the upper bounds of values of the goal function of the problem at optimal cooperative and noncooperative solutions. Simultaneously with the calculation of the upper bound, the initial approximate solution is set up. Algorithms of the local search for improving this solution are suggested. The algorithms involve two stages: at the first stage the locally optimal solution is found, while at the second stage the locally optimal solution relative to the neighborhood called the generalized one is found. The results of computational experiments demonstrating the possibilities of the suggested algorithms are displayed.