A robust and efficient algorithm for planar competitive location problems

Abstract

In this paper we empirically analyze several algorithms for solving a Huff-like competitive location and design model for profit maximization in the plane. In particular, an exact interval branch-and-bound method and a multistart heuristic already proposed in the literature are compared with UEGO (Universal Evolutionary Global Optimizer), a recent evolutionary algorithm. Both the multistart heuristic and UEGO use a Weiszfeld-like algorithm as local search procedure. The computational study shows that UEGO is superior to the multistart heuristic, and that by properly fine-tuning its parameters it usually (in the computational study, always) find the global optimal solution, and this in much less time than the interval branch-and-bound method. Furthermore, UEGO can solve much larger problems than the interval method.

Competitive location: a state-of-art review

“…Four parallelization of UEGO have been presented. Redondo et al (2009a) empirically analyzed several algorithms for solving the same model. In particular, an exact interval branch-and-bound method and a multi-start heuristic was compared with UEGO.…”

Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding

“…This algorithm is a meta-heuristic global optimization method [34][35][36] based on a hybridization between a genetic algorithm (GA) 37 (which approximates the solution of (8)) with a multi-layer secant algorithm (MSA) 38,39 (which provides suitable initial populations for the GA). In the following, both GA and MSA methods are described in more details.…”

Heuristics for the facility location and design (1|1)-centroid problem on the plane

“…A local method is proposed in [13] (see also [26]) for solving the follower problem. The algorithm is a steepest descent type method which takes discrete steps along the search directions and, usually, converges to a local optimum.…”

“…Next, we present another heuristic procedure, UEGO, introduced in [26], which is rather robust, in the sense that it usually finds the global optimum. Furthermore, its running times are competitive, for small to medium size problems, with the multistart technique starting from 1000 points, and it can handle big size problems without any difficulties.…”

“…A multistart Weiszfeld-like method was presented in [3] to solve the (1|X 1 ) medianoid problem with Huff patronizing behavior when the quality of the new facility is supposed to be fixed, and it was extended in [13] to handle the case where the quality is also variable and there are constraints in the problem. Recently, in [26], the evolutionary algorithm UEGO (Universal Evolutionary Global Optimizer), described in [23], was proposed for the (1|X 1 ) medianoid problem, and it proved to be more reliable than the multistart heuristic introduced in [13]. Other metaheuristics, such as tabu search, have also been proposed to cope with medianoid problems when the feasible space is a network (see [1]).…”