Some Discrete Location Models And Algorithms

In this article, we present several discrete location models and propose some meta-heuristic algorithms for solving them.Firstly, this article describes the importance of falicity location problems, the development of facility location problems, the current research state of stochastic facility location problems and some of classical facility location problems, including Weber problem, set covering problem etc. Facilty location problems are related to optimization problems, many of which are NP-hard. There have been many algorithms to solve discrete facility location problems. This article describes some traditional methods and meta-heuristic algorithms. Traditional methods include Branch and Bound algorithm, Lagrangean relaxation algorithm etc, while meta-heuristic algorithms include Tabu Search algorithm, Variable Neighborhood Search algorithm, Genetic algorithm etc.Secondly, in consideration of the vast multi-objective facility location problems a multi-objective anti p-center problem are considered in this paper. This article is first transformed into a single objective problem by using the linear weighted sum method and then a partheno-genetic simulated annealing algorithm is proposed to solve it. We also carry out the numerical experiments for different weights and the experimental results show that this algorithm is efficient for this problem.Thirdly, taking into account many uncertainty in our life, a multi-risk p-median problem is presented to analyze possible scenarios in the future, which is based on the classical p-median problem. Two improved genetic algorithms are proposed for this multi-risk p-median problem, and the experimental results are reported which verify the effictiveness of the proposed algorithms. Fourthly, from the two perspectives of customers and the system a queueing service stochastic location problem with unknown p is considered and an improved tabu search algorithm is proposed for solving this problem. In order to verify the effectiveness of the improved tabu search algorithm, it is compared with two greedy algorithms and the experimental results are reported.Finally, we give a brief summary of our paper and point out future research.