A simple filter-and-fan approach to the facility location problem (original) (raw)
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Networks, 2015
We develop a variant of the variable neighborhood search (VNS) metaheuristic called the multilayer VNS (MLVNS). It consists in partitioning the neighborhood structures into multiple layers. For each layer l , a VNS defined on the associated neighborhood structures is invoked, each move being evaluated and completed by a recursive call to the MLVNS at layer l −1. A specific MLVNS is developed to solve approximately a class of two-level uncapacitated facility location problems with single assignment (TUFLPS), when only mild assumptions are imposed on the cost functions. Two special cases are used to illustrate the efficiency of the MLVNS: the classical TUFLPS and a problem with modular costs derived from a real-life case. To assess the efficiency of the MLVNS, computational results on a large set of instances are compared with those obtained by slope scaling heuristic methods and by solving integer programming models using a state-of-the-art commercial solver.
Discrete Optimization Neighborhood search heuristics for the uncapacitated facility location problem
2003
The uncapacitated facility location problem is one of choosing sites among a set of candidates in which facilities can be located, so that the demands of a given set of clients are satisfied at minimum costs. Applications of neighborhood search methods to this problem have not been reported in the literature. In this paper we first describe and compare several neighborhood structures used by local search to solve this problem. We then describe neighborhood search heuristics based on tabu search and complete local search with memory to solve large instances of the uncapacitated facility location problem. Our computational experiments show that on medium sized problem instances, both these heuristics return solutions with costs within 0.075% of the optimal with execution times that are often several orders of magnitude less than those required by exact algorithms. On large sized instances, the heuristics generate low cost solutions quite fast, and terminate with solutions whose costs ...
A Tabu Search Heuristic for the Uncapacitated Facility Location Problem
Operations Research/Computer Science Interfaces Series, 2005
A tabu search heuristic procedure for the capacitated facility location problem is developed, implemented and computationally tested. The heuristic procedure uses both short term and long term memories to perform the main search process as well as the diversification and intensification functions. Visited solutions are stored in a primogenitary linked quad tree as a long term memory. The recent iteration at which a facility changed its status is stored for each facility site as a short memory. Lower bounds on the decreases of total cost are used to measure the attractiveness of switching the status of facilities and are used to select a move in the main search process. A specialized transportation algorithm is developed and employed to exploit the problem structure in solving transportation problems. The performance of the heuristic procedure is tested through computational experiments using test problems from the literature and new test problems randomly generated. It found optimal solutions for almost all test problems used. As compared to the Lagrangean and the surrogate/Lagrangean heuristic methods, the tabu search heuristic procedure found much better solutions using much less CPU time.
Solving the uncapacitated facility location problem using tabu search
Computers & Operations Research, 2006
The Semi-Lagrangian Relaxation (SLR) method has been introduced in [BTV06] to solve the p-median problem. In this paper we apply the method to the Uncapacitated Facility Location (UFL) problem. We perform computational experiments on two main collections of UFL problems with unknown optimal values. On one collection, we manage to solve to optimality 16 out of the 18 instances. On the second collection we solve 2 out of 18 instances and improve the Lagrangian lower bound. In this way, we prove that the Hybrid Multistart heuristic of [RW06] provides near optimal solutions.
A tabu search heuristic procedure for the capacitated facility location problem
Journal of Heuristics, 2012
A tabu search heuristic procedure for the capacitated facility location problem is developed, implemented and computationally tested. The heuristic procedure uses both short term and long term memories to perform the main search process as well as the diversification and intensification functions. Visited solutions are stored in a primogenitary linked quad tree as a long term memory. The recent iteration at which a facility changed its status is stored for each facility site as a short memory. Lower bounds on the decreases of total cost are used to measure the attractiveness of switching the status of facilities and are used to select a move in the main search process. A specialized transportation algorithm is developed and employed to exploit the problem structure in solving transportation problems. The performance of the heuristic procedure is tested through computational experiments using test problems from the literature and new test problems randomly generated. It found optimal solutions for almost all test problems used. As compared to the Lagrangean and the surrogate/Lagrangean heuristic methods, the tabu search heuristic procedure found much better solutions using much less CPU time.
Neighborhood search heuristics for the uncapacitated facility location problem
2003
The uncapacitated facility location problem is one of choosing sites among a set of candidates in which facilities can be located, so that the demands of a given set of clients are satisfied at minimum costs. Applications of neighborhood search methods to this problem have not been reported in the literature. In this paper we first describe and compare several neighborhood structures used by local search to solve this problem.
Analysis of a Local Search Heuristic for Facility Location Problems
Journal of Algorithms, 2000
In this paper, we study approximation algorithms for several NP-hard facility location problems. We prove that a simple local search heuristic yields polynomialtime constant-factor approximation bounds for the metric versions of the uncapacitated k-median problem and the uncapacitated facility location problem. (For the k-median problem, our algorithms require a constantfactor blowup in the parameter k.) This local search heuristic was first proposed several decades ago, and has been shown to exhibit good practical performance in empirical studies. We also extend the above results to obtain constant-factor approximation bounds for the metric versions of capacitated k-median and facility location problems.
An Exponential Neighborhood Local Search Algorithm for the Single Row Facility Location Problem
IIMA Working Papers, 2011
In this work we present a local search algorithm for the single row facility location problem. In contrast to other local search algorithms for the problem, our algorithm uses an exponential neighborhood structure. Our computations indicate that our local search algorithm generates solutions to benchmark instances of the problem whose costs are on average within 2% of costs of optimal solutions within reasonable execution time.
International Journal of Production Economics, 2006
Algorithms to solve Facility Location Problems (FLP) optimally suffer from combinatorial explosion and resources required to solve such problems repeatedly as required in practical applications become prohibitive. In these cases heuristic methods are the only viable alternative. We compare the relative performance of Tabu Search (TS), Simulated Annealing (SA) and Genetic Algorithms (GA) on various types of FLP under time-limited, solution-limited, and unrestricted conditions. The results indicate that TS shows very good performance in most cases. The performance of SA and GA are more partial to problem type and the criterion used. Thus, in general we may conclude that TS should be tried first to the extent that it always yields as good or better results and is easy to develop and implement.