The p-Median Problem with Concave Costs (original) (raw)
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A parallel variable neighborhood search approach for the obnoxious p -median problem
International Transactions in Operational Research
The obnoxious p-median problem consists of selecting p locations, considered facilities, in a way that the sum of the distances from each nonfacility location, called customers, to its nearest facility is maximized. This is an N P-hard problem that can be formulated as an integer linear program. In this paper, we propose the application of a variable neighborhood search (VNS) method to effectively tackle this problem. First, we develop new and fast local search procedures to be integrated into the basic VNS methodology. Then, some parameters of the algorithm are tuned in order to improve its performance. The best VNS variant is parallelized and compared with the best previous methods, namely branch and cut, tabu search, and GRASP over a wide set of instances. Experimental results show that the proposed VNS outperforms previous methods in the state of the art. This fact is finally confirmed by conducting nonparametric statistical tests.
An effective VNS for the capacitated p-median problem
European Journal of Operational Research, 2008
In the capacitated p-median problem (CPMP), a set of n customers is to be partitioned into p disjoint clusters, such that the total dissimilarity within each cluster is minimized subject to constraints on maximum cluster capacities. Dissimilarity of a cluster is the sum of the dissimilarities between each customer who belongs to the cluster and the median associated with the cluster. An effective variable neighbourhood search heuristic for this problem is proposed. The heuristic is characterized by the use of easily computed lower bounds to assess whether undertaking computationally expensive calculation of the worth of moves, within the neighbourhood search, is necessary. The small proportion of moves that need to be assessed fully are then evaluated by an exact solution of a relatively small subproblem. Computational results on five standard sets of benchmark problem instances show that the heuristic finds all the best-known solutions. For one instance, the previously best-known solution is improved, if only marginally.
2010
We present a new general variable neighborhood search approach for the uncapacitated single allocation p-hub median problem in networks. This NP hard problem is concerned with locating hub facilities in order to minimize the traffic between all origin-destination pairs. We use three neighborhoods and efficiently update data structures for calculating new total flow in the network. In addition to the usual sequential strategy, a new nested strategy is proposed in designing a deterministic variable neighborhood descent local search. Our experimentation shows that general variable neighborhood search based heuristics outperform the best-known heuristics in terms of solution quality and computational effort. Moreover, we improve the best-known objective values for some large Australia Post and PlanetLab instances. Results with the new nested variable neighborhood descent show the best performance in solving very large test instances.
Dynamic facility location: The progressive p-median problem
Location Science, 1995
A dynamic p-median problem is considered. Demand is changing over a given time horizon and the facilities are built one at a time at given times. Once a new facility is built, some of the customers will use its services and some of the customers will patronize an existing facility. At any given time, customers patronize the closest facility. The problem is to find the best locations for the new facilities. The problem is formulated and the two facilities case is solved by a special algorithm. The general problem is solved using the standard mathematical programming code AMPL.
The Parallel Variable Neighborhood Search for the P-Median Problem
Journal of …, 2002
The Variable Neighborhood Search (VNS) is a recent metaheuristic that combines series of random and improving local searches based on systematically changed neighborhoods. When a local minimum is reached, a shake procedure performs a random search. This determines a new starting point for running an improving search. The use of interchange moves provides a simple implementation of the VNS algorithm for the p-Median Problem. Several strategies for the parallelization of the VNS are considered and coded in C using OpenMP. They are compared in a shared memory machine with large instances.
Chapter 6 LAGRANGEAN / SURROGATE HEURISTICS FOR p-MEDIAN PROBLEMS
The p-median problem is the problem of locating p facilities (medians) on a network so as to minimize the sum of all the distances from each demand point to its nearest facility. A successful approach to approximately solve this problem is the use of Lagrangean heuristics, based upon Lagrangean relaxation and subgradient optimization. The Lagrangean/surrogate is an alternative relaxation proposed recently to correct the erratic behavior of subgradient like methods employed to solve the Lagrangean dual. We propose in this paper Lagrangean/surrogate heuristics to p-median problems. Lagrangean and surrogate relaxations are combined relaxing in the surrogate way the assignment constraints in the p-median formulation. Then, the Lagrangean relaxation of the surrogate constraint is obtained and approximately optimized (one-dimensional dual). Lagrangean/surrogate relaxations are very stable (low oscillating) and reach the same good results of Lagrangean (alone) heuristics in less computatio...
Improved starting solutions for the planar p-median problem
Yugoslav Journal of Operations Research, 2020
In this paper we present two new approaches for finding good starting solutions to the planar p-median problem. Both methods rely on a discrete approximation of the continuous model that restricts the facility locations to the given set of demand points. The first method adapts the first phase of a greedy random construction algorithm proposed for the minimum sum of squares clustering problem. The second one implements a simple descent procedure based on vertex exchange. The resulting solution is then used as a starting point in a local search heuristic that iterates between the well-known Cooper?s alternating locate-allocate method and a transfer follow-up step with a new and more effective selection rule. Extensive computational experiments show that (1) using good starting solutions can significantly improve the performance of local search, and (2) using a hybrid algorithm that combines good starting solutions with a \deep" local search can be an effective strategy for solvi...
A Solution Proposal for the Capacitated P-Median Problem with Tabu Search
Research in Computing Science
This work presents the Capacitated P-Median problem, which seeks to solve the optimal location of p distributors. In understanding the computational complexity of this problem, partitioning principles are applied in the process of associating a distribution center with customers to be serviced. These are treated as clusters containing each distribution center and its customers. The optimization of the implicit cost function within the partitioning (distance minimization) is performed using Tabu Search with a diversified search. A series of computational experiences is performed aided by the OR-Library test instances, where in most cases an optimal solution is reached in reasonable computing time. As Tabu Search does not obtain all expected optima, OR-Library test instances are solved with the help of Lingo 16.0 and the obtained results are compared with those resulting from Tabu Search.