Combining Lagrangian Decomposition with Very Large Scale Neighborhood Search for Capacitated Connected Facility Location (original) (raw)

An effective heuristic for large-scale capacitated facility location problems

Journal of Heuristics, 2008

The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for largescale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of "promising" variables forming the core problem and on a Branch-and-Cut algorithm that solves the core problem. Computational results on very large scale instances (up to 4 million variables) are reported.

Primal-Dual Algorithms for Connected Facility Location Problems

2002

We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {c e } on the edges, a set of facilities F ⊆ V , and a set of clients D ⊆ V . Facility i has a facility opening cost f i and client j has d j units of demand. We are also given a parameter M ≥ 1. A solution opens some facilities, say F , assigns each client j to an open facility i(j), and connects the open facilities by a Steiner tree T . The total cost incurred is i∈F f i + j∈D d j c i(j)j + M e∈T c e . We want a solution of minimum cost.

Improved Approximation Algorithm for Connected Facility Location Problems

2007

We study the Connected Facility Location problems. We are given a connected graph G = (V, E) with non-negative edge cost c e for each edge e ∈ E, a set of clients D ⊆ V such that each client j ∈ D has positive demand d j and a set of facilities F ⊆ V each has non-negative opening cost f i and capacity to serve all client demands. The objective is to open a subset of facilities, say \(\hat F\) , to assign each client j ∈ D to exactly one open facility i(j) and to connect all open facilities by a Steiner tree T such that the cost \(\sum_{i \in \hat F} f_i + \sum_{j \in D} d_j c_{i(j)j}+M\sum_{e \in T}c_e\) is minimized. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55. We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm.

A Comparison of Exact and Heuristic Methods for a Facility Location Problem

International journal of simulation: systems, science & technology

We formulate a facility location problem where the demand of any single client must be allocated to a single facility and a prize is obtained by allocating the demand of a client to a certain facility, i.e. a prize-based variant of the Single Source Capacitated Facility Location Problem. For this problem we pursue both an exact approach through Integer Linear Programming and a heuristic approach based on a local search algorithm. We compare both approaches by considering 500+ instances. The heuristic approach allows to obtain a reduction of the computational time by a factor larger than 10 in 92% of instances and 100 in 64% of instances. The time reduction is obtained with a small sacrifice in the value of the objective function that is achieved, smaller than 10% in nearly 70% of cases.

A two-stage method for the capacitated multi-facility location-allocation problem

International Journal of Operational Research, 2019

This paper examines the capacitated planar multi-facility location-allocation problem, where the number of facilities to be located is specified and each of which has a capacity constraint. A two-stage method is put forward to deal with the problem where in the first stage a technique that discretises continuous space into discrete cells is used to generate a relatively good initial facility configurations. In Stage 2, a Variable Neighbourhood Search (VNS) is implemented to improve the quality of solution obtained by the previous stage. The performance of the proposed method is evaluated using benchmark data sets from the literature. The numerical experiments show that the proposed method yields competitive results when compared to the best known results from the literature. In addition, some future research avenues are also suggested.

Heuristics for a continuous multi-facility location problem with demand regions

Computers & Operations Research, 2015

We consider a continuous multi-facility location problem where the demanding entities are regions in the plane instead of points. Each region may consist of a finite or an infinite number of points. The service point of a station can be anywhere in the region that is assigned to it. We do not allow fractional assignments, that is, each region is assigned to exactly one facility. The problem we consider can be stated as follows: given m demand regions in the plane, find the locations of q facilities and allocate regions to the facilities so as to minimize the sum of squares of the maximum Euclidean distances of the demand regions to the facility locations they are assigned to. We assume that the regions are closed polygons as any region can be approximated within any desired accuracy with a polygon. We first propose mathematical programming formulations of single and multiple facility location problems. The single facility location problem is formulated as a second order cone program (SOCP) which can be solved in polynomial time. The multiple facility location problem is formulated as a mixed integer SOCP. This formulation is weak and does not even solve medium-size problems. We therefore propose heuristics to solve larger instances of the problem. We develop three heuristics that work when the regions are polygons. When the demand regions are rectangles with sides parallel to coordinate axes, a special heuristic is developed. We compare our heuristics in terms of both solution quality and computational time.

Approximate algorithms for the competitive facility location problem

Journal of Applied and Industrial Mathematics, 2011

We consider the competitive facility location problem in which two competing sides (the Leader and the Follower) open in succession their facilities, and each consumer chooses one of the open facilities basing on its own preferences. The problem amounts to choosing the Leader's facility locations so that to obtain maximal profit taking into account the subsequent facility location by the Follower who also aims to obtain maximal profit. We state the problem as a two-level integer programming problem. A method is proposed for calculating an upper bound for the maximal profit of the Leader. The corresponding algorithm amounts to constructing the classical maximum facility location problem and finding an optimal solution to it. Simultaneously with calculating an upper bound we construct an initial approximate solution to the competitive facility location problem. We propose some local search algorithms for improving the initial approximate solutions. We include the results of some simulations with the proposed algorithms, which enable us to estimate the precision of the resulting approximate solutions and give a comparative estimate for the quality of the algorithms under consideration for constructing the approximate solutions to the problem.

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 ...

Semi-Lagrangian relaxation applied to the uncapacitated facility location problem

Computational Optimization and Applications, 2012

We show how the performance of general purpose Mixed Integer Programming (MIP) solvers, can be enhanced by using the Semi-Lagrangian Relaxation (SLR) method. To illustrate this procedure we perform computational experiments on large-scale instances of the Uncapacitated Facility Location (UFL) problems with unknown optimal values. CPLEX solves 3 out of the 36 instances. By combining CPLEX with SLR, we manage to solve 18 out of the 36 instances and improve the best known lower bound for the other instances. The key point has been that, on average, the SLR approach, has reduced by more than 90% the total number of relevant UFL variables.