Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem

Abstract

T he variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15 000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7 000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15 000.

New local searches for solving the multi-source Weber problem

“…Furthermore, if the discrete problem is not solved optimally, the algorithm may terminate prematurely since the objective function is less likely to improve in Step 5. Exact solution methods such as the DUALOC procedure by Erlenkotter (1978) or the Primal-Dual VNS by Hansen et al (2007), should be considered in future studies.…”

Variable neighbourhood search: methods and applications

“…In Hansen et al (2007a) it is shown that VNS with decomposition is a very powerful technique for large-scale simple plant location problems (SPLP) with up to 15,000 facilities and 15,000 users. In the second phase, this approach is designed to find an exact solution to the relaxed dual problem.…”

“…Ljubic (2007) proposes a hybrid VNS for a connected facility location problem which combines the facility location problem and the Steiner tree problem in graphs. Hansen et al (2007a) apply a primal-dual VNS for the simple plant location problem. Finally, Bischoff and Dächert (2008) use VNS and other heuristics for a generalized class of continuous location-allocation problems and Jabalameli and Ghaderi (2008) propose hybrid algorithms which combine Genetic Algorithm (GA) and VNS for the uncapacitated continuous location-allocation problem.…”

Variable neighbourhood search: methods and applications

“…In the first stage an heuristic procedure based on VNS is used to obtain a near optimal solution. In Hansen et al (2007a) it is shown that VNS with decomposition is a very powerful technique for large-scale simple plant location problems (SPLP) with up to 15 000 facilities and 15 000 users. In the second phase, this approach is designed to find an exact solution to the relaxed dual problem.…”

“…apply VNS to the maximum return-on-investment plant location problem with market share Ljubic (2007). proposes a hybrid VNS for a connected facility location problem which combines the facility location problem and the Steiner tree problem in graphs Hansen et al (2007a). apply a primal-dual VNS for the simple plant location problem.…”