Variable Neighborhood Search Algorithms for the Node Placement Problem in Multihop Networks

We consider a problem of finding an optimal node placement that minimizes the amount of traffic by reducing the weighted hop distances in multihop networks. The problem is called Node Placement Problem (NPP) and is known to be NP-hard. Therefore, several heuristic and metaheuristic algorithms have been proposed for solving NPP, such as local search, genetic algorithm, simulated annealing, tabu search, iterated local search, ant colony optimization, etc. Although Variable Neighborhood Search (VNS) is known to be one of the most promising and efficient metaheuristic algorithms for optimization problems, VNS has not been shown for NPP yet. In this paper we propose VNS algorithms for NPP. The proposed VNSs consist of two phases: local search phase to obtain a local optimum and perturbation phase to get out of the corresponding valley in the search space. We show six types of neighborhood change schemes for the perturbation phase of VNS, and through computational experiments, we compare each performance of six VNSs incorporating k-swap local search, called VNS1, VNS2, ... , VNS6. The experimental results indicate that VNS4 outperformed the others for large problem instances particularly, which adopts a suitable perturbation size selected by exploring from the upper bound that is adaptively lower in the search.