On Neighborhood Tree Search

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by exploring different paths of the tree in a heuristic way. We show that allowing the search to 'backtrack' to a previously visited solution and resuming the iterative variable neighborhood descent by 'pruning' the already explored neighborhood branches leads to the design of effective and efficient search heuristics. We describe this idea by discussing its basic design components within a generic algorithmic scheme and we propose some simple and intuitive strategies to guide the search when traversing the neighborhood tree. We conduct a thorough experimental analysis of this approach by considering two different problem domains, namely, the Total Weighted Tardiness Problem (SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show that independently of the considered domain, the approach is highly competitive. In particular, we show that using different branching and backtracking strategies when exploring the neighborhood tree allows us to achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012

Solving Medium to Large Sized Euclidean Generalized Minimum Spanning Tree Problems

The generalized minimum spanning tree problem is a generalization of the minimum spanning tree problem. This network design problems finds several practical applications, especially when one considers the design of a large-capacity backbone network connecting several individual networks. In this paper we study the performance of six neighborhood search heuristics based on tabu search and variable neighborhood search on this problem domain. Our principal finding is that a tabu search heuristic almost always provides the best quality solution for small to medium sized instances within short execution times while variable neighborhood decomposition search provides the best quality solutions for most large instances.

Progressive Tree Neighborhood applied to the Maximum Parsimony Problem

The Maximum Parsimony (MP) problem aims at reconstructing a phylogenetic tree from DNA sequences while minimizing the number of genetic transformations. To solve this NP-complete problem, heuristic methods have been developed, often based on local search. In this paper, we focus on the influence of the neighborhood relations. After analyzing the advantages and drawbacks of the well-known Nearest Neighbor Interchange (NNI), Subtree Pruning Regrafting (SPR), and Tree-Bisection-Reconnection (TBR) neighborhoods, we introduce the concept of Progressive Neighborhood (PN), which consists of constraining progressively the size of the neighborhood as the search advances. We empirically show that applied to the MP problem, this PN turns out to be more efficient and robust than the classic neighborhoods using a descent algorithm. Indeed, it allows us to find better solutions with a smaller number of iterations or trees evaluated

Local Search for the Maximum Parsimony Problem

Four local search algorithms are investigated for the phylogenetic tree reconstruction problem under the Maximum Parsimony criterion. A new subtree swapping neighborhood is introduced and studied in combination with an effective array-based tree representation. Computational results are shown on a set of randomly generated benchmark instances as well as on 8 real problems (sequences of phytopathogen γ-proteobacteria) and compared with two references from the literature