On Neighborhood Tree Search

TL;DR

This paper introduces a novel neighborhood tree search method that explores multiple solution paths with backtracking and pruning, improving local search heuristics for complex optimization problems.

Contribution

It proposes a new heuristic framework for neighborhood tree exploration with backtracking and pruning, applicable across different problem domains.

Findings

The approach is highly competitive in total weighted tardiness and location routing problems.

Different strategies enable trade-offs between solution quality and computational effort.

Experimental results demonstrate the effectiveness of neighborhood tree backtracking.

Abstract

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.