A Chunking Based Selection Strategy for Integrating Meta-Heuristics with Branch and Bound

Abstract

Mathematical programming problems with some or all variables constrained to take on integer values are important in a large number of applications and are receiving a great deal of research attention. Meta-heuristics such as tabu search have been proposed for such problems and have been very successful in some settings but they suffer from the disadvantage that they cannot typically, by themselves, produce provably optimal solutions. Exact methods of solving these problems often include ‘quick’ heuristics to help solve sub-problems and/or improve bounds but incorporation of meta-heuristics has not received very much attention.

In this paper we examine an architecture for incorporating meta-heuristics in branch and bound algorithms. Since the meta-heuristics consume non-trivial computational resources, a major issue is deciding whether to launch a search from a node in the branch and bound tree. We propose methods for making this decision that make use of simple priorities, sampling and chunking to facilitate tests for novelty. Computational results are reported for 0–1 problems using XPRESS-MP for the branch and bound processing and a version of Reactive Tabu Search modified to support a novel two-level intensification/diversification strategy for those nodes selected as a starting point for heuristic search.