Advancing Tabu and Restart in Local Search for Maximum Weight Cliques

TL;DR

This paper enhances local search algorithms for the Maximum Weight Clique problem by introducing novel tabu and restart strategies based on local search scenarios, leading to improved solver performance on standard benchmarks.

Contribution

It proposes new tabu and restart strategies utilizing local search scenarios, improving upon existing methods like configuration checking.

Findings

Outperforms state-of-the-art solvers on DIMACS and BHOSLIB benchmarks.

Effective in practical application benchmarks.

Reduces cycling and enhances search efficiency.

Abstract

The tabu and restart are two fundamental strategies for local search. In this paper, we improve the local search algorithms for solving the Maximum Weight Clique (MWC) problem by introducing new tabu and restart strategies. Both the tabu and restart strategies proposed are based on the notion of a local search scenario, which involves not only a candidate solution but also the tabu status and unlocking relationship. Compared to the strategy of configuration checking, our tabu mechanism discourages forming a cycle of unlocking operations. Our new restart strategy is based on the re-occurrence of a local search scenario instead of that of a candidate solution. Experimental results show that the resulting MWC solver outperforms several state-of-the-art solvers on the DIMACS, BHOSLIB, and two benchmarks from practical applications.