Reactive search, a history-sensitive heuristic for MAX-SAT

Abstract

The Reactive Search (RS) method proposes the integration of a simple history-sensitive (machine learning) scheme into local search for the on-line determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component based on local search with temporary prohibitions (Tabu Search) is complemented with a reactive scheme that determines the appropriate value of the prohibition parameter by monitoring the Hamming distance along the search trajectory. The proposed algorithm (H-RTS) can therefore be characterized as a dynamic version of Tabu Search. In addition, the non-oblivious functions recently introduced in the framework of approximation algorithms are used to discover a better local optimum in the initial part of the search The algorithm is developed in two phases. First the bias-diversification properties of individual candidate components are analyzed by extensive empirical evaluation, then a reactive scheme is added to the winning component, based on Tabu Search. The final tests on a benchmark of random MAX-3-SAT and MAX-4-SAT problems demonstrate the superiority of H-RTS with respect to alternative heuristics.