Analysis of reactive search optimisation techniques for the maximum clique problem and applications

Abstract

This thesis introduces analysis tools for improving the current state of the art of heuristics for the Maximum Clique (MC) problem. The analysis focusses on algorithmic building blocks, on their contribution in solving hard instances of the MC problem, and on the development of new tools for the visualisation of search landscapes. As a result of the analysis on the algorithmic building blocks, we re-engineer an existing Reactive Local Search heuristic for the Maximum Clique (RLS-MC). We propose implementation and algorithmic improvements over the original RLS-MC aimed at faster restarts and greater diversification. The newly designed algorithm (RLS-LTM) is one order of magnitude faster than the original RLS-MC on some benchmark instances; but the proposed algorithmic changes impact also on the dynamically adjusted tabu tenure, which grows wildly on some hard instances. A more in depth analysis of the search dynamics of RLS-MC and RLS-LTM reveals the reasons behind the tabu tenure explosion and sheds some new light on the reactive mechanism. We design and implement RLS-fast which cures the issues with the tabu tenure explosion in RLS-LTM while retaining the performance improvement over RLS-MC.Moreover, building on the knowledge gained from the analysis, we propose a new hyper-heuristic which defines the new state of the art, and a novel supervised clustering technique based on a clique-finding component. Special thanks go to Thomas Stützle, Holger H. Hoos, Andrea Passerini and Wayne Pullan for giving me the opportunity to appreciate them both as teachers and collaborators.