Cooperating local search for the maximum clique problem

Abstract

The advent of desktop multi-core computers has dramatically improved the usability of parallel algorithms which, in the past, have required specialised hardware. This paper introduces cooperating local search (CLS), a parallelised hyper-heuristic for the maximum clique problem. CLS utilises cooperating low level heuristics which alternate between sequences of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, where vertices of the current clique are swapped with vertices not in the current clique. These low level heuristics differ primarily in their vertex selection techniques and their approach to dealing with plateaus. To improve the performance of CLS, guidance information is passed between low level heuristics directing them to particular areas of the search domain. In addition, CLS dynamically reconfigures the allocation of low level heuristics to cores, based on information obtained during a trial, to ensure that the mix of low level heuristics is appropriate for the instance being optimised. CLS has no problem instance dependent parameters, improves the state-of-the-art performance for the maximum clique problem over all the BHOSLIB benchmark instances and attains unprecedented consistency over the state-of-the-art on the DIMACS benchmark instances.

Reactive and dynamic local search for max-clique: Engineering effective building blocks

“…Our results confirm that the penalty heuristic tends to be less robust than the prohibition-based heuristic. A significant dependency between DLS-MC performance and the choice of the penalty delay parameter is also discussed in [14]. Further investigations, summarized in Fig.…”

“…The plateau phase does not increment the size of the current clique and it terminates as soon as there is at least an element in the PossibleAdd set, or if no candidates are available in OneMissing. As it is done in [14], nodes cannot be selected twice in the same plateau phase. In order to avoid infinite loops, the number of plateau searches is limited to maxPlateauSteps.…”

“…Recently, a stochastic local search algorithm (DLS-MC) is developed in [14]. It is based on a clique expansion phase followed by a plateau search after a maximal clique is encountered.…”

“…To achieve diversification during the search, penalties are assigned to vertices of the graph [14]. The algorithm alternates between expansion and plateau phases.…”

“…All penalties are decremented by one after pd (penalty delay) restarts, see [14] for additional details and results.…”