  In this paper, we introduce DLS-MC, a new stochastic local search algorithm
for the maximum clique problem. DLS-MC alternates between phases of iterative
improvement, during which suitable vertices are added to the current clique,
and plateau search, during which vertices of the current clique are swapped
with vertices not contained in the current clique. The selection of vertices is
solely based on vertex penalties that are dynamically adjusted during the
search, and a perturbation mechanism is used to overcome search stagnation. The
behaviour of DLS-MC is controlled by a single parameter, penalty delay, which
controls the frequency at which vertex penalties are reduced. We show
empirically that DLS-MC achieves substantial performance improvements over
state-of-the-art algorithms for the maximum clique problem over a large range
of the commonly used DIMACS benchmark instances.
