A replicator equations-based evolutionary algorithm for the maximum clique problem

2002 ◽  
Author(s):  
C. Rossi
Keyword(s):  
Evolutionary Algorithm ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Replicator Equations ◽  
Clique Problem

scholarly journals MEAMCP: A Membrane Evolutionary Algorithm for Solving Maximum Clique Problem

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 108360-108370 ◽  
Author(s):  
Ping Guo ◽  
Xuekun Wang ◽  
Yi Zeng ◽  
Haizhu Chen
Keyword(s):  
Evolutionary Algorithm ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Clique Problem

scholarly journals Payoff-Monotonic Game Dynamics and the Maximum Clique Problem

2006 ◽  
Vol 18 (5) ◽  
pp. 1215-1258 ◽  
Author(s):  
Marcello Pelillo ◽  
Andrea Torsello
Keyword(s):  
Regularization Parameter ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Quadratic Program ◽  
Local Optima ◽  
Replicator Equations ◽  
Dynamical Properties ◽  
Clique Problem

Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties of these models, which, under a certain symmetry assumption, possess a Lyapunov function. In this letter, we generalize previous work along these lines in several respects. We introduce a wide family of game-dynamic equations known as payoff-monotonic dynamics, of which replicator dynamics are a special instance, and show that they enjoy precisely the same dynamical properties as standard replicator equations. These properties make any member of this family a potential heuristic for solving standard quadratic programs and, in particular, the maximum clique problem. Extensive simulations, performed on random as well as DIMACS benchmark graphs, show that this class contains dynamics that are considerably faster than and at least as accurate as replicator equations. One problem associated with these models, however, relates to their inability to escape from poor local solutions. To overcome this drawback, we focus on a particular subclass of payoff-monotonic dynamics used to model the evolution of behavior via imitation processes and study the stability of their equilibria when a regularization parameter is allowed to take on negative values. A detailed analysis of these properties suggests a whole class of annealed imitation heuristics for the maximum clique problem, which are based on the idea of varying the parameter during the imitation optimization process in a principled way, so as to avoid unwanted inefficient solutions. Experiments show that the proposed annealing procedure does help to avoid poor local optima by initially driving the dynamics toward promising regions in state space. Furthermore, the models outperform state-of-the-art neural network algorithms for maximum clique, such as mean field annealing, and compare well with powerful continuous-based heuristics.

An effective local search for the maximum clique problem

2005 ◽  
Vol 95 (5) ◽  
pp. 503-511 ◽  
Author(s):  
Kengo Katayama ◽  
Akihiro Hamamoto ◽  
Hiroyuki Narihisa
Keyword(s):  
Local Search ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Clique Problem
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