On the effectiveness of genetic search in combinatorial optimization
SAC '95 Proceedings of the 1995 ACM symposium on Applied computing
Genetic, Iterated and Multistart Local Search for the Maximum Clique Problem
Proceedings of the Applications of Evolutionary Computing on EvoWorkshops 2002: EvoCOP, EvoIASP, EvoSTIM/EvoPLAN
Multi-hop scatternet formation and routing for large scale Bluetooth networks
International Journal of Ad Hoc and Ubiquitous Computing
A comparison of evolutionary algorithms for finding optimal error-correcting codes
CI '07 Proceedings of the Third IASTED International Conference on Computational Intelligence
A complete resolution of the Keller maximum clique problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Abstract This paper investigates the power of genetic algorithms at solving the MAX-CLIQUE problem. We measure the performance of a standard genetic algorithm on an elementary set of problem instances consisting of embedded cliques in random graphs. We indicate the need for improvement, and introduce a new genetic algorithm, the {\em multi-phase annealed GA}, which exhibits superior performance on the same problem set. As we scale up the problem size and test on ``hard'''' benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modifications are implemented ranging from changes in input representation to systematic local search. The most recent version, called {\em union GA}, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size found. We discuss issues related to the SIMD implementation of the genetic algorithms on a Thinking Machines CM-5, which was necessitated by the intrinsically high time complexity ($O(n^3)$) of the serial algorithm for computing one iteration. Our preliminary conclusions are: (1) a genetic algorithm needs to be heavily customized to work ``well'''' for the clique problem; (2) a GA is computationally very expensive, and its use is only recommended if it is known to find larger cliques than other algorithms; (3) although our customization effort is bringing forth continued improvements, there is no clear evidence, at this time, that a GA will have better success in circumventing local minima.