A novel evolutionary formulation of the maximum independent set problem

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs

Approximately Solving Maximum Clique using Neural Network and Related Heuristics

We explore neural network and related heuristic methods for the fast approximate solution of the Maximum Clique problem. One of these algorithms, Mean Field Annealing, is implemented on the Connection Machine CM-5 and a fast annealing schedule is experimentally evaluated on random graphs, as well as on several benchmark graphs. The other algorithms, which perform certain randomized local search operations, are evaluated on the same benchmark graphs, and on Sanchis graphs. One of our algorithms adjusts its internal parameters as its computation evolves. On Sanchis graphs, it finds significantly larger cliques than the other algorithms do. Another algorithm, GSD(;), works best overall, but is slower than the others. All our algorithms obtain significantly larger cliques than other simpler heuristics but run slightly slower; they obtain significantly smaller cliques on average than exact algorithms or more sophisticated heuristics but run considerably faster. All our algorithms are simple..