A Competitive - Cooperative Approach to ComplexCombinatorial

Combinatorial optimization problems confront us with the problem of searching in a huge connguration space. Associated with each of these conngura-tions is the value of a utility function and the optimization task generally consists of nding the connguration which has either the lowest or the highest cost of all. Among the most diicult of these problems are those which belong to the NP-complete class for which, it is conjectured, there does not exist a polynomial-time algorithm that can give optimal solutions. We have designed a Competitive-Cooperative Search to deal with these problems. A number of distinguishable individuals, arranged in a certain topology, compete and cooperate with the other individuals during the search. The method uses techniques from Simulated Annealing and Genetic Algorithms and is inspired by analogies with evolving systems, both social and biological. Its performance is being tested on large Traveling Salesman Problem instances, like the Lin-Kernighan 318-cities, for which the optimal tour is known, among the 10 655 tours that compose the connguration space. The approach shows natural parallelism in which competition and cooperation between individuals enhances its performance. It is therefore an excellent method for implementation on parallel computers. Owing to the surprisingly good results obtained during the testing, and the generality of the approach, it promises excellent results in other scientiic and technological optimization problems.