A hybrid genetic algorithm for an NP-complete problem with an expensive evaluation function

In this paper, a non-standard hybrid genetic algorithm is presented. The approach is non-standard in that it violates some of the common attributes associated with genetic algorithms in the literature. The algorithm presented uses local maxima to locate the global maximum value, uses haploid chromosomes with dominance mating instead of crossover, generates one offspring per set of parents, has no specific mutation operator, and is designed for rapid convergence. When applied to an NP-Complete problem, the results of this hybrid algorithm are shown to be very successful in reducing the complexity of the problem

Considerations for Rapidly Converging Genetic Algorithms Designed for Application to Problems with Expensive Evaluation Functions

A genetic algorithm is a technique designed to search large problem spaces using the Darwinian concepts of evolution. Solution representations are treated as living organisms. The procedure attempts to evolve increasingly superior solutions. As in natural genetics, however, there is no guarantee that the optimum organism will be produced. One of the problems in producing optimal organisms in a genetic algorithm is the difficulty of premature convergence. Premature convergence occurs when the organisms converge in similarity to a pattern which is sub-optimal, but insufficient genetic material is present to continue the search beyond this sub-optimal level, called a local maximum. The prevention of premature convergence of the organisms is crucial to the success of most genetic algorithms. In order to prevent such convergence, numerous operators have been developed and refined. All such operators, however, rely on the property of the underlying problem that the evaluation of individuals is a computationally inexpensive process. In this paper, the design of genetic algorithms which intentionally converge rapidly is addressed. The design considerations are outlined, and the concept is applied to an NP-Complete problem, known as a Crozzle, which does not have an inexpensive evaluation function. This property would normally make the Crozzle unsuitable for processing by a genetic algorithm. It is shown that a rapidly converging genetic algorithm can successfully reduce the effective complexity of the problem