PDGA: the Primal-Dual Genetic Algorithm

Genetic algorithms (GAs) are a class of search algorithms based on principles of natural evolution. Hence, incorporating mechanisms used in nature may improve the performance of GAs. In this paper inspired by the mechanisms of complementarity and dominance that broadly exist in nature, we present a new genetic algorithm — Primal-Dual Genetic Algorithm (PDGA). PDGA operates on a pair of chromosomes that are primal-dual to each other through the primal-dual mapping, which maps one to the other with a maximum distance away in a given distance space in genotype. The primal-dual mapping improves the exploration capacity of PDGA and thus its searching efficiency in the search space. To test the performance of PDGA, experiments were carried out to compare PDGA over traditional simple GA (SGA) and a peer GA, called Dual Genetic Algorithm (DGA), over a typical set of test problems. The experimental results demonstrate that PDGA outperforms both SGA and DGA on the test set. The results show that PDGA is a good candidate genetic algorithm.