Migration and Population Dynamics in Distributed Coevolutionary Algorithm

Abstract

An optimization in both stable as well as in a changing environment is studied by a modification of a genetic algorithm, where two kinds of chromosomes are optimized — candidate solutions to a given problem and test cases. Similar problems without time-dependent function optimization were already well studied as the host-parasite coevolutionary genetic algorithms. Solutions are tested by test cases, either randomly selected, or from the vicinity of solutions in case of a space distribution. During this process solutions gather fitness according to their ability to pass correctly the test cases and test cases gather fitness, when a solution fails them. Three modifications of such an algorithm are compared. The first one is most closely related to a genetic algorithm, with fixed sizes of both solution and test cases populations, and no space distribution of chromosomes. The second algorithm tries to modify the size of solution-population and number of used test cases in the inverse proportion to the success of the other species. It means, that when the solutions fail test cases, there is no need to increase the number of test cases, but the number of newly generated solutions should increase. When solutions are good, the opposite strategy is applied. The third algorithm uses spatial distribution of chromosomes, but instead of a standardly used two-dimensional grid, algorithm uses populations situated on two circles, which rotate in opposite directions. The investigated problem uses sorting networks as candidate solutions and permutations as test cases. The changing environment is simulated by disabling some of possibilities for an exchange of couples of entries, changing thus the fitness function of sorting networks.