A genetic algorithm for combinational optimization problems with uncertainties

This paper describes a genetic algorithm (GA) applied to combinational optimization problems in which the objective functions include uncertain constant parameters. In the present method, noises whose probabilistic distribution is assumed based on the problem environments are added to the parameters during the evaluations process. It is assumed that this allows us to make approximate evaluation of the expected values of the objective function under uncertainties. It is shown that the present method results in the robust solutions, which have higher expectation values than the ones obtained by the conventional GA, to the traveling salesman and knapsack problems with uncertainties.