Use of non-geometric binary crossover as mutation

Standard binary crossover operators such as uniform and one-point crossover are referred to as being “geometric” since they always generate an offspring between its two parents under the Hamming distance. That is, the sum of the Hamming distances from the offspring to its two parents is the same as the Hamming distance between the two parents. In our former studies, we proposed the probabilistic use of a non-geometric binary crossover operator in evolutionary multiobjective optimization (EMO) algorithms to increase the spread of solutions along the Pareto front in the objective space. Our crossover operator generates an offspring outside its two parents with respect to the Hamming distance. That is, the distance from the offspring to one parent is larger than the distance between the two parents. In this paper, we use our crossover operator as mutation to further examine its effects on the behavior of EMO algorithms. Experimental results show that the use of our crossover operator as mutation improves the performance of NSGA-II on a two-objective knapsack problems by increasing the spread of solutions along the Pareto front. Good results, however, are not obtained when only our crossover operator is used in NSGA-II. The best results are obtained when both our non-geometric crossover and the standard uniform crossover are used.