Diversity Improvement by Non-Geometric Binary Crossover in Evolutionary Multiobjective Optimization

In the design of evolutionary multiobjective optimization (EMO) algorithms, it is important to strike a balance between diversity and convergence. Traditional mask-based crossover operators for binary strings (e.g., one-point, two-point, and uniform) tend to decrease the spread of solutions along the Pareto front in EMO algorithms while they improve the convergence to part of the Pareto front. This is because such a crossover operator, which is called geometric crossover, always generates an offspring in the segment between its two parents under the Hamming distance in the genotype space. That is, the sum of the distances from the generated offspring to its two parents is always equal to the distance between the two parents. In this paper, we first propose a non-geometric binary crossover operator to generate an offspring outside the segment between its two parents. Next, we show some properties of our crossover operator. Then we examine its effects on the behavior of EMO algorithms through computational experiments on knapsack problems with two, four, and six objectives. Experimental results show that our crossover operator can increase the spread of solutions along the Pareto front in EMO algorithms without severely degrading their convergence property. As a result, our crossover operator improves some overall performance measures such as the hypervolume.