Seeding the initial population of a multi-objective evolutionary algorithm using gradient-based information

In the field of single-objective optimization, hybrid variants of gradient-based methods and evolutionary algorithms have been shown to perform better than an evolutionary method by itself. This same idea has been recently used in Evolutionary Multiobjective Optimization (EMO), obtaining also very promising results. In most cases, gradient information is used along the whole process, which involves a high computational cost, mainly related to the computation of the step lengths required. In contrast, in this paper we propose the use of gradient information only at the beginning of the search process. We will show that this sort of scheme maintains results of good quality while considerably decreasing the computational cost. In our work, we adopt a steepest descent method to generate some nondominated points which are then used to seed the initial population of a multi-objective evolutionary algorithm (MOEA), which will spread them along the Pareto front. The MOEA adopted in our case is the NSGA-II, which is representative of the state-of-the-art in the area. To validate our proposal, we adopt box-constrained continuous problems (the ZDT test suite). The gradients required are approximated using quadratic regressions. Our proposed approach performs a total of 2000 objective function evaluations, which is much lower than the number of evaluations normally adopted with the ZDT test suite in the specialized literature. Our results are compared with respect to the “pure” NSGA-II (i.e., without using gradient-based information) so that the potential benefit of these initial solutions fed into the population can be properly assessed.