The Gradient Subspace Approximation as Local Search Engine within Evolutionary Multi-objective Optimization Algorithms

In this paper, we argue that the gradient subspace approximation (GSA) is a powerful local search tool within memetic algorithms for the treatment of multi-objective optimization problems. The GSA utilizes the neighborhood information within the current population in order to compute the best approximation of the gradient at a given candidate solution. The computation of the search direction comes hence for free in terms of additional function evaluations within population based search algorithms such as evolutionary algorithms. Its benefits have recently been discussed in the context of scalar optimization. Here, we discuss and adapt the GSA for the case that multiple objectives have to be considered concurrently. We will further on hybridize line searchers that utilize GSA to obtain the search direction with two different multi-objective evolutionary algorithms. Numerical results on selected benchmark problems indicate the strength of the GSA-based local search within the evolutionary strategies.