The gradient free directed search method as local search within multi-objective evolutionary algorithms

Recently, the Directed Search Method has been proposed as a point-wise iterative search procedure that allows to steer the search, in any direction given in objective space, of a multi-objective optimization problem. While the original version requires the objectives' gradients, we consider here a possible modification that allows to realize the method without gradient information. This makes the novel algorithm in particular interesting for hybridization with set oriented search procedures, such as multi-objective evolutionary algorithms. In this paper, we propose the DDS, a gradient free Directed Search method, and make a first attempt to demonstrate its benefit, as a local search procedure within a memetic strategy, by integrating the DDS into the well-known algorithmMOEA/D. Numerical results on some benchmark models indicate the advantage of the resulting hybrid.