GRASP/Δ: An efficient algorithm for the multi-objective portfolio optimization problem

The multi-objective portfolio optimization problem with fuzzy trapezoidal parameters involves a search for a subset of projects that, within the given available resources, maximizes the benefits while reducing the uncertainty. Traditionally, evolutionary algorithms are used to solve this problem; however, they do not exploit the locality structure of a solution or compute the values of its objective functions using the full set of n decision variables. As a result, the number of evaluations that can be computed within a fixed amount of time decreases as the size of the instances increases, yielding poor performance. This work proposes a new non-evolutionary GRASP/Δ algorithm that includes a novel local search with an efficient local computation strategy. The use of local computation reduces the number of operations required to compute the values of the objective functions from O(n) to O(1). Consequently, the increment in evaluations performed in the proposed approach increases the quality of the obtained solutions, particularly as the search space grows. An experiment conducted with instances of different sizes demonstrates the overall competitiveness of GRASP/Δ compared to other state-of-the-art algorithms. Our results show, as expected, that the differences in performance become statistically more significant when dealing with instances defined by large search spaces. These results were validated using non-parametric statistical tests.