Unconstrained robust optimization using a descent-based crossover operator

Most of the practical optimization problems involve variables and parameters that are not reliable and often vary around their nominal values. If the optimization problem is solved at the nominal values without taking the uncertainty into account, it can lead to severe operational implications. In order to avoid consequences that can be detrimental for the system, one resorts to the robust optimization paradigm that attempts to optimize the “worst case” solution arising as a result of perturbations. In this paper, we propose an evolutionary algorithm for robust optimization of unconstrained problems involving uncertainty. The algorithm utilizes a novel crossover operator that identifies a cone-based descent region to produce the offspring. This leads to a large saving in function evaluations, but still guarantees convergence on difficult multimodal problems. A number of test cases are constructed to evaluate the proposed algorithm and comparisons are drawn against two benchmark cases.