A Scalability Study of Many-Objective Optimization Algorithms

Over the past few decades, a plethora of computational intelligence algorithms designed to solve multiobjective problems have been proposed in the literature. Unfortunately, it has been shown that a large majority of these optimizers experience performance degradation when tasked with solving problems possessing more than three objectives, referred to as many-objective problems (MaOPs). The downfall of these optimizers is that simultaneously maintaining a uniformly-spread set of solutions along with appropriate selection pressure to converge toward the Pareto-optimal front becomes significantly difficult as the number of objectives increases. This difficulty is further compounded for large-scale MaOPs, i.e., MaOPs with a large number of decision variables. In this paper, insight is given into the current state of many-objective research by investigating scalability of state-of-the-art algorithms using 3-15 objectives and 30-1000 decision variables. Results indicate that evolutionary optimizers are generally the best performers when the number of decision variables is low, but are outperformed by the swarm intelligence optimizers in several large-scale MaOP instances. However, a recently proposed evolutionary algorithm which combines dominance and subregion-based decomposition is shown to be promising for handling the immense search spaces encountered in large-scale MaOPs.