Outperforming the Best with Minimal Effort: Algorithm Selection for Constrained Multi-objective Optimization

The present study performs algorithm selection on a suite of optimization algorithms targeting the constrained multi-objective optimization problems. The idea is to utilize the existing, relevant algorithmic experience in the literature to deliver an improved solver with limited effort. The reason being that algorithm development, in general, is a challenging and time-consuming process, especially with the goal of outperforming the existing methods from varying perspectives such as performance, speed, and robustness. Concerning the multi-objective optimization problems, the required development efforts happen to be even harder than addressing the single-objective ones. Furthermore, referring to the fact that the number of candidate algorithms has been consistently increasing, it is likely to see that a recently introduced algorithm is being surpassed by another one after a short period of time following its introduction. Additionally, it should be noted that those incoming algorithms tend to be the modified variants of the existing ones. This aspect suggests that developing a new state-of-the-art algorithm on multi-objective optimization requires extensive literature knowledge besides a certain level of expertise in both the problem domains and the algorithm design. Unlike those traditional studies offering a new algorithm, this work accommodates the present algorithms under an algorithm recommendation system. To be specific, algorithm selection is incorporated to automatically determine the algorithm to be applied for a particular, given problem instance. An empirical evaluation is carried out on 51 constrained multi-objective optimization problem instances, with 6 candidate algorithms. An existing algorithm selection system, ALORS, showed that it is possible to outperform the best standalone algorithm with limited efforts, meaning that a modest amount of relevant knowledge and expertise. The follow-up analysis, both on the candidate algorithm space and the problem instances, reveals practical insights that can support the new algorithm development and performance evaluation efforts.