Problem

The field of artificial intelligence highly values real parameter single objective optimization, especially for long-term search where the difficulty exponentially increases with dimensionality. While established evolutionary algorithms like Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) perform well, ensembles such as EA4eig, which combines these methods, still frequently encounter stagnation. Improving EA4eig by simply adding more equally competitive algorithms isn't efficient due to marginal effects. There's a need for methods to specifically process particular, inferior individuals to vary population distribution and break stagnation without overhauling the main ensemble structure.

Method

The authors introduce EA4eigCS, an extension of the EA4eig ensemble, by incorporating Crisscross Search (CSO) and Sparrow Search Algorithm (SSA) as "secondary" evolutionary algorithms. These secondary algorithms are specifically designed to process "inferior" individuals rather than the best ones, which is a key methodological contribution. Crisscross Search, with its horizontal and vertical crossover operations, is applied to the worst Rc * NP individuals when the best fitness hasn't improved for Tgen generations, aiming to disrupt stagnation. Additionally, a step from Sparrow Search, which involves updating individuals based on their fitness relative to the best and worst, is applied to a portion of the Rs * NP worst individuals at the end of every generation. This targeted application ensures that population distribution is varied, helping the main constituent algorithms (CoBiDE, IDEbd, jSO, CMA-ES) to make further progress.

Results

Extensive experiments were conducted on the CEC 2021 and 2022 benchmark test suites, comparing EA4eigCS against state-of-the-art algorithms including IMODE, NL-SHADE-RSP, APGSK-IMODE, MLS-L-SHADE, EA4eig, NL-SHADE-LBC, and AMCDE. Results, evaluated using Wilcoxon rank sum and Friedman tests, consistently demonstrated the superiority of EA4eigCS over EA4eig and its competitiveness with other advanced algorithms. An ablation study further confirmed that both Crisscross Search and Sparrow Search contribute to the performance improvement, and their selective application to inferior individuals is particularly effective. While the integration of these secondary methods didn't significantly alter the overall convergence manner, it led to better final solutions.

Implications

The development of EA4eigCS highlights a valuable strategy for enhancing ensemble evolutionary algorithms: the strategic integration of secondary evolutionary algorithms to process inferior individuals. This approach effectively addresses the problem of stagnation in long-term real parameter single objective optimization by promoting population diversity and allowing the main algorithms to find better solutions. The success of EA4eigCS suggests a promising direction for future research in designing more powerful and adaptable ensembles by considering a wider range of evolutionary algorithms as specialized secondary components.