Evolutionary External Archive for Gaining-Sharing Knowledge–Based Algorithm

Real-parameter single-objective optimization has become a prominent focus within artificial intelligence in recent years. Among population-based metaheuristics, differential evolution (DE) and covariance matrix adaptation evolution strategy (CMA-ES) have consistently demonstrated strong performance. However, the difficulty of solving optimization problems increases exponentially with the dimensionality of the objective function, resulting in a corresponding rise in the number of required function evaluations. To address this challenge, a novel algorithm—the Gaining-Sharing Knowledge (GSK)–based algorithm—has emerged as a promising solution. GSK’s development trajectory currently resembles the early stages of DE. Nevertheless, further enhancements are necessary to unlock its full potential. In this paper, we propose an evolutionary external archive (EEA) for GSK and its variants, inspired by the external archive mechanism used in DE. The proposed EEA integrates individuals from both the current population and the archive into the evolutionary process. To promote diversity, we apply an evolutionary procedure based on CMA-ES within the archive and exclude individuals from the archive if identical counterparts exist in the current generation. We evaluate our approach using three benchmark test suites from the Congress on Evolutionary Computation (CEC) and real-world optimization problems from CEC 2011. Our experimental analysis compares GSK and its variants with and without the EEA. Results show that the EEA significantly improves the performance of GSK and its variants. Consequently, the GSK variant, AGSK, with the EEA is selected for further comparison against benchmark algorithms. Experimental results confirm that our proposed method is highly competitive.