A Collaborative Auto-Diversified Optimization Scheme 

Abstract

We present a Collaborative Auto-Diversified Optimization Scheme (CADOS) for solving continuous and combinatorial optimization problems. CADOS aims to explore the synergy of various optimization algorithms and enhance their effectiveness and efficiency, particularly in higher-dimensional problems. It incorporates an enhanced version of the previously proposed approach Auto-Diversified Ameliorated MultiPopulation-based Ensemble Differential Evolution (AD-AMPEDE), Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES), and a local search (LS) algorithm. AD-AMPEDE has demonstrated good performance in solving continuous optimization problems. However, its competitiveness wanes in higher dimensions. CADOS improves AD-AMPEDE’s detection/re-diversification processes and parameters adaptation, making it effective for higher-dimensional problem classes. To explore nearby regions during stagnation, a trust-region local search is employed. For re-diversification, CADOS utilizes both CMA-ES, known for its efficiency in complex fitness landscapes, and the Auto-Enhanced Population Diversity (AEPD) technique. We tested CADOS on the COmparing Continuous Optimizers (COCO) platform and the results demonstrated excellent performance of CADOS. In addition, to show the proposed scheme’s efficacy in tackling real-world issues, we employed it to optimize the design of water distribution networks (WDS). The results we obtained underscore the remarkable competitiveness of our strategy when compared to widely recognized existing algorithms.

Keywords

• Auto-Diversified Algorithms
• Covariance Matrix Ada