An adaptive coordinate systems for constrained differential evolution

Constrained optimization problems (COPs) are essential in many real-world applications. Existing methods often rely on a fixed coordinate system to explore the solution space of COPs, limiting their adaptability to complex and varying landscapes, particularly when constraints are involved. Solving COPs using evolutionary algorithms remains challenging due to the need to balance objective optimization and constraint satisfaction. To overcome these limitations, this paper proposes an Adaptive Coordinate System for Constrained Differential Evolution (ACSCDE). ACSCDE introduces two specialized coordinate systems: one focuses on guiding the search to the objective space, while the other directs the search toward feasible solutions. These coordinate systems are built using an archive-based covariance matrix that captures the characteristics of the fitness landscape and constraints. An adaptive selection process dynamically chooses the most suitable coordinate system based on feedback from the evolutionary process. Additionally, the original coordinate system is retained to enhance population diversity, and a tailored mutation strategy is applied to each system. The proposed method was tested on benchmark suites CEC2010 and CEC2017, designed to challenge state-of-the-art algorithms. The results demonstrate that ACSCDE achieves competitive performance, outperforming advanced techniques in complex constrained optimization scenarios. These findings highlight ACSCDE as a promising approach for improving the performance of evolutionary algorithms in constrained optimization tasks.