An Enhanced Equilibrium Optimizer Based on Rural Tourism Inspiration Strategy for Global Optimization and Engineering Applications

As the complexity, scale, and nonlinearity of modern engineering optimization problems continue to increase, traditional optimization algorithms face significant challenges in achieving high solution accuracy, fast convergence, and robust performance. To address these issues, this paper proposes a Rural Tourism Migration-based Improved Equilibrium Optimizer (RTM-IEO), aiming to enhance the global search capability and adaptive balance between exploration and exploitation. Specifically, an adaptive lens imaging opposition-based learning strategy is introduced to effectively expand the search space and maintain population diversity. A dynamic elite-guided elimination mechanism is designed to strengthen exploitation capability and accelerate convergence by reconstructing inferior individuals using high-quality solutions. In addition, a multi-stage rural tourism migration strategy is developed to dynamically regulate the search behavior across different optimization phases, enabling a more flexible and efficient search process. The effectiveness of the proposed algorithm is comprehensively validated on the CEC2021 and CEC2022 benchmark suites, where RTM-IEO demonstrates superior performance in terms of convergence accuracy, convergence speed, and robustness compared with several representative state-of-the-art algorithms. The statistical superiority of the proposed method is further confirmed through Friedman mean ranking and Wilcoxon rank-sum tests. To further evaluate its practical applicability, RTM-IEO is applied to the sustainable economic dispatch problem of a microgrid integrating renewable energy sources, including wind power and photovoltaic generation, along with energy storage systems and controllable units. The optimization objective simultaneously considers economic cost minimization and sustainable operation requirements, such as improving renewable energy utilization and reducing dependence on fossil-fuel-based generation. Experimental results indicate that the proposed method achieves a significant reduction in daily operating cost (exceeding 52% compared with benchmark algorithms), while effectively promoting low-carbon energy utilization and enhancing overall system sustainability. Overall, the proposed RTM-IEO provides an efficient and reliable optimization framework for addressing complex global optimization problems, particularly in scenarios requiring a coordinated balance between economic performance and sustainable development.