Chasing the Pareto Frontier: Adaptive Economic–Environmental Microgrid Dispatch via a Lévy–Triangular Walk Dung Beetle Optimizer

With the rapid penetration of renewable energy, grid-connected microgrids have become a cornerstone of low-carbon power systems, while also posing major challenges for coordinated scheduling under coupled economic and environmental goals. The resulting dispatch problem is highly nonlinear and high-dimensional, featuring tight operational constraints and conflicting cost–emission trade-offs that often undermine the efficiency and reliability of conventional optimization methods, thereby limiting overall economic productivity. This paper presents an adaptive economic–environmental dispatch framework for grid-connected microgrids formulated as a multi-objective optimization problem that simultaneously minimizes operating cost and environmental protection cost. To navigate the rugged and constrained search landscape, we develop an enhanced metaheuristic termed the Lévy–Triangular Walk Dung Beetle Optimizer (LTWDBO). The LTWDBO integrates (i) chaotic population initialization to improve diversity and feasibility coverage, (ii) a geometry-inspired triangular walk operator to strengthen local exploitation, and (iii) an adaptive Lévy-flight strategy to boost global exploration, achieving a robust exploration–exploitation balance over the entire optimization process, representing a process innovation in metaheuristic-driven dispatch optimization. The proposed method is validated on a representative grid-connected microgrid comprising photovoltaic generation, wind turbines, micro gas turbines, and battery energy storage. Comparative experiments against representative baselines (DBO, WOA, TDBO, and NSGA-II) demonstrate that the LTWDBO achieves consistently better solution quality. Our LTWDBO attains the lowest optimal objective value of 255,718.34 Yuan, compared with 357,702.68 Yuan (DBO), 347,369.28 Yuan (TDBO), and 3,854,359.36 Yuan (WOA). The LTWDBO also yields the best average objective value of 673,842.24 Yuan, an improvement of over 1,001,813.10 Yuan (DBO).