Multi‐Objective Goose Algorithm Based on Density Driven Radius and Diversity Perception Penalty Function for Solving Combined Economic Emission Dispatch Problem

For the Combined Economic and Emission Dispatch (CEED) problem, existing optimization methods often suffer from insufficient solution diversity, inadequate boundary coverage of Pareto‐optimal solutions, and limited adaptability of conventional penalty functions under complex constraints. So, a novel Multi‐Objective Goose Algorithm (MOGO) incorporating a density‐driven adaptive radius mechanism and a diversity‐aware penalty function was proposed. A density‐aware circular segmentation strategy and an adaptive radius adjustment mechanism are developed to improve Pareto front distribution and boundary exploration, thereby enhancing the balance between convergence and diversity. Secondly, a diversity‐aware dynamic penalty function is introduced to guide the search process toward high‐quality feasible regions while preserving population diversity under complex constraints. Then, a non‐dominated solution archive and roulette wheel‐based leader selection strategy are employed to strengthen global search performance. The effectiveness of the proposed algorithm is first validated on several standard multi‐objective benchmark functions. Experimental results demonstrate that MOGO achieves superior performance in terms of Generational Distance (GD), Inverted Generational Distance (IGD), and Hypervolume (HV), indicating excellent convergence accuracy and solution diversity. Furthermore, the proposed method is applied to three CEED systems of different scales. Comparative studies, ablation experiments, generality verification tests, and Wilcoxon rank‐sum analyses consistently confirm the effectiveness of the proposed framework.