Cai Xinyu, Wang Weibin, Wang Yijiang
College of Business, Jiaxing University, Jiaxing, 314001, China.
School of Labor and Human Resources, Renmin University of China, Beijing, 100872, China.
Sci Rep. 2025 Mar 27;15(1):10538. doi: 10.1038/s41598-025-93754-3.
Enterprise Development Optimizer (EDO) is a meta-heuristic algorithm inspired by the enterprise development process with strong global search capability. However, the analysis of the EDO algorithm shows that it suffers from the defects of rapidly decreasing population diversity and weak exploitation ability when dealing with complex optimization problems, while its algorithmic structure has room for further enhancement in the optimization process. In order to solve these challenges, this paper proposes a multi-strategy enterprise development optimizer called MSEDO based on basic EDO. A leader-based covariance learning strategy is proposed, aiming to strengthen the quality of search agents and alleviate the weak population diversity of the EDO algorithm in the later search stage through the guiding role of the dominant group and the modifying role of the leader. To dynamically improve the local exploitation capability of the EDO algorithm, a fitness and distance-based leader selection strategy is proposed. In addition, the structure of EDO algorithm is reconstructed and a diversity-based population restart strategy is presented. The strategy is utilized to assist the population to jump out of the local optimum when the population is stuck in search stagnation. Ablation experiments verify the effectiveness of the strategies of the MSEDO algorithm. The performance of the MSEDO algorithm is confirmed by comparing it with five different types of basic and improved metaheuristic algorithms. The experimental results of CEC2017 and CEC2022 show that MSEDO is effective in escaping from local optimums with its favorable exploitation and exploration capabilities. The experimental results of ten engineering constrained problems show that MSEDO has the ability to competently solve real-world complex optimization problems.
企业发展优化器（EDO）是一种受企业发展过程启发的元启发式算法，具有强大的全局搜索能力。然而，对EDO算法的分析表明，在处理复杂优化问题时，它存在种群多样性迅速下降和开发能力较弱的缺陷，同时其算法结构在优化过程中还有进一步改进的空间。为了解决这些挑战，本文基于基本的EDO算法提出了一种多策略企业发展优化器，称为MSEDO。提出了一种基于领导者的协方差学习策略，旨在通过优势群体的引导作用和领导者的修正作用，提高搜索代理的质量，缓解EDO算法在后期搜索阶段种群多样性较弱的问题。为了动态提高EDO算法的局部开发能力，提出了一种基于适应度和距离的领导者选择策略。此外，对EDO算法的结构进行了重构，并提出了一种基于多样性的种群重启策略。当种群陷入搜索停滞时，该策略用于帮助种群跳出局部最优。消融实验验证了MSEDO算法各策略的有效性。通过与五种不同类型的基本和改进元启发式算法进行比较，验证了MSEDO算法的性能。CEC2017和CEC2022的实验结果表明，MSEDO算法具有良好的开发和探索能力，能够有效地逃离局部最优。十个工程约束问题的实验结果表明，MSEDO算法有能力胜任地解决实际世界中的复杂优化问题。
