一种基于混合距离建模的混合变量优化萤火虫算法
A Firefly Algorithm for Mixed-Variable Optimization Based on Hybrid Distance Modeling
AI总结：
本文提出一种混合变量优化萤火虫算法，通过改进的距离吸引机制整合连续和离散变量，有效处理异构搜索空间，实验显示其在混合变量优化中表现优异。
摘要：
几种现实世界优化问题涉及混合变量搜索空间，其中连续、有序和分类决策变量共存。然而，大多数基于种群的元启发式算法设计用于连续或离散优化问题，无法自然处理异构变量类型。本文提出了一种针对混合变量优化问题的萤火虫算法改进方法（FAmv）。该方法依赖于一种改进的距离基吸引力机制，将连续和离散成分整合到统一的公式中。这种混合距离方法使异构搜索空间的建模更加合适，同时在探索和开发之间保持平衡。所提出的方法在CEC2013混合变量基准上进行了评估，该基准包括单峰、多峰和组合函数。结果表明，FAmv在混合变量优化中表现出竞争力，往往优于现有算法。此外，工程设计问题的实验进一步突显了所提出方法的鲁棒性和实用性。这些结果表明，将适当的距离公式纳入萤火虫算法中，为解决复杂的混合变量优化问题提供了一种有效策略。
英文摘要：
Several real-world optimization problems involve mixed-variable search spaces, where continuous, ordinal, and categorical decision variables coexist. However, most population-based metaheuristic algorithms are designed for either continuous or discrete optimization problems and do not naturally handle heterogeneous variable types. In this paper, we propose an adaptation of the Firefly Algorithm for mixed-variable optimization problems (FAmv). The proposed method relies on a modified distance-based attractiveness mechanism that integrates continuous and discrete components within a unified formulation. This mixed-distance approach enables a more appropriate modeling of heterogeneous search spaces while maintaining a balance between exploration and exploitation. The proposed method is evaluated on the CEC2013 mixed-variable benchmark, which includes unimodal, multimodal, and composition functions. The results show that FAmv achieves competitive, and often superior, performance compared with state-of-the-art mixed-variable optimization algorithms. In addition, experiments on engineering design problems further highlight the robustness and practical applicability of the proposed approach. These results indicate that incorporating appropriate distance formulations into the Firefly Algorithm provides an effective strategy for solving complex mixed-variable optimization problems.
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