多目标野马算法求解开放同时送取货选址路径问题

Multi-Objective Wild Horse Algorithm for Solving the Open Simultaneous Pickup and Delivery Location-Routing Problem

摘要: 针对原始野马算法WHO在解决优化问题中存在的早熟收敛、易陷入局部最优等问题，提出改进多目标野马算法MOIWHO。通过引入模拟二进制交叉算子与正态分布交叉算子以及自适应混沌变异机制，提高算法跳出局部最优的能力。根据帕累托前沿评价解的质量，引入均衡接近度确定最优解。进一步结合以最大满意度和最小成本为目标的模糊时间窗开放同时送取货选址路径问题，提出了一种全新的融合编码解码方式，通过6组算例证明了算法的有效性，并通过13个标准算例与4种算法对比，分析了算法性能。研究结果证明了所提出的多目标改进野马算法在各种规模问题上的有效性与实用价值。

Abstract: To tackle the issues of premature convergence and local optimum entrapment in the original Wild Horse Optimizer (WHO) for optimization problems, this paper proposes a Multi-objective Improved Wild Horse Optimizer (MOIWHO). By integrating simulated binary crossover (SBX), normal distribution crossover (NDCO) operators, and an adaptive chaos mutation mechanism, the algorithm’s ability to escape local optima is enhanced. Solution quality is evaluated using the Pareto front, with a balanced closeness metric identifying optimal solutions. A novel integrated encoding-decoding scheme is developed for the open simultaneous pickup and delivery location-routing problem with fuzzy time windows, targeting maximum customer satisfaction and minimum operational cost. Effectiveness is validated via 6 test instances, and performance is analyzed by comparing with 4 algorithms on 13 standard benchmarks. Results demonstrate MOIWHO’s effectiveness and practical value across problem scales.