ADPSO-ERLS：用于旅行商问题的混合离散粒子群优化算法与增强局部搜索
ADPSO-ERLS: A Hybrid Discrete PSO with Enhanced Local Search for the Traveling Salesman Problem
中文总结 AI 辅助
提出用于旅行商问题的ADPSO-ERLS算法，结合记忆引导变异等技术，在TSPLIB实例上表现最优，运行时间缩短约38倍，可高效解决大规模TSP问题。
中文摘要 AI 辅助
旅行商问题是研究基于种群的方法如何在探索与逐步增强的局部强化之间分配固定搜索预算的经典场景。我们提出ADPSO-ERLS，一种离散群体算法，将这种分配视为明确的可调设计变量。该算法结合了记忆引导的交换变异、异构初始化、进化过程中选择性候选限制的2-opt操作，以及仅针对当前最优解的最终优化，后者结合了候选限制、可选的完全2-opt操作与双桥扰动。该方法受粒子群优化（PSO）启发，使用个体和全局记忆，但摒弃了速度、惯性和加速度系数。所有六种算法均用Rust实现，在相同硬件上运行，且在严格记录的100000个候选解评估限制下停止，因此编程语言、硬件和评估预算在各方法间保持一致；实际运行时间单独报告，因为相同的评估次数不一定对应相同的算术工作量。在整数EUC_2D约定下的五个对称TSPLIB实例上进行50多次运行，ADPSO-ERLS在每个实例上均达到最低的最优解和平均成本，最优路径间隙为1.93%至4.17%，相对误差为3.04%至5.50%。它在Friedman检验中排名第一，所有25次多重控制的Wilcoxon比较均以大的、近乎完全的分布分离支持它。使用相同种子的配对 ablation 实验将初始化、运行中局部搜索和最终优化与质量提升相关联，而候选限制主要将运行时间缩短了约38倍。对多达16862个城市的进一步实验使最优路径间隙保持在6.7%以下，在不到11分钟内解决了最大案例。
英文摘要
The Traveling Salesman Problem is a canonical setting for studying how a population-based method should allocate a fixed search budget between exploration and progressively stronger local intensification. We propose ADPSO-ERLS, a discrete swarm algorithm that treats this allocation as an explicit, tunable design variable. It couples memory-guided swap mutation, heterogeneous initialization, selective candidate-restricted 2-opt during evolution, and an incumbent-only final refinement combining candidate-restricted and optional full 2-opt with double-bridge perturbations. The method is PSO-inspired, using personal and global memories yet dispensing with velocity, inertia, and acceleration coefficients. All six algorithms are implemented in Rust, run on identical hardware, and stopped at a strict, recorded limit of 100,000 candidate-solution assessments, so that programming language, hardware, and evaluation budget are held common across methods; wall-clock time is reported separately because equal assessment counts need not correspond to equal arithmetic work. Over 50 runs on five symmetric TSPLIB instances under the integer \texttt{EUC\_2D} convention, ADPSO-ERLS attains the lowest best and mean cost on every instance, with best-tour Gap of $1.93$--$4.17\%$ and relative error of $3.04$--$5.50\%$. It ranks first under the Friedman test, and all twenty-five multiplicity-controlled Wilcoxon comparisons favor it with large, near-complete distributional separation. A paired ablation with common seeds links initialization, in-run local search, and final refinement to quality gains, while candidate restriction chiefly cuts runtime, by up to a factor of roughly $38$. Further experiments up to $16{,}862$ cities keep best-tour Gaps below $6.7\%$, solving the largest case in under eleven minutes.
