Yurtkuran Alkın, Emel Erdal
Department of Industrial Engineering, Uludag University, Görükle Campus, 16059 Bursa, Turkey.
ScientificWorldJournal. 2014 Feb 27;2014:871242. doi: 10.1155/2014/871242. eCollection 2014.
The traveling salesman problem with time windows (TSPTW) is a variant of the traveling salesman problem in which each customer should be visited within a given time window. In this paper, we propose an electromagnetism-like algorithm (EMA) that uses a new constraint handling technique to minimize the travel cost in TSPTW problems. The EMA utilizes the attraction-repulsion mechanism between charged particles in a multidimensional space for global optimization. This paper investigates the problem-specific constraint handling capability of the EMA framework using a new variable bounding strategy, in which real-coded particle's boundary constraints associated with the corresponding time windows of customers, is introduced and combined with the penalty approach to eliminate infeasibilities regarding time window violations. The performance of the proposed algorithm and the effectiveness of the constraint handling technique have been studied extensively, comparing it to that of state-of-the-art metaheuristics using several sets of benchmark problems reported in the literature. The results of the numerical experiments show that the EMA generates feasible and near-optimal results within shorter computational times compared to the test algorithms.
带时间窗的旅行商问题（TSPTW）是旅行商问题的一个变体，其中每个客户都应在给定的时间窗内被访问。在本文中，我们提出了一种类电磁算法（EMA），该算法使用一种新的约束处理技术来最小化TSPTW问题中的旅行成本。EMA利用多维空间中带电粒子之间的吸引-排斥机制进行全局优化。本文使用一种新的变量边界策略研究了EMA框架针对特定问题的约束处理能力，其中引入了与客户相应时间窗相关的实编码粒子的边界约束，并与惩罚方法相结合，以消除违反时间窗的不可行性。通过与文献中报道的几组基准问题的现有最优元启发式算法进行比较，对所提算法的性能和约束处理技术的有效性进行了广泛研究。数值实验结果表明，与测试算法相比，EMA能在更短的计算时间内生成可行且接近最优的结果。
