Solving Large-Scale TSP Using a Fast Wedging Insertion Partitioning Approach

Abstract

A new partitioning method, called Wedging Insertion, is proposed for solving large-scale symmetric Traveling Salesman Problem (TSP). The idea of our proposed algorithm is to cut a TSP tour into four segments by nodes' coordinate (not by rectangle, such as Strip, FRP, and Karp). Each node is located in one of their segments, which excludes four particular nodes, and each segment does not twist with other segments. After the partitioning process, this algorithm utilizes traditional construction method, that is, the insertion method, for each segment to improve the quality of tour, and then connects the starting node and the ending node of each segment to obtain the complete tour. In order to test the performance of our proposed algorithm, we conduct the experiments on various TSPLIB instances. The experimental results show that our proposed algorithm in this paper is more efficient for solving large-scale TSPs. Specifically, our approach is able to obviously reduce the time complexity for running the algorithm; meanwhile, it will lose only about 10% of the algorithm's performance.

Traveling Transporter Problem: Arranging a New Circular Route in a Public Transportation System Based on Heterogeneous Non-Monotonic Urban Data

“…To solve TSP, several methods have been proposed, including exact methods [19,35], heuristic approaches [54], evolutionary algorithms [73], genetic algorithms [60], bio-inspired optimizations [26,59], and neural-network-based methods [13]. Several construction-based (including nearestneighbor [44], insertion [70], and patching [42]) and improvement-based (including r-opt [2,37,50] and simulated annealing [43]) procedures have flourished in the past decades [62]. Meanwhile, some focus on a very-large problem space by using a partial optimization metaheuristic under special intensification conditions [36,38,67].…”

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

“…In more complex cases, like [44], the method constructs a hierarchy of segmentations in order to provide a cluster leaves with small amount of graph nodes. In Reference [17], the graph nodes are separated into four disjoint groups corresponding to the different sides of a rectangle. In Reference [45], the route generated by merging the cluster level clusters is refined with a genetic algorithm heuristic.…”

“…The Fast Recursive Partitioning method [17] performs a hierarchical clustering of the nodes corresponding to points in the Euclidean space. The points are structured into a hierarchical tree, similarly to the R-tree structure.…”

Solving the Large-Scale TSP Problem in 1 h: Santa Claus Challenge 2020

“…One obvious approach to attack the issue is to divide the problem into smaller subproblems. Different space partitioning methods have been used, such as Karp, Strip, and Wedging insertion ( Valenzuela and Jones, 1995 ; Xiang et al, 2015 ). The affinity propagation clustering algorithm was used by Jiang et al (2014) for problems of size N < 3,000 and hierarchical k-means for problems of size N > 3,000.…”