App. Res. of Comp. Accepted Paper
Vol. 43, 2026 No. 12

Geometry-aware MILP initialization for min-max multi-depot multiple traveling salesman problem

Xu Ruoyia
Du Haob
Sun Jingluc
a. School of Information and Network Security, b. Institute of Big Data and Network Security, c. Laboratory of Public Safety Risk Governance, Zhejiang Police College, Hangzhou Zhejiang 310053, China
DOI: 10.19734/j.issn.1001-3695.2026.04.0107

Abstract

The min-max multi-depot multiple traveling salesman problem requires multiple salesmen departing from their respective depots to visit all cities while minimizing the longest route. Under limited time budgets, existing solvers face a common dilemma: greedy construction produces imbalanced solutions that burden subsequent search. To address this problem, this paper proposed the Geometry-Aware MILP Initialization (GAMI) algorithm, whose core idea is to combine geometry-aware spatial clustering with mixed-integer linear programming. The algorithm constructed a spatial adjacency graph based on Delaunay triangulation and partitioned spatially coherent subregions, established a mixed-integer linear programming model to solve the min-max load-balanced assignment, generated high-quality initial solutions within seconds, and injected them in a plug-and-play manner into an existing memetic search framework for subsequent optimization. Experiments on 58 benchmark instances across two benchmark sets demonstrate that GAMI achieved an average improvement of 11.62% and 12.94% over greedy construction, significantly outperformed the state-of-the-art under both 15-second and 30-second budgets, and was on par with the baseline at 60 seconds. Ablation studies reveal the synergistic contributions of the geometry-aware clustering and MILP assignment components to overall performance, validating the effectiveness of the proposed design strategy.

Foundation Support

浙江省科技计划项目"尖兵领雁+X"科技计划(2025C01030)

Publish Information

DOI: 10.19734/j.issn.1001-3695.2026.04.0107
Publish at: Application Research of Computers Accepted Paper, Vol. 43, 2026 No. 12

Publish History

[2026-08-04] Accepted Paper

Cite This Article

徐若易, 杜镐, 孙靖璐. 面向最小最大多仓库多旅行商问题的几何感知MILP初始化算法 [J]. 计算机应用研究, 2026, 43 (12). (2026-08-25). https://doi.org/10.19734/j.issn.1001-3695.2026.04.0107. (Xu Ruoyi, Du Hao, Sun Jinglu. Geometry-aware MILP initialization for min-max multi-depot multiple traveling salesman problem [J]. Application Research of Computers, 2026, 43 (12). (2026-08-25). https://doi.org/10.19734/j.issn.1001-3695.2026.04.0107. )

About the Journal

  • Application Research of Computers Monthly Journal
  • Journal ID ISSN 1001-3695
    CN  51-1196/TP

Application Research of Computers, founded in 1984, is an academic journal of computing technology sponsored by Sichuan Institute of Computer Sciences under the Science and Technology Department of Sichuan Province.

Aiming at the urgently needed cutting-edge technology in this discipline, Application Research of Computers reflects the mainstream technology, hot technology and the latest development trend of computer application research at home and abroad in a timely manner. The main contents of the journal include high-level academic papers in this discipline, the latest scientific research results and major application results. The contents of the columns involve new theories of computer discipline, basic computer theory, algorithm theory research, algorithm design and analysis, blockchain technology, system software and software engineering technology, pattern recognition and artificial intelligence, architecture, advanced computing, parallel processing, database technology, computer network and communication technology, information security technology, computer image graphics and its latest hot application technology.

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