{"title":"Neural Network Estimators for Optimal Tour Lengths of Traveling Salesperson Problem Instances with Arbitrary Node Distributions","authors":"Taha Varol, Okan Örsan Özener, Erinç Albey","doi":"10.1287/trsc.2022.0015","DOIUrl":null,"url":null,"abstract":"It is essential to solve complex routing problems to achieve operational efficiency in logistics. However, because of their complexity, these problems are often tackled sequentially using cluster-first, route-second frameworks. Unfortunately, such two-phase frameworks can suffer from suboptimality due to the initial phase. To address this issue, we propose leveraging information about the optimal tour lengths of potential clusters as a preliminary step, transforming the two-phase approach into a less myopic solution framework. We introduce quick and highly accurate Traveling Salesperson Problem (TSP) tour length estimators based on neural networks (NNs) to facilitate this. Our approach combines the power of NNs and theoretical knowledge in the routing domain, utilizing a novel feature set that includes node-level, instance-level, and solution-level features. This hybridization of data and domain knowledge allows us to achieve predictions with an average deviation of less than 0.7% from optimality. Unlike previous studies, we design and employ new instances replicating real-life logistics networks and morphologies. These instances possess characteristics that introduce significant computational costs, making them more challenging. To address these challenges, we develop a novel and efficient method for obtaining lower bounds and partial solutions to the TSP, which are subsequently utilized as solution-level predictors. Our computational study demonstrates a prediction error up to six times lower than the best machine learning (ML) methods on their training instances and up to 100 times lower prediction error on out-of-distribution test instances. Furthermore, we integrate our proposed ML models with metaheuristics to create an enumeration-like solution framework, enabling the improved solution of massive-scale routing problems. In terms of solution time and quality, our approach significantly outperforms the state-of-the-art solver, demonstrating the potential of our features, models, and the proposed method.History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods and Applications in Large-Scale Route Planning Problems.Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0015 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transportation Science","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1287/trsc.2022.0015","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
It is essential to solve complex routing problems to achieve operational efficiency in logistics. However, because of their complexity, these problems are often tackled sequentially using cluster-first, route-second frameworks. Unfortunately, such two-phase frameworks can suffer from suboptimality due to the initial phase. To address this issue, we propose leveraging information about the optimal tour lengths of potential clusters as a preliminary step, transforming the two-phase approach into a less myopic solution framework. We introduce quick and highly accurate Traveling Salesperson Problem (TSP) tour length estimators based on neural networks (NNs) to facilitate this. Our approach combines the power of NNs and theoretical knowledge in the routing domain, utilizing a novel feature set that includes node-level, instance-level, and solution-level features. This hybridization of data and domain knowledge allows us to achieve predictions with an average deviation of less than 0.7% from optimality. Unlike previous studies, we design and employ new instances replicating real-life logistics networks and morphologies. These instances possess characteristics that introduce significant computational costs, making them more challenging. To address these challenges, we develop a novel and efficient method for obtaining lower bounds and partial solutions to the TSP, which are subsequently utilized as solution-level predictors. Our computational study demonstrates a prediction error up to six times lower than the best machine learning (ML) methods on their training instances and up to 100 times lower prediction error on out-of-distribution test instances. Furthermore, we integrate our proposed ML models with metaheuristics to create an enumeration-like solution framework, enabling the improved solution of massive-scale routing problems. In terms of solution time and quality, our approach significantly outperforms the state-of-the-art solver, demonstrating the potential of our features, models, and the proposed method.History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods and Applications in Large-Scale Route Planning Problems.Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0015 .
期刊介绍:
Transportation Science, published quarterly by INFORMS, is the flagship journal of the Transportation Science and Logistics Society of INFORMS. As the foremost scientific journal in the cross-disciplinary operational research field of transportation analysis, Transportation Science publishes high-quality original contributions and surveys on phenomena associated with all modes of transportation, present and prospective, including mainly all levels of planning, design, economic, operational, and social aspects. Transportation Science focuses primarily on fundamental theories, coupled with observational and experimental studies of transportation and logistics phenomena and processes, mathematical models, advanced methodologies and novel applications in transportation and logistics systems analysis, planning and design. The journal covers a broad range of topics that include vehicular and human traffic flow theories, models and their application to traffic operations and management, strategic, tactical, and operational planning of transportation and logistics systems; performance analysis methods and system design and optimization; theories and analysis methods for network and spatial activity interaction, equilibrium and dynamics; economics of transportation system supply and evaluation; methodologies for analysis of transportation user behavior and the demand for transportation and logistics services.
Transportation Science is international in scope, with editors from nations around the globe. The editorial board reflects the diverse interdisciplinary interests of the transportation science and logistics community, with members that hold primary affiliations in engineering (civil, industrial, and aeronautical), physics, economics, applied mathematics, and business.