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This study proposes a regression-based framework that predicts the objective values of vehicle routing problems solved by a genetic algorithm, using input-output data generated from the genetic algorithm rather than optimizing the problem with operations research solvers. Experiments evaluate candidate regression models and identify random forest regression, a generalized linear model with a Poisson distribution, and ridge regression with cross-validation as best performers.","Article  \nRegression Machine Learning Models for the Short-Time Prediction of Genetic Algorithm Results in a Vehicle Routing Problem  \nIvan Kristianto Singgih 1,2,3 and Moses Laksono Singgih 4, *  \nCitation: Singgih, I.K.; Singgih, M.L. Regression Machine Learning Models for the Short-Time Prediction of Genetic Algorithm Results in a Vehicle Routing Problem. World Electr. Veh. J. 2024, 15, 308. [https://doi.org/](https://doi.org/)[ ](https://doi.org/)[10.3390/wevj15070308](10.3390/wevj15070308)  \nAcademic Editor: Grzegorz Sierpi ´nski  \nReceived: 29 June 2024  \nRevised: 4 July 2024  \nAccepted: 8 July 2024  \nPublished: 14 July 2024  \nCopyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Department of Industrial Engineering, University of Surabaya, Surabaya 60293, Indonesia; [ivanksinggih@staff.ubaya.ac.id](ivanksinggih@staff.ubaya.ac.id)  \n2 The Indonesian Researcher Association in South Korea (APIK), Seoul 07342, Republic of Korea  \n3 Kolaborasi Riset dan Inovasi Industri Kecerdasan Artifisial (KORIKA), Jakarta 10340, Indonesia  \n4 Department of Industrial and Systems Engineering, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia  \n* [Correspondence: moseslsinggih@its.ac.id](Correspondence: moseslsinggih@its.ac.id)  \nAbstract: Machine learning techniques have advanced rapidly, leading to better prediction accuracy within a short computational time. Such advancement encourages various novel applications, including in the field of operations research. This study introduces a novel way to utilize regression machine learning models to predict the objectives of vehicle routing problems that are solved using a genetic algorithm. Previous studies have generally discussed how (1) operations research methods are used independently to generate optimized solutions and (2) machine learning techniques are used independently to predict values from a given dataset. Some studies have discussed the collaborations between operations research and machine learning fields as follows: (1) using machine learning techniques to generate input data for operations research problems,(2) using operations research techniques to optimize the hyper-parameters of machine learning models, and (3) using machine learning to improve the quality of operations research algorithms. This study differs from the types of collaborative studies listed above. This study focuses on the prediction of the objective of the vehicle routing problem directly given the input and output data, without optimizing the problem using operations research algorithms. This study introduces a straightforward framework that captures the input data characteristics for the vehicle routing problem. The proposed framework is applied by generating the input and output data using the genetic algorithm and then using regression machine learning models to predict the obtained objective values. The numerical experiments show that the best models are random forest regression, a generalized linear model with a Poisson distribution, and ridge regression with cross-validation.  \nKeywords: vehicle routing problem; genetic algorithm; prediction; regression machine learning; smart logistics  \n1. Introduction  \nIn recent years, machine learning studies have advanced rapidly and encouraged collaboration with various research fields, including the operations research field. There are several main frameworks used when conducting research in both areas simultaneously. The first framework applies machine learning techniques to predict input data for operations research problems. One application is estimating the energy consumption of electric vehicles on different paths and routes before solving t","cbCaidj2HAriEp6f","https://ap.wps.com/l/cbCaidj2HAriEp6f","pdf",1462257,1,15,"English","en",105,"# Introduction\n## Motivation and collaboration frameworks\n## Problem formulation and proposed approach","[{\"question\":\"What is the main goal of the proposed study?\",\"answer\":\"To predict the objective values of vehicle routing problems solved by a genetic algorithm using regression machine learning models, without applying operations research optimization to tune solutions.\"},{\"question\":\"How are the training data for the regression models generated?\",\"answer\":\"The study generates input and output data using the genetic algorithm, then trains regression models to predict the obtained objective values from those inputs.\"},{\"question\":\"Which regression models show the best numerical performance?\",\"answer\":\"Random forest regression, a generalized linear model with a Poisson distribution, and ridge regression with cross-validation are reported as the best models.\"}]","Regression Machine Learning Models for the Short-Time Prediction of Genetic Algorithm Results in a Vehicle Routing Problem | 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is the main goal of the proposed study?","Question",{"text":75,"@type":76},"To predict the objective values of vehicle routing problems solved by a genetic algorithm using regression machine learning models, without applying operations research optimization to tune solutions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are the training data for the regression models generated?",{"text":80,"@type":76},"The study generates input and output data using the genetic algorithm, then trains regression models to predict the obtained objective values from those inputs.",{"name":82,"@type":73,"acceptedAnswer":83},"Which regression models show the best numerical performance?",{"text":84,"@type":76},"Random forest regression, a generalized linear model with a Poisson distribution, and ridge regression with cross-validation are reported as the best 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