An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem

The Semi-Soft Clustered Vehicle Routing Problem (SemiSoftCluVRP) is a relaxed version of the Clustered Vehicle Routing Problem (CluVRP) and an enhanced variant of the Soft Clustered Vehicle Routing Problem (SoftCluVRP). In the SemiSoftCluVRP, all customers are partitioned into several clusters, and...

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Main Authors: Yihao Miao, Xiaoguang Bao
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Applied Sciences
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Online Access:https://www.mdpi.com/2076-3417/15/9/4871
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author Yihao Miao
Xiaoguang Bao
author_facet Yihao Miao
Xiaoguang Bao
author_sort Yihao Miao
collection DOAJ
description The Semi-Soft Clustered Vehicle Routing Problem (SemiSoftCluVRP) is a relaxed version of the Clustered Vehicle Routing Problem (CluVRP) and an enhanced variant of the Soft Clustered Vehicle Routing Problem (SoftCluVRP). In the SemiSoftCluVRP, all customers are partitioned into several clusters, and these clusters are further divided into two types: hard clusters and soft clusters. Within a hard cluster, customers must be served by the same vehicle without interruption, whereas within a soft cluster, customers must also be served by the same vehicle, but interruptions are permitted. To solve this problem, a mathematical model is first developed, followed by the design of a two-level genetic algorithm that integrates a variable neighborhood descent method. Computational experiments demonstrate that the proposed algorithm produces high-quality solutions and exhibits excellent performance. Compared with the results of CluVRP and SoftCluVRP, the results of SemiSoftCluVRP can reduce and increase logistics costs by up to 6.50% and 7.52%, respectively. In practical applications, by adjusting the hard and soft attributes of clusters, more flexible decision-making references can be provided for relevant decision-makers.
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spelling doaj-art-73c73116c4ef490a9d74368613691a982025-08-20T01:49:50ZengMDPI AGApplied Sciences2076-34172025-04-01159487110.3390/app15094871An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing ProblemYihao Miao0Xiaoguang Bao1College of Information Technology, Shanghai Ocean University, Shanghai 201306, ChinaCollege of Information Technology, Shanghai Ocean University, Shanghai 201306, ChinaThe Semi-Soft Clustered Vehicle Routing Problem (SemiSoftCluVRP) is a relaxed version of the Clustered Vehicle Routing Problem (CluVRP) and an enhanced variant of the Soft Clustered Vehicle Routing Problem (SoftCluVRP). In the SemiSoftCluVRP, all customers are partitioned into several clusters, and these clusters are further divided into two types: hard clusters and soft clusters. Within a hard cluster, customers must be served by the same vehicle without interruption, whereas within a soft cluster, customers must also be served by the same vehicle, but interruptions are permitted. To solve this problem, a mathematical model is first developed, followed by the design of a two-level genetic algorithm that integrates a variable neighborhood descent method. Computational experiments demonstrate that the proposed algorithm produces high-quality solutions and exhibits excellent performance. Compared with the results of CluVRP and SoftCluVRP, the results of SemiSoftCluVRP can reduce and increase logistics costs by up to 6.50% and 7.52%, respectively. In practical applications, by adjusting the hard and soft attributes of clusters, more flexible decision-making references can be provided for relevant decision-makers.https://www.mdpi.com/2076-3417/15/9/4871vehicle routing problemclustered vehicle routing problemhard clusterssoft clustersgenetic algorithmvariable neighborhood descent
spellingShingle Yihao Miao
Xiaoguang Bao
An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
Applied Sciences
vehicle routing problem
clustered vehicle routing problem
hard clusters
soft clusters
genetic algorithm
variable neighborhood descent
title An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
title_full An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
title_fullStr An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
title_full_unstemmed An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
title_short An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
title_sort improved genetic algorithm for solving the semi soft clustered vehicle routing problem
topic vehicle routing problem
clustered vehicle routing problem
hard clusters
soft clusters
genetic algorithm
variable neighborhood descent
url https://www.mdpi.com/2076-3417/15/9/4871
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AT yihaomiao improvedgeneticalgorithmforsolvingthesemisoftclusteredvehicleroutingproblem
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