77427bc92cd902ed65d0675e476c3c3c mathematics-13-02488.pdf 52dfadff4bdb591b794a04a856e9dc6dc26b04ff mathematics-13-02488.pdf 9d6db2173c16c890f3144eac8ff4688e40983fa60ae3028e68717dee30453e76 mathematics-13-02488.pdf Title: A Biased–Randomized Iterated Local Search with Round-Robin for the Periodic Vehicle Routing Problem Subject: The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional features such as depot configurations, tight visitation frequency constraints, and heterogeneous fleets. In this paper, we present a two-phase biased–randomized algorithm that addresses these complexities. In the first phase, a round-robin assignment quickly generates feasible and promising solutions, ensuring each customer's frequency requirement is met across the multi-day horizon. The second phase refines these assignments via an iterative search procedure, improving route efficiency and reducing total operational costs. Extensive experimentation on standard PVRP benchmarks shows that our approach is able to generate solutions of comparable quality to established state-of-the-art algorithms in relatively low computational times and stands out in many instances, making it a practical choice for real life multi-day vehicle routing applications. Keywords: combinatorial optimization; metaheuristics; periodic vehicle routing problem; local search Author: Juan F. Gomez, Antonio R. Uguina, Javier Panadero and Angel A. Juan Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Sat Aug 2 08:17:57 2025 CEST ModDate: Sat Aug 2 08:31:27 2025 CEST Custom Metadata: yes Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 19 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 1186833 bytes Optimized: no PDF version: 1.5 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- UTXNMW+URWPalladioL-Roma Type 1 Custom yes yes yes 98 0 FDJOXP+URWPalladioL-Ital Type 1 Custom yes yes yes 99 0 MMYNHL+URWPalladioL-Bold Type 1 Custom yes yes yes 100 0 DVTHKG+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 87 0 JISHOS+CMSY10 Type 1 Builtin yes yes yes 204 0 SOSTRQ+CMR10 Type 1 Builtin yes yes yes 205 0 DXJXEP+CMEX10 Type 1 Builtin yes yes yes 206 0 ETSXFM+PazoMath-Italic Type 1 Builtin yes yes yes 207 0 HVSBKL+PazoMath Type 1 Builtin yes yes yes 208 0 GWJWRV+CMMI10 Type 1 Builtin yes yes yes 209 0 LDMJRY+URWPalladioL-BoldItal Type 1 Custom yes yes yes 328 0 PDXFNG+PazoMath-Bold Type 1 Builtin yes yes yes 376 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-09-17 03:09:14 CEST RepresentationInformation: mathematics-13-02488.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-09-16 04:12:44 CEST Size: 1186833 Format: PDF Version: 1.5 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 457 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: true CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Item: Title: Related Work Item: Title: A Mathematical Model for the Periodic Vehicle Routing Problem Item: Title: Solution Approaches for the Periodic Vehicle Routing Problem Children: Item: Title: Phase 1: Map Generation Item: Title: Phase 2: Refinement via ILS Item: Title: Numerical Experiments Children: Item: Title: Selection of Parameter Values Item: Title: Stochastic Extension of the PVRP Item: Title: Analysis of Results Item: Title: Conclusions and Future Work Item: Title: References Info: Title: A Biased–Randomized Iterated Local Search with Round-Robin for the Periodic Vehicle Routing Problem Author: Juan F. Gomez, Antonio R. Uguina, Javier Panadero and Angel A. Juan Subject: The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional features such as depot configurations, tight visitation frequency constraints, and heterogeneous fleets. In this paper, we present a two-phase biased–randomized algorithm that addresses these complexities. In the first phase, a round-robin assignment quickly generates feasible and promising solutions, ensuring each customer's frequency requirement is met across the multi-day horizon. The second phase refines these assignments via an iterative search procedure, improving route efficiency and reducing total operational costs. Extensive experimentation on standard PVRP benchmarks shows that our approach is able to generate solutions of comparable quality to established state-of-the-art algorithms in relatively low computational times and stands out in many instances, making it a practical choice for real life multi-day vehicle routing applications. 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