98e611f87a84635cea5feda021c41527 mathematics-12-00909.pdf e3708a94c2536816b49e19259f4bca4b81358ea4 mathematics-12-00909.pdf b46a84b5f70c1082a27730a925730560c6d8b8722f59579550f96d8c4363dd31 mathematics-12-00909.pdf Title: A Forward–Backward Simheuristic for the Stochastic Capacitated Dispersion Problem Subject: In an effort to balance the distribution of services across a given territory, dispersion and diversity models typically aim to maximize the minimum distance between any pair of facilities. Specifically, in the capacitated dispersion problem (CDP), each facility has an associated capacity or level of service, and the objective is to select a set of facilities so that the minimum distance between any pair of them (dispersion) is maximized, while ensuring a user-defined level of service. This problem can be formulated as a linear integer model, where the sum of the capacities of the selected facilities must match or exceed the total demand in the network. Real-life applications often necessitate considering the levels of uncertainty affecting the capacity of the nodes. Failure to account for this uncertainty could lead to low-quality or infeasible solutions in practical scenarios. However, research addressing the stochastic version of the CDP is scarce. This paper introduces two models for the CDP with stochastic capacities, incorporating soft constraints and penalty costs for violating the total capacity constraint. The first model includes a probabilistic constraint to ensure the required level of service with a certain probability, while the second model introduces a soft constraint with penalty costs for violations. To solve both variants of the model, a forward–backward simheuristic algorithm is proposed. Our approach combines a metaheuristic algorithm with Monte Carlo simulation, enabling the efficient handling of the random behavior of node capacities and obtaining reliable solutions regardless of their probability distribution. Keywords: dispersion problem; stochastic optimization problems; metaheuristics; simulation Author: Juan F. Gomez, A. Martínez-Gavara, Javier Panadero, Angel A. Juan, and Rafael Martí Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Wed Mar 20 09:23:45 2024 CET ModDate: Wed Mar 20 09:30:03 2024 CET Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 22 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 734910 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- QFYVMW+URWPalladioL-Bold Type 1 Custom yes yes yes 10 0 JDQSCH+URWPalladioL-Roma Type 1 Custom yes yes yes 16 0 TQHCCG+URWPalladioL-Ital Type 1 Custom yes yes yes 21 0 SYFPBV+CMMI10 Type 1 Builtin yes yes yes 26 0 GIGFZE+CMR10 Type 1 Builtin yes yes yes 31 0 LMOQYR+CMSY10 Type 1 Builtin yes yes yes 36 0 DVTHKG+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 52 0 XNDIHY+PazoMath Type 1 Builtin yes yes yes 70 0 CYJUZW+CMEX10 Type 1 Builtin yes yes yes 89 0 GQKWYN+PazoMath-Italic Type 1 Builtin yes yes yes 94 0 QREYCM+SFTT1000 Type 1 Custom yes yes yes 102 0 RIEGSC+SFTT0900 Type 1 Custom yes yes yes 124 0 IUQYOR+PazoMath-BoldItalic Type 1 Builtin yes yes yes 140 0 CQMSJA+URWPalladioL-BoldItal Type 1 Custom yes yes yes 145 0 GGZKKH+CMBX10 Type 1 Builtin yes yes yes 150 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2024-12-17 02:58:00 CET RepresentationInformation: mathematics-12-00909.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2024-12-13 05:43:39 CET Size: 734910 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 455 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: section.1 Item: Title: black Literature Review Destination: section.2 Children: Item: Title: Review of the Literature on Diversity and Dispersion Problems Destination: subsection.2.1 Item: Title: Related Work on Stochastic Facility Location Problems Destination: subsection.2.2 Item: Title: Problem Description and Formulation Destination: section.3 Item: Title: black Solution Methods Destination: section.4 Children: Item: Title: Previous Constructive-Destructive Neighborhood Searches Destination: subsection.4.1 Item: Title: A Hybrid Simheuristic Algorithm Destination: subsection.4.2 Children: Item: Title: A Probabilistic Tabu Search Algorithm Destination: subsubsection.4.2.1 Item: Title: Extending the PTS to a Simheuristic Approach Destination: subsubsection.4.2.2 Item: Title: Computational Experiments Destination: section.5 Children: Item: Title: Numerical Experiments and Results for the SCDP-PC Destination: subsection.5.1 Item: Title: Numerical Experiments and Results for the SCDP-SC Destination: subsection.5.2 Item: Title: Conclusions and Future Work Destination: section.6 Item: Title: References Destination: section.7 Info: Title: A Forward Backward Simheuristic for the Stochastic Capacitated Dispersion Problem Author: Juan F. Gomez, A. Martínez-Gavara, Javier Panadero, Angel A. Juan, and Rafael Martí Subject: In an effort to balance the distribution of services across a given territory, dispersion and diversity models typically aim to maximize the minimum distance between any pair of facilities. Specifically, in the capacitated dispersion problem (CDP), each facility has an associated capacity or level of service, and the objective is to select a set of facilities so that the minimum distance between any pair of them (dispersion) is maximized, while ensuring a user-defined level of service. This problem can be formulated as a linear integer model, where the sum of the capacities of the selected facilities must match or exceed the total demand in the network. Real-life applications often necessitate considering the levels of uncertainty affecting the capacity of the nodes. Failure to account for this uncertainty could lead to low-quality or infeasible solutions in practical scenarios. However, research addressing the stochastic version of the CDP is scarce. This paper introduces two models for the CDP with stochastic capacities, incorporating soft constraints and penalty costs for violating the total capacity constraint. The first model includes a probabilistic constraint to ensure the required level of service with a certain probability, while the second model introduces a soft constraint with penalty costs for violations. To solve both variants of the model, a forward backward simheuristic algorithm is proposed. Our approach combines a metaheuristic algorithm with Monte Carlo simulation, enabling the efficient handling of the random behavior of node capacities and obtaining reliable solutions regardless of their probability distribution. 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