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Mathematics
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Combinatorial Optimization and Applications
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Combinatorial Optimization and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 4453

Special Issue Editor

Prof. Dr. Anna Sciomachen

E-Mail Website
Guest Editor
Department of Economics and Business Studies, University of Genoa, 16126 Genoa, Italy
Interests: heuristic methods to solve combinatorial optimization problems; optimization models and methods in distributive logistics

Special Issue Information

Dear Colleagues,

This Special Issue of Mathematics is devoted to the new challenges that real combinatorial optimization problems impose on us today in a wide variety of fields of application. Indeed, from logistics to healthcare, and from services to manufacturing, today's decision-making problems require us to consider large models of these NP-hard problems, both in terms of the number of variables and constraints. For this reason, increasingly efficient models and heuristic methods capable of obtaining good solutions in increasingly shorter calculation times are required, in addition to the need to minimize calculation times in order to reduce energy consumption.

Therefore, we welcome articles on new models, heuristic algorithms and successful case studies that can contribute to the development and application of these new proposals in the real world.

Prof. Dr. Anna Sciomachen
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • optimization
  • mixed-integer linear programming
  • large-size models
  • Boolean problems
  • heuristics

Published Papers (5 papers)

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Research

14 pages, 1542 KiB  
Article
Unregulated Cap-and-Trade Model for Sustainable Supply Chain Management
by Massimiliano Caramia and Giuseppe Stecca
Mathematics 2024, 12(3), 477; https://doi.org/10.3390/math12030477 - 02 Feb 2024
Viewed by 623
Abstract
Cap-and-trade models have been largely studied in the literature when it comes to reducing emissions in a supply chain. In this paper, further pursuing the goal of analyzing the effectiveness of cap-and-trade strategies in reducing emissions in supply chains, we propose a mathematical [...] Read more.
Cap-and-trade models have been largely studied in the literature when it comes to reducing emissions in a supply chain. In this paper, further pursuing the goal of analyzing the effectiveness of cap-and-trade strategies in reducing emissions in supply chains, we propose a mathematical model for sustainable supply chain management. This optimization program aims at reducing emissions and supply chain costs in an unregulated scenario w.r.t. the cap definition, i.e., trading CO2 is allowed but no formal limit on the CO2 emissions is imposed. Also, we considered an initial budget for technological investments by the facilities in the considered supply chain, allowing plants to reduce their unit production emissions at a different unit production cost. For this model, differently from what exists in the literature, we derive some theoretical conditions guaranteeing that, if obeyed, the emissions over time have a non-increasing trend meaning that decreasing caps over time can be attained with a self-regulated scenario. Computational results show the effectiveness of our approach. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
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19 pages, 378 KiB  
Article
A Matheuristic Approach for the Multi-Depot Periodic Petrol Station Replenishment Problem
by Pasquale Carotenuto, Stefano Giordani and Alessio Salvatore
Mathematics 2024, 12(3), 416; https://doi.org/10.3390/math12030416 - 27 Jan 2024
Viewed by 490
Abstract
Planning petrol station replenishment is an important logistics activity for all the major oil companies. The studied Multi-Depot Periodic Petrol Station Replenishment problem derives from a real case in which the company must replenish a set of petrol stations from a set of [...] Read more.
Planning petrol station replenishment is an important logistics activity for all the major oil companies. The studied Multi-Depot Periodic Petrol Station Replenishment problem derives from a real case in which the company must replenish a set of petrol stations from a set of depots, during a weekly planning horizon. The company must ensure refuelling according to available visiting patterns, which can be different from customer to customer. A visiting pattern predefines how many times (days) the replenishment occurs during a week and in which visiting days a certain amount of fuel must be delivered. To fulfill the weekly demand of each petrol station, one of the available replenishment plans must be selected among a given set of visiting patterns. The aim is to minimize the total distance travelled by the fleet of tank trucks during the entire planning horizon. A matheuristic approach is proposed, based on the cluster-first route-second paradigm, to solve it. The proposed approach is thoroughly tested on a set of realistic random instances. Finally, a weekly large real instance is considered with 194 petrol stations and two depots. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
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22 pages, 905 KiB  
Article
The Budgeted Labeled Minimum Spanning Tree Problem
by Raffaele Cerulli, Ciriaco D'Ambrosio, Domenico Serra and Carmine Sorgente
Mathematics 2024, 12(2), 230; https://doi.org/10.3390/math12020230 - 10 Jan 2024
Viewed by 602
Abstract
In order to reduce complexity when designing multi-media communication networks, researchers often consider spanning tree problems defined on edge-labeled graphs. The earliest setting addressed in the literature aims to minimize the number of different media types, i.e., distinct labels, used in the network. [...] Read more.
In order to reduce complexity when designing multi-media communication networks, researchers often consider spanning tree problems defined on edge-labeled graphs. The earliest setting addressed in the literature aims to minimize the number of different media types, i.e., distinct labels, used in the network. Despite being extensively addressed, such a setting completely ignores edge costs. This led to the definition of more realistic versions, where budgets for the total cost, or the number of distinct labels allowed, were introduced. In this paper, we introduce and prove the NP-hardness of the Budgeted Labeled Minimum Spanning Tree problem, consisting in minimizing the cost of a spanning tree while satisfying specified budget constraints for each label type. This problem combines the challenges of cost efficiency and label diversity within a fixed budgetary framework, providing a more realistic and practical approach to network design. We provide three distinct mathematical programming formulations of the problem and design a Lagrangian approach to derive tighter lower bounds for the optimal solution of the problem. The performances of the proposed methods are assessed by conducting a series of computational experiments on a variety of randomly generated instances, which showed how the complexity of the problem increases as the size of the network, as well as the number of labels, increase and the budget restrictions are tightened. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
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14 pages, 2778 KiB  
Article
Intrusion Detection in Networks by Wasserstein Enabled Many-Objective Evolutionary Algorithms
by Andrea Ponti, Antonio Candelieri, Ilaria Giordani and Francesco Archetti
Mathematics 2023, 11(10), 2342; https://doi.org/10.3390/math11102342 - 17 May 2023
Cited by 1 | Viewed by 982
Abstract
This manuscript explores the problem of deploying sensors in networks to detect intrusions as effectively as possible. In water distribution networks, intrusions can cause a spread of contaminants over the whole network; we are searching for locations for where to install sensors in [...] Read more.
This manuscript explores the problem of deploying sensors in networks to detect intrusions as effectively as possible. In water distribution networks, intrusions can cause a spread of contaminants over the whole network; we are searching for locations for where to install sensors in order to detect intrusion contaminations as early as possible. Monitoring epidemics can also be modelled into this framework. Given a network of interactions between people, we want to identify which “small” set of people to monitor in order to enable early outbreak detection. In the domain of the Web, bloggers publish posts and refer to other bloggers using hyperlinks. Sensors are a set of blogs that catch links to most of the stories that propagate over the blogosphere. In the sensor placement problem, we have to manage a trade-off between different objectives. To solve the resulting multi-objective optimization problem, we use a multi-objective evolutionary algorithm based on the Tchebycheff scalarization (MOEA/D). The key contribution of this paper is to interpret the weight vectors in the scalarization as probability measures. This allows us to use the Wasserstein distance to drive their selection instead of the Euclidean distance. This approach results not only in a new algorithm (MOEA/D/W) with better computational results than standard MOEA/D but also in a new design approach that can be generalized to other evolutionary algorithms. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
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18 pages, 1617 KiB  
Article
An Exact Approach for Selecting Pickup-Delivery Stations in Urban Areas to Reduce Distribution Emission Costs
by Anna Sciomachen and Maria Truvolo
Mathematics 2023, 11(8), 1876; https://doi.org/10.3390/math11081876 - 15 Apr 2023
Viewed by 956
Abstract
This paper deals with a variant of the multifacility location-routing problem in urban areas. The distribution network is modelled by an undirected graph, in which the nodes are split into a set of pickup-delivery stations, a depot, and a set of customers. The [...] Read more.
This paper deals with a variant of the multifacility location-routing problem in urban areas. The distribution network is modelled by an undirected graph, in which the nodes are split into a set of pickup-delivery stations, a depot, and a set of customers. The arcs represent the minimum-cost connections between nodes. A customer is assigned to a pickup-delivery station if he or she can reach it at the lowest sustainable cost, i.e., on foot or by bicycle, without exceeding a predefined maximum distance. The goal is to minimise the goods’ total delivery cost, including pollutant emissions. In this perspective, both travel distance and means of transport play a key role. We present an exact novel approach based on partitioning the research space of the solutions of a Mixed Integer Linear Programming model. In the model, Boolean decisional variables, representing the selection of the locations for the pickup-delivery stations, are fixed simultaneously with the solution of the classical Travelling Salesman Problem. A branching constraint allows us to determine the route that serves the selected pickup-delivery stations and the route, if any, that serves customers who do not go to any pickup-delivery station. We conduct extensive experimentation to test the proposed approach’s computational efficiency and analyse the optimal solution’s robustness with respect to the maximum distance of customers from the stations, their activation cost and the pollutant emissions. The effectiveness of the proposed approach in terms of solution quality and computation time is certified by a set of computational tests based on randomly generated instances with up to 150 customers and 30 pickup-delivery stations. The application of the proposed exact method to a case study related to a district of the city of Genoa (Italy) confirms its validity also for sustainably addressing real-size urban delivery problems. An evaluation of incentives for customers using pickup-delivery stations, possibly by implementing discount policies on orders, is also proposed. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
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