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Mathematics
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The Recent Advances in Combinatorial Optimization and Its Applications
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The Recent Advances in Combinatorial Optimization and Its Applications

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

Deadline for manuscript submissions: closed (31 January 2025) | Viewed by 5999

Special Issue Editor

Dr. Tibor Szkaliczki

E-Mail Website
Guest Editor
eLearning Department, Institute for Computer Science and Control, Budapest, Hungary
Interests: optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, the combinatorial optimization problem (COP) has impacted various fields such as industry, transportation, telecommunication, national defense, bioinformatics, finance and life (see Special Issue "Combinatorial Optimization Problems in Planning and Decision Making"). Moreover, traditional operational research methods are primarily used to solve combinatorial optimization problems. However, with the increasing difficulty of practical applications and the increasing demands for real-time optimization, a limitation of the traditional operation optimization algorithm is becoming increasingly serious. Many new methods using deep reinforcement learning have recently emerged to solve combinatorial optimization problems, which have the advantages of fast solving speed and strong model generalization ability, and provide a new way of thinking for solving combinatorial optimization problems.

This Special Issue will focus on the recent theoretical studies and methods used to solve combinatorial optimization problems. Topics include, but are not limited to, the following:

  • combinatorial optimization;
  • multi-objective combinatorial optimization;
  • optimization;
  • optimization in multimedia systems;
  • stochastic algorithms for combinatorial optimization;
  • metaheuristics for combinatorial optimization.

Dr. Tibor Szkaliczki
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

  • combinatorial optimization
  • multi-objective combinatorial optimization
  • optimization
  • optimization in multimedia systems
  • stochastic algorithms for combinatorial optimization
  • metaheuristics for combinatorial optimization
  • graph optimization problems
  • matroid optimization problems
  • set cover problem
  • scheduling
  • VLSI routing
  • knapsack problem
  • bin packing
  • computational compexity of optimization problems
  • approximation algorithms

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

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24 pages, 2626 KiB  
Article
Coverage Optimization with Balanced Capacitated Fragmentation
by Milos Seda and Pavel Seda
Mathematics 2025, 13(5), 808; https://doi.org/10.3390/math13050808 - 28 Feb 2025
Viewed by 499
Abstract
This paper investigates a specialized variant of the set covering problem, addressing the optimal allocation of service centers to ensure that all customers (or larger entities, such as urban areas) have access to specialized services within a predefined acceptable distance, referred to as [...] Read more.
This paper investigates a specialized variant of the set covering problem, addressing the optimal allocation of service centers to ensure that all customers (or larger entities, such as urban areas) have access to specialized services within a predefined acceptable distance, referred to as the threshold. In addition to minimizing the number of service centers required or their total cost, this study emphasizes the critical importance of balancing capacity fragmentation—defined as the uneven distribution of service demand across facilities—to enhance accessibility and ensure equitable service delivery for customers. We propose an innovative mathematical model with additional practical constraints related to service deployment and designed to optimize both coverage and capacity fragmentation within a defined region. The model is validated through simulations implemented in GAMS, which document that this software tool is capable of solving even large problem instances in a reasonable amount of time. The results demonstrate the model’s effectiveness in addressing real-world challenges associated with equitable and efficient service allocation. Full article
(This article belongs to the Special Issue The Recent Advances in Combinatorial Optimization and Its Applications)
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30 pages, 2408 KiB  
Article
An Iterative Procurement Combinatorial Auction Mechanism for the Multi-Item, Multi-Sourcing Supplier-Selection and Order-Allocation Problem under a Flexible Bidding Language and Price-Sensitive Demand
by Omar Abbaas and Jose A. Ventura
Mathematics 2024, 12(14), 2228; https://doi.org/10.3390/math12142228 - 17 Jul 2024
Viewed by 1293
Abstract
This study addresses the multi-item, multi-sourcing supplier-selection and order-allocation problem. We propose an iterative procurement combinatorial auction mechanism that aims to reveal the suppliers’ minimum acceptable selling prices and assign orders optimally. Suppliers use a flexible bidding language to submit procurement bids. The [...] Read more.
This study addresses the multi-item, multi-sourcing supplier-selection and order-allocation problem. We propose an iterative procurement combinatorial auction mechanism that aims to reveal the suppliers’ minimum acceptable selling prices and assign orders optimally. Suppliers use a flexible bidding language to submit procurement bids. The buyer solves a Mixed Integer Non-linear Programming (MINLP) model to determine the winning bids for the current auction iteration. We introduce a buyer’s profit-improvement factor that constrains the suppliers to reduce their selling prices in subsequent bids. Moreover, this factor enables the buyer to strike a balance between computational effort and optimality gap. We develop a separate MINLP model for updating the suppliers’ bids while satisfying the buyer’s profit-improvement constraint. If none of the suppliers can find a feasible solution, the buyer reduces the profit-improvement factor until a pre-determined threshold is reached. A randomly generated numerical example is used to illustrate the proposed mechanism. In this example, the buyer’s profit improved by as much as 118% compared to a single-round auction. The experimental results show that the proposed mechanism is most effective in competitive environments with several suppliers and comparable costs. These results reinforce the importance of fostering competition and diversification in a supply chain. Full article
(This article belongs to the Special Issue The Recent Advances in Combinatorial Optimization and Its Applications)
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29 pages, 8328 KiB  
Article
Assessing the Compatibility of Railway Station Layouts and Mixed Heterogeneous Traffic Patterns by Optimization-Based Capacity Estimation
by Zhengwen Liao and Ce Mu
Mathematics 2023, 11(17), 3727; https://doi.org/10.3390/math11173727 - 30 Aug 2023
Viewed by 1970
Abstract
The operations performance of a railway station depends on the compatibility of its layout and the traffic pattern. It is necessary to determining an adaptable station layout for a railway station in accordance with its complex traffic pattern during the design phase. This [...] Read more.
The operations performance of a railway station depends on the compatibility of its layout and the traffic pattern. It is necessary to determining an adaptable station layout for a railway station in accordance with its complex traffic pattern during the design phase. This paper assesses the railway station layout from a capacity perspective. In particular, this paper addresses an optimization-based capacity estimation approach for the layout variants of a railway station (i.e., the number of siding tracks and the structure of the connections in between) considering the traffic pattern variants. A mixed integer programming model for microscopic timetable compression is applied to calculate the occupation rate of the given traffic pattern with flexible route choices and train orders. A novel “schedule-and-fix” heuristic algorithm is proposed to solve large-scale instances efficiently. In the case study, we evaluate the performance of the schedule-and-fix method compared with the benchmark solvers Gurobi and CP-SAT. Applying the proposed method, we compare the capacity performances of the two station design schemes, i.e., one with a flyover and the other without. The result shows that, for the given instance, building a flyover gains capacity benefits as it reduces the potential conflict in the throat area. However, the level of benefit depends on the combination of trains. It is necessary to build the flyover when the proportion of turn-around trains is more than 70% from the perspective of station capacity. Full article
(This article belongs to the Special Issue The Recent Advances in Combinatorial Optimization and Its Applications)
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Review

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35 pages, 2692 KiB  
Review
Solution Methods for the Multiple-Choice Knapsack Problem and Their Applications
by Tibor Szkaliczki
Mathematics 2025, 13(7), 1097; https://doi.org/10.3390/math13071097 - 27 Mar 2025
Viewed by 1175
Abstract
The Knapsack Problem belongs to the best-studied classical problems in combinatorial optimization. The Multiple-choice Knapsack Problem (MCKP) represents a generalization of the problem, with various application fields such as industry, transportation, telecommunication, national defense, bioinformatics, finance, and life. We found a lack of [...] Read more.
The Knapsack Problem belongs to the best-studied classical problems in combinatorial optimization. The Multiple-choice Knapsack Problem (MCKP) represents a generalization of the problem, with various application fields such as industry, transportation, telecommunication, national defense, bioinformatics, finance, and life. We found a lack of survey papers on MCKP. This paper overviews MCKP and presents its variants, solution methods, and applications. Traditional operational research methods solving the knapsack problem, such as dynamic programming, greedy heuristics, and branch-and-bound algorithms, can be adapted to MCKP. Only a few algorithms appear to have solved the problem in recent years. We found various related problems during the literature study and explored the broad spectrum of application areas. We intend to inspire research into MCKP algorithms and motivate experts from different domains to apply MCKP. Full article
(This article belongs to the Special Issue The Recent Advances in Combinatorial Optimization and Its Applications)
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