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Mathematics
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Combinatorial Optimization: Trends and Applications
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Combinatorial Optimization: Trends and Applications

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

Deadline for manuscript submissions: closed (15 August 2024) | Viewed by 7918

Special Issue Editors

Dr. Takfarinas Saber

E-Mail Website
Guest Editor
School of Computer Science, University of Galway, Galway, Ireland
Interests: operations research; metaheuristics; multi-objective optimization; complex systems
Dr. Aman Singh

E-Mail Website
Guest Editor
1. Higher Polytechnic School, European Atlantic University, 39011 Santander, Spain
2. Department of Engineering, Iberoamerican International University, Arecibo, PR 00613, USA
Interests: ai; academic loafing; data preprocessing; education ecosystem; higher education; intelligent modal
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The world is facing several optimization challenges which can be expressed as combinatorial problems. Whether it is the in-car navigation system, the software used to create school timetables, or the decision support systems in manufacturing and logistics environments, it is almost certain that modern techniques of combinatorial optimization were used to program these applications.

Challenges held by combinatorial problems have attracted a large community within operations research seeking to devise advanced algorithms specifically tailored to take advantage of their particularity (where, arguably, the most important question is: how quickly can you find the optimal solution?). However, given the large-scale and complex real-life problems, finding the optimal solution in a timely manner is often unlikely. Therefore, the question that combinatorial optimization aims to answer becomes: what is the best quality solution that an efficient algorithm can offer in a given time frame?

The successes of combinatorial optimization and its impact on various application domains have motivated several decision makers to formalize and propose their own combinatorial problems, and to seek better and more refined computational methods from operations research and machine learning approaches to address them.

In this Special Issue, we invite the research community to submit their original contributions to the topic of the trends and applications of combinatorial optimization. We welcome studies investigating exact to approximate approaches for optimization from both the theoretical and the applied angle, regardless of the nature of the combinatorial problem (single-objective, multi-objective, dynamic, etc.). Authors are encouraged to submit their formal and technically sound manuscripts to cover (not exhaustively) the following aspects:

  • Approximation algorithms;
  • Branch-and-bound, branch-and-cut, and branch-and-price algorithms;
  • Computational complexity;
  • Computational geometry;
  • Cutting plane algorithms;
  • Exact and parameterized algorithms;
  • Metaheuristics, hybrid-metaheuristics; matheuristics;
  • Hyperheuristics;
  • Machine learning-empowered searches;
  • Meta-modeling;
  • Surrogate modeling;
  • Linear and nonlinear (mixed-)integer programming;
  • Local search algorithms;
  • Evolutionary algorithms, bio-inspired algorithms;
  • Multi-objective optimization;Scheduling algorithms.
  • Scheduling algorithms.

Dr. Takfarinas Saber
Dr. Aman Singh
Guest Editors

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
  • operations research
  • exact approaches
  • approximate approaches
  • metaheuristics
  • hyperheuristics
  • machine learning-empowered search
  • applications

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Published Papers (4 papers)

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Research

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21 pages, 1090 KiB  
Article
Sustainable Road Infrastructure Decision-Making: Custom NSGA-II with Repair Operators for Multi-Objective Optimization
by Andrés Ruiz-Vélez, José García, Julián Alcalá and Víctor Yepes
Mathematics 2024, 12(5), 730; https://doi.org/10.3390/math12050730 - 29 Feb 2024
Cited by 3 | Viewed by 1610
Abstract
The integration of sustainability principles into the structural design and decision-making processes for transportation infrastructure, particularly concerning reinforced concrete precast modular frames (RCPMF), is recognized as crucial for ensuring outcomes that are environmentally responsible, economically feasible, and socially beneficial. In this study, this [...] Read more.
The integration of sustainability principles into the structural design and decision-making processes for transportation infrastructure, particularly concerning reinforced concrete precast modular frames (RCPMF), is recognized as crucial for ensuring outcomes that are environmentally responsible, economically feasible, and socially beneficial. In this study, this challenge is addressed, with the significance of sustainable development in modern engineering practices being underscored. A novel approach, which is a combination of multi-objective optimization (MOO) with multi-criteria decision-making (MCDM) techniques, is proposed, tailored specifically for the design and selection of RCPMF. The effectiveness of three repair operators—statistical-based, random, and proximity-based—in optimizing economic, environmental, and social objectives is evaluated. Precise evaluation of objective functions is facilitated by a customized Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, complemented by a detailed life cycle analysis (LCA). The utilization of simple additive weighting (SAW) and fair un choix adéquat (FUCA) methods for the scoring and ranking of the MOO solutions has revealed that notable excellence in meeting the RCPMF design requirements is exhibited by the statistical-based repair operator, which offers solutions with lower impacts across all dimensions and demonstrates minimal variability. MCDM techniques produced similar rankings, with slight score variations and a significant correlation of 0.9816, showcasing their consistent evaluation capacity despite distinct operational methodologies. Full article
(This article belongs to the Special Issue Combinatorial Optimization: Trends and Applications)
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18 pages, 1522 KiB  
Article
An Evolutionary Algorithm for Task Clustering and Scheduling in IoT Edge Computing
by Adil Yousif, Mohammed Bakri Bashir and Awad Ali
Mathematics 2024, 12(2), 281; https://doi.org/10.3390/math12020281 - 15 Jan 2024
Cited by 3 | Viewed by 1316
Abstract
The Internet of Things (IoT) edge is an emerging technology of sensors and devices that communicate real-time data to a network. IoT edge computing was introduced to handle the latency concerns related to cloud computing data management, as the data are processed closer [...] Read more.
The Internet of Things (IoT) edge is an emerging technology of sensors and devices that communicate real-time data to a network. IoT edge computing was introduced to handle the latency concerns related to cloud computing data management, as the data are processed closer to their point of origin. Clustering and scheduling tasks on IoT edge computing are considered a challenging problem due to the diverse nature of task and resource characteristics. Metaheuristics and optimization methods are widely used in IoT edge task clustering and scheduling. This paper introduced a new task clustering and scheduling mechanism using differential evolution optimization on IoT edge computing. The proposed mechanism aims to optimize task clustering and scheduling to find optimal execution times for submitted tasks. The proposed mechanism for task clustering is based on the degree of similarity of task characteristics. The proposed mechanisms use an evolutionary mechanism to distribute system tasks across suitable IoT edge resources. The clustering tasks process categorizes tasks with similar requirements and then maps them to appropriate resources. To evaluate the proposed differential evolution mechanism for IoT edge task clustering and scheduling, this study conducted several simulation experiments against two established mechanisms: the Firefly Algorithm (FA) and Particle Swarm Optimization (PSO). The simulation configuration was carefully created to mimic real-world IoT edge computing settings to ensure the proposed mechanism’s applicability and the simulation results’ relevance. In the heavyweight workload scenario, the proposed DE mechanism started with an execution time of 916.61 milliseconds, compared to FA’s 1092 milliseconds and PSO’s 1026.09 milliseconds. By the 50th iteration, the proposed DE mechanism had reduced its execution time significantly to around 821.27 milliseconds, whereas FA and PSO showed lesser improvements, with FA at approximately 1053.06 milliseconds and PSO stabilizing at 956.12 milliseconds. The simulation results revealed that the proposed differential evolution mechanism for edge task clustering and scheduling outperforms FA and PSO regarding system efficiency and stability, significantly reducing execution time and having minimal variation across simulation iterations. Full article
(This article belongs to the Special Issue Combinatorial Optimization: Trends and Applications)
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23 pages, 1141 KiB  
Article
A Discrete JAYA Algorithm Based on Reinforcement Learning and Simulated Annealing for the Traveling Salesman Problem
by Jun Xu, Wei Hu, Wenjuan Gu and Yongguang Yu
Mathematics 2023, 11(14), 3221; https://doi.org/10.3390/math11143221 - 22 Jul 2023
Cited by 4 | Viewed by 1759
Abstract
The JAYA algorithm is a population-based meta-heuristic algorithm proposed in recent years which has been proved to be suitable for solving global optimization and engineering optimization problems because of its simplicity, easy implementation, and guiding characteristic of striving for the best and avoiding [...] Read more.
The JAYA algorithm is a population-based meta-heuristic algorithm proposed in recent years which has been proved to be suitable for solving global optimization and engineering optimization problems because of its simplicity, easy implementation, and guiding characteristic of striving for the best and avoiding the worst. In this study, an improved discrete JAYA algorithm based on reinforcement learning and simulated annealing (QSA-DJAYA) is proposed to solve the well-known traveling salesman problem in combinatorial optimization. More specially, firstly, the basic Q-learning algorithm in reinforcement learning is embedded into the proposed algorithm such that it can choose the most promising transformation operator for the current state to update the solution. Secondly, in order to balance the exploration and exploitation capabilities of the QSA-DJAYA algorithm, the Metropolis acceptance criterion of the simulated annealing algorithm is introduced to determine whether to accept candidate solutions. Thirdly, 3-opt is applied to the best solution of the current iteration at a certain frequency to improve the efficiency of the algorithm. Finally, to evaluate the performance of the QSA-DJAYA algorithm, it has been tested on 21 benchmark datasets taken from TSPLIB and compared with other competitive algorithms in two groups of comparative experiments. The experimental and the statistical significance test results show that the QSA-DJAYA algorithm achieves significantly better results in most instances. Full article
(This article belongs to the Special Issue Combinatorial Optimization: Trends and Applications)
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Review

Jump to: Research

36 pages, 537 KiB  
Review
Set-Based Particle Swarm Optimisation: A Review
by Jean-Pierre van Zyl and Andries Petrus Engelbrecht
Mathematics 2023, 11(13), 2980; https://doi.org/10.3390/math11132980 - 4 Jul 2023
Cited by 16 | Viewed by 2410
Abstract
The set-based particle swarm optimisation algorithm is a swarm-based meta-heuristic that has gained popularity in recent years. In contrast to the original particle swarm optimisation algorithm, the set-based particle swarm optimisation algorithm is used to solve discrete and combinatorial optimisation problems. The main [...] Read more.
The set-based particle swarm optimisation algorithm is a swarm-based meta-heuristic that has gained popularity in recent years. In contrast to the original particle swarm optimisation algorithm, the set-based particle swarm optimisation algorithm is used to solve discrete and combinatorial optimisation problems. The main objective of this paper is to review the set-based particle swarm optimisation algorithm and to provide an overview of the problems to which the algorithm has been applied. This paper starts with an examination of previous attempts to create a set-based particle swarm optimisation algorithm and discusses the shortcomings of the existing attempts. The set-based particle swarm optimisation algorithm is established as the only suitable particle swarm variant that is both based on true set theory and does not require problem-specific modifications. In-depth explanations are given regarding the general position and velocity update equations, the mechanisms used to control the exploration–exploitation trade-off, and the quantifiers of swarm diversity. After the various existing applications of set-based particle swarm optimisation are presented, this paper concludes with a discussion on potential future research. Full article
(This article belongs to the Special Issue Combinatorial Optimization: Trends and Applications)
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