Advances in Combinatorial Optimization and Discrete Mathematics with Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 4349

Special Issue Editors


E-Mail Website
Guest Editor
Tecnologico de Monterrey, School of Engineering and Sciences, Monterrey 64849, Mexico
Interests: hyperheuristics; combinatorial optimization; metaheuristics; heuristics

E-Mail Website
Guest Editor
Tecnologico de Monterrey, School of Engineering and Sciences, Monterrey 64849, Mexico
Interests: heuristics; hyperheuristics; combinatorial optimization; soft computing; computational intelligence

Special Issue Information

Dear Colleagues,

Combinatorial optimization refers to the process of finding the best solution for problems in which the number of candidate solutions is finite, and each variable has a set of fixed values that it may take. Although this hints at the idea of enumerating all candidate solutions and simply selecting the best one, this is unfeasible in practice, as the number of solutions grows exponentially. Hence, these combinatorial optimization problems (COPs) quickly become intractable through exhaustive approaches. Due to this, several alternatives have appeared throughout the years, one of them relating to exact methods. Although these alternatives guarantee to find an optimal solution, they also exhibit a high computing burden, with the other one befalling approximate solvers. In this case, the opposite happens. Approximate solvers brandish a low computing cost but no longer guarantee optimality, thus, none of them are ideal and constant research is required to develop them further.

Moreover, COPs can be related to real-life problems; for example, warehouses for e-commerce must deal with the dispatch of customer orders, e.g., through robotic mobile fulfilment systems (RMFSs). This complex problem integrates several COPs, such as path planning to pick items from the stock and put them into the current orders, order scheduling to deal with critical orders quickly and efficiently, and resource allocation to better distribute items and pickers throughout the warehouse. Hence, it is paramount to develop better methods for tackling increasingly complex COPs.

This Special Issue is devoted to state-of-the-art research on combinatorial optimization and overall discrete mathematics, particularly applications related to both. Therefore, the guest editors wish to provide a platform for the presentation of the latest advances in all aspects of combinatorial optimization and discrete mathematics, especially those dealing with practical applications. Among the topics that this Special Issue aims to address, we may consider such as those mentioned in the nonexhaustive list below:

Mathematical models for combinatorial optimization problems (COPs), such as job shop scheduling, knapsack problems, bin packing, traveling thief, balanced partition, constraint satisfaction, etc., representing a contribution to the field (such as more general models or novel hybrid models); solution approaches for tackling COPs; application of current COPs to real-life problems; modeling of complex environments (such as robotic mobile fulfilment systems) as COPs; mathematical methods for tackling COPs; etc.

We hope this initiative proves to be attractive to researchers specializing in the above-mentioned fields. Contributions may be submitted continuously before the deadline, and, after a peer-review process, are to be selected for publication based on their quality and relevance.

Dr. Ivan Mauricio Amaya-Contreras
Dr. José Carlos Ortiz-Bayliss
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. Axioms is an international peer-reviewed open access monthly 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 2400 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 problems
  • combinatorics
  • mathematical programming
  • real-life applications
  • job shop scheduling
  • path planning
  • bin packing
  • resource allocation

Published Papers (4 papers)

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Research

18 pages, 4766 KiB  
Article
Widest Path in Networks with Gains/Losses
by Javad Tayyebi, Mihai-Lucian Rîtan and Adrian Marius Deaconu
Axioms 2024, 13(2), 127; https://doi.org/10.3390/axioms13020127 - 18 Feb 2024
Viewed by 916
Abstract
In this paper, the generalized widest path problem (or generalized maximum capacity problem) is studied. This problem is denoted by the GWPP. The classical widest path problem is to find a path from a source (s) to a sink (t) with the highest [...] Read more.
In this paper, the generalized widest path problem (or generalized maximum capacity problem) is studied. This problem is denoted by the GWPP. The classical widest path problem is to find a path from a source (s) to a sink (t) with the highest capacity among all possible s-t paths. The GWPP takes into account the presence of loss/gain factors on arcs as well. The GWPP aims to find an s-t path considering the loss/gain factors while satisfying the capacity constraints. For solving the GWPP, three strongly polynomial time algorithms are presented. Two algorithms only work in the case of losses. The first one is less efficient than the second one on a CPU, but it proves to be more efficient on large networks if it parallelized on GPUs. The third algorithm is able to deal with the more general case of losses/gains on arcs. An example is considered to illustrate how each algorithm works. Experiments on large networks are conducted to compare the efficiency of the algorithms proposed. Full article
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17 pages, 411 KiB  
Article
Constrained Binary Optimization Approach for Pinned Node Selection in Pinning Control of Complex Dynamical Networks
by Alma Y. Alanis, Jesus Hernandez-Barragan, Daniel Ríos-Rivera, Oscar D. Sanchez and Gabriel Martinez-Soltero
Axioms 2023, 12(12), 1088; https://doi.org/10.3390/axioms12121088 - 28 Nov 2023
Viewed by 868
Abstract
In complex dynamical networks, pinning control techniques are often applied to control a small fraction of the nodes in order to stabilize the network with reduced control effort and energy, facilitating adequate development of the complex network. Selecting the controlled nodes is a [...] Read more.
In complex dynamical networks, pinning control techniques are often applied to control a small fraction of the nodes in order to stabilize the network with reduced control effort and energy, facilitating adequate development of the complex network. Selecting the controlled nodes is a key challenge to achieving optimal performance. Theoretical analysis of the network provides the minimum quantity of nodes to control but does not specify which ones should be controlled. Analytically, controllability analysis of the entire network would be ideal, but this becomes difficult for complex networks with a large number of nodes and non-linear dynamics. Another option is to evaluate all possible combinations with the minimum number of necessary nodes or the nodes that can be controlled, but this presents a computational challenge due to the large number of possible combinations. Therefore, the remaining option is the use of metaheuristic algorithms for the rapid and practical evaluation of these combinations. In this work, we propose to optimize the selection of nodes for pinning control based on binary optimization algorithms, subject to control and development constraints. The proposed approach involves finding a binary combination with a fixed number of controlled nodes that best stabilizes the network state to zero. This paper includes a comparative study among state-of-the-art binary optimization algorithms and modified classic optimization algorithms. The applicability of the proposed approach is validated through simulations considering a dynamical discrete-time complex network. Full article
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18 pages, 905 KiB  
Article
RPCGB Method for Large-Scale Global Optimization Problems
by Abderrahmane Ettahiri and Abdelkrim El Mouatasim
Axioms 2023, 12(6), 603; https://doi.org/10.3390/axioms12060603 - 18 Jun 2023
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Abstract
In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and [...] Read more.
In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency. Full article
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19 pages, 1079 KiB  
Article
Multi-Objective ABC-NM Algorithm for Multi-Dimensional Combinatorial Optimization Problem
by Muniyan Rajeswari, Rajakumar Ramalingam, Shakila Basheer, Keerthi Samhitha Babu, Mamoon Rashid and Ramar Saranya
Axioms 2023, 12(4), 395; https://doi.org/10.3390/axioms12040395 - 19 Apr 2023
Cited by 2 | Viewed by 1009
Abstract
This article addresses the problem of converting a single-objective combinatorial problem into a multi-objective one using the Pareto front approach. Although existing algorithms can identify the optimal solution in a multi-objective space, they fail to satisfy constraints while achieving optimal performance. To address [...] Read more.
This article addresses the problem of converting a single-objective combinatorial problem into a multi-objective one using the Pareto front approach. Although existing algorithms can identify the optimal solution in a multi-objective space, they fail to satisfy constraints while achieving optimal performance. To address this issue, we propose a multi-objective artificial bee colony optimization algorithm with a classical multi-objective theme called fitness sharing. This approach helps the convergence of the Pareto solution set towards a single optimal solution that satisfies multiple objectives. This article introduces multi-objective optimization with an example of a non-dominated sequencing technique and fitness sharing approach. The experimentation is carried out in MATLAB 2018a. In addition, we applied the proposed algorithm to two different real-time datasets, namely the knapsack problem and the nurse scheduling problem (NSP). The outcome of the proposed MBABC-NM algorithm is evaluated using standard performance indicators such as average distance, number of reference solutions (NRS), overall count of attained solutions (TNS), and overall non-dominated generation volume (ONGV). The results show that it outperforms other algorithms. Full article
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