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Axioms
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Optimization Algorithms and Applications
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Optimization Algorithms and Applications

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

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 19688

Special Issue Editor

Prof. Dr. Nodari Vakhania

E-Mail Website
Guest Editor
Department of Computer Sciences, Universidad Autónoma del Estado de Morelos, Cuernavaca 62209, Morelos, Mexico
Interests: scheduling; combinatorial optimization; algorithm development; multi-objective optimization; graphs; integer programming; algorithm analysis; computation; discrete optimization; dynamic programming; optimization theory

Special Issue Information

Dear Colleagues,

We invite you to submit your research in the area of discrete optimization and its applications to the Special Issue, “Optimization Algorithms and Applications”, in the journal Axioms. Efficient algorithms for the solution of classical discrete optimization and real-life practical optimization problems are welcome, including new mathematical models for real-life optimization problems and novel solution methods. High-quality papers are solicited to address both theoretical and practical issues in the development of efficient solution methods and a theoretical analysis of the optimization problems. Submissions that present new theoretical results, models and algorithms, as well as new applications, are welcome. Potential topics include, but are not limited to, applications of linear and integer programming, scheduling and routing, packing and partitioning, optimization in graphs, multi-criteria optimization, time complexity analysis.

Prof. Dr. Nodari Vakhania
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. 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

  • discrete optimization
  • multi-criteria optimization
  • time complexity analysis
  • implicit enumeration and branch-and-bound
  • dynamic programming
  • heuristics and meta-heuristics
  • linear and integer programming
  • deterministic scheduling
  • stochastic scheduling
  • batch scheduling
  • routing and transportation
  • packing and partitioning
  • optimization in graph problems

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Published Papers (7 papers)

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Research

17 pages, 461 KiB  
Article
Mathematical Modeling and Exact Optimizing of University Course Scheduling Considering Preferences of Professors
by Mo Chen, Frank Werner and Mohammad Shokouhifar
Axioms 2023, 12(5), 498; https://doi.org/10.3390/axioms12050498 - 19 May 2023
Cited by 3 | Viewed by 2820
Abstract
University course scheduling (UCS) is one of the most important and time-consuming issues that all educational institutions face yearly. Most of the existing techniques to model and solve UCS problems have applied approximate methods, which differ in terms of efficiency, performance, and optimization [...] Read more.
University course scheduling (UCS) is one of the most important and time-consuming issues that all educational institutions face yearly. Most of the existing techniques to model and solve UCS problems have applied approximate methods, which differ in terms of efficiency, performance, and optimization speed. Accordingly, this research aims to apply an exact optimization method to provide an optimal solution to the course scheduling problem. In other words, in this research, an integer programming model is presented to solve the USC problem. In this model, the constraints include the facilities of classrooms, courses of different levels and compression of students’ curriculum, courses outside the faculty and planning for them, and the limited time allocated to the professors. The objective is to maximize the weighted sum of allocating available times to professors based on their preferences in all periods. To evaluate the presented model’s feasibility, it is implemented using the GAMS software. Finally, the presented model is solved in a larger dimension using a real data set from a college in China and compared with the current program in the same college. The obtained results show that considering the mathematical model’s constraints and objective function, the faculty courses’ timetable is reduced from 4 days a week to 3 working days. Moreover, master courses are planned in two days, and the courses in the educational groups do not interfere with each other. Furthermore, by implementing the proposed model for the real case study, the maximum teaching hours of the professors are significantly reduced. The results demonstrate the efficiency of the proposed model and solution method in terms of optimization speed and solution accuracy. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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18 pages, 892 KiB  
Article
A New Parameterless Filled Function Method for Global Optimization
by Haiyan Liu, Siyan Xue, Yuan Cheng and Shouheng Tuo
Axioms 2022, 11(12), 746; https://doi.org/10.3390/axioms11120746 - 19 Dec 2022
Cited by 1 | Viewed by 1800
Abstract
The filled function method is an effective way to solve global optimization problems. However, its effectiveness is greatly affected by the selection of parameters, and the non-continuous or non-differentiable properties of the constructed filled function. To overcome the above-mentioned drawbacks, in this paper, [...] Read more.
The filled function method is an effective way to solve global optimization problems. However, its effectiveness is greatly affected by the selection of parameters, and the non-continuous or non-differentiable properties of the constructed filled function. To overcome the above-mentioned drawbacks, in this paper, a new parameterless filled function is proposed that is continuous and differentiable. Theoretical proofs have been made to show the properties of the proposed filled function. Based on the new filled function, a filled function algorithm is proposed to solve unconstrained global optimization problems. Experiments are carried out on widely used test problems and an application of supply chain problems with equality and inequality constraints. The numerical results show that the proposed filled function is effective. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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18 pages, 1030 KiB  
Article
Efficient Modified Meta-Heuristic Technique for Unconstrained Optimization Problems
by Khalid Abdulaziz Alnowibet, Ahmad M. Alshamrani, Adel Fahad Alrasheedi, Salem Mahdi, Mahmoud El-Alem, Abdallah Aboutahoun and Ali Wagdy Mohamed
Axioms 2022, 11(9), 483; https://doi.org/10.3390/axioms11090483 - 19 Sep 2022
Cited by 4 | Viewed by 1950
Abstract
In this paper, a new Modified Meta-Heuristic algorithm is proposed. This method contains some modifications to improve the performance of the simulated-annealing algorithm (SA). Most authors who deal with improving the SA algorithm presented some improvements and modifications to one or more of [...] Read more.
In this paper, a new Modified Meta-Heuristic algorithm is proposed. This method contains some modifications to improve the performance of the simulated-annealing algorithm (SA). Most authors who deal with improving the SA algorithm presented some improvements and modifications to one or more of the five standard features of the SA algorithm. In this paper, we improve the SA algorithm by presenting some suggestions and modifications to all five standard features of the SA algorithm. Through these suggestions and modifications, we obtained a new algorithm that finds the approximate solution to the global minimum of a non-convex function. The new algorithm contains novel parameters, which are updated at each iteration. Therefore, the variety and alternatives in choosing these parameters demonstrated a noticeable impact on the performance of the proposed algorithm. Furthermore, it has multiple formulas by which the candidate solutions are generated. Diversity in these formulas helped the proposed algorithm to escape a local point while finding the global minimizer of a non-convex function. The efficiency of the proposed algorithm is reported through extensive numerical experiments on some well-known test problems. The performance profiles are used to evaluate and compare the performance of our proposed algorithm against the other five meta-heuristic algorithms. The comparison results between the performance of our suggested algorithm and the other five algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the five algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions. This superiority of the new proposed algorithm is due to those five modified standard features. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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28 pages, 4806 KiB  
Article
A Multi-Phase Method for Euclidean Traveling Salesman Problems
by Víctor Hugo Pacheco-Valencia, Nodari Vakhania, Frank Ángel Hernández-Mira and José Alberto Hernández-Aguilar
Axioms 2022, 11(9), 439; https://doi.org/10.3390/axioms11090439 - 30 Aug 2022
Cited by 3 | Viewed by 2005
Abstract
The Traveling Salesman Problem (TSP) aims to find the shortest tour for a salesman who starts and ends in the same city and visits the remaining n−1 cities exactly once. There are a number of common generalizations of the problem including [...] Read more.
The Traveling Salesman Problem (TSP) aims to find the shortest tour for a salesman who starts and ends in the same city and visits the remaining n−1 cities exactly once. There are a number of common generalizations of the problem including the Multiple Traveling Salesman Problem (MTSP), where instead of one salesman, there are k salesmen and the same amount of individual tours are to be constructed. We consider the Euclidean version of the problem where the distances between the cities are calculated in two-dimensional Euclidean space. Both general the TSP and its Euclidean version are strongly NP-hard. Hence, approximation algorithms with a good practical behavior are of primary interest. We describe a general method for the solution of the Euclidean versions of the TSP (including MTSP) that yields approximation algorithms with a favorable practical behavior for large real-life instances. Our method creates special types of convex hulls, which serve as a basis for the constructions of our initial and intermediate partial solutions. Here, we overview three algorithms; one of them is for the bounded version of the MTSP. The proposed novel algorithm for the Euclidean TSP provides close-to-optimal solutions for some real-life instances. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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18 pages, 1326 KiB  
Article
Home Health Care Planning with the Consideration of Flexible Starting/Ending Points and Service Features
by Pouria Khodabandeh, Vahid Kayvanfar, Majid Rafiee and Frank Werner
Axioms 2022, 11(8), 362; https://doi.org/10.3390/axioms11080362 - 26 Jul 2022
Cited by 2 | Viewed by 2157
Abstract
One of the recently proposed strategies in health systems is providing services to patients at home and improving the service quality in addition to reducing the health system costs. In the real world, some services, such as biological tests or blood sampling, force [...] Read more.
One of the recently proposed strategies in health systems is providing services to patients at home and improving the service quality in addition to reducing the health system costs. In the real world, some services, such as biological tests or blood sampling, force the nurses to start or end his/her route from/at the laboratory instead of the depot, changing the whole optimal planning. The effect of these special service requirements and features has not been considered so far. In this study, a new mathematical model is suggested considering the flexibility of starting/ending places of each nurse’s route according to the specific characteristics of each service. Then, several sets of problems in various sizes are solved using the proposed model, where the results confirm the efficiency of the proposed approach. In addition, some sensitivity analyses are performed on the parameters of the required features of the services, followed by some managerial insights and directions for future studies. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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25 pages, 2189 KiB  
Article
A New Interior Search Algorithm for Energy-Saving Flexible Job Shop Scheduling with Overlapping Operations and Transportation Times
by Lu Liu, Tianhua Jiang, Huiqi Zhu and Chunlin Shang
Axioms 2022, 11(7), 306; https://doi.org/10.3390/axioms11070306 - 24 Jun 2022
Cited by 4 | Viewed by 1765
Abstract
Energy-saving scheduling has been pointed out as an interesting research issue in the manufacturing field, by which energy consumption can be effectively reduced through production scheduling from the operational management perspective. In recent years, energy-saving scheduling problems in flexible job shops (ESFJSPs) have [...] Read more.
Energy-saving scheduling has been pointed out as an interesting research issue in the manufacturing field, by which energy consumption can be effectively reduced through production scheduling from the operational management perspective. In recent years, energy-saving scheduling problems in flexible job shops (ESFJSPs) have attracted considerable attention from scholars. However, the majority of existing work on ESFJSPs assumed that the processing of any two consecutive operations in a job cannot be overlapped. In order to be close to real production, the processing overlapping of consecutive operations is allowed in this paper, while the job transportation tasks are also involved between different machines. To formulate the problem, a mathematical model is set up to minimize total energy consumption. Due to the NP-hard nature, a new interior search algorithm (NISA) is elaborately proposed following the feature of the problem. A number of experiments are conducted to verify the effectiveness of the NISA algorithm. The experimental results demonstrate that the NISA provides promising results for the considered problem. In addition, the computational results indicate that the increasing transportation time and sub-lot number will increase the transportation energy consumption, which is largely responsible for the increase in total energy consumption. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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29 pages, 3919 KiB  
Article
A Modified Ant Lion Optimization Method and Its Application for Instance Reduction Problem in Balanced and Imbalanced Data
by Lamiaa M. El Bakrawy, Mehmet Akif Cifci, Samina Kausar, Sadiq Hussain, Md. Akhtarul Islam, Bilal Alatas and Abeer S. Desuky
Axioms 2022, 11(3), 95; https://doi.org/10.3390/axioms11030095 - 24 Feb 2022
Cited by 15 | Viewed by 4842
Abstract
Instance reduction is a pre-processing step devised to improve the task of classification. Instance reduction algorithms search for a reduced set of instances to mitigate the low computational efficiency and high storage requirements. Hence, finding the optimal subset of instances is of utmost [...] Read more.
Instance reduction is a pre-processing step devised to improve the task of classification. Instance reduction algorithms search for a reduced set of instances to mitigate the low computational efficiency and high storage requirements. Hence, finding the optimal subset of instances is of utmost importance. Metaheuristic techniques are used to search for the optimal subset of instances as a potential application. Antlion optimization (ALO) is a recent metaheuristic algorithm that simulates antlion’s foraging performance in finding and attacking ants. However, the ALO algorithm suffers from local optima stagnation and slow convergence speed for some optimization problems. In this study, a new modified antlion optimization (MALO) algorithm is recommended to improve the primary ALO performance by adding a new parameter that depends on the step length of each ant while revising the antlion position. Furthermore, the suggested MALO algorithm is adapted to the challenge of instance reduction to obtain better results in terms of many metrics. The results based on twenty-three benchmark functions at 500 iterations and thirteen benchmark functions at 1000 iterations demonstrate that the proposed MALO algorithm escapes the local optima and provides a better convergence rate as compared to the basic ALO algorithm and some well-known and recent optimization algorithms. In addition, the results based on 15 balanced and imbalanced datasets and 18 oversampled imbalanced datasets show that the instance reduction proposed method can statistically outperform the basic ALO algorithm and has strong competitiveness against other comparative algorithms in terms of four performance measures: Accuracy, Balanced Accuracy (BACC), Geometric mean (G-mean), and Area Under the Curve (AUC) in addition to the run time. MALO algorithm results show increment in Accuracy, BACC, G-mean, and AUC rates up to 7%, 3%, 15%, and 9%, respectively, for some datasets over the basic ALO algorithm while keeping less computational time. Full article
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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