Optimization Algorithms: Theory and Applications

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

Deadline for manuscript submissions: 15 March 2024 | Viewed by 10627

Special Issue Editor

Faculty of Mathematics, Otto-von-Guericke-University, P.O. Box 4120, D-39016 Magdeburg, Germany
Interests: scheduling, in particular development of exact and approximate algorithms; stability investigations is discrete optimization; scheduling with interval processing times; complexity investigations for scheduling problems; train scheduling; graph theory; logistics; supply chains; packing; simulation and applications
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Special Issue Information

I invite you to submit your latest research in the area of mathmatical optimization to this Special Issue, “Optimization Algorithms: Theory and Applications” in the journal Mathematics. Optimization problems arise in all fields in the real world and have immense importance. This Issue deals with aspects of mathematical modelíng and the development of innovative novel algorithms for the solution of various types of optimization problems. High-quality papers that address both theoretical and practical issues in the area of optimization, and 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 discrete and continuous optimization, stochastic optimization, vector optimization, optimization problems on graphs, scheduling, manufacturing, logistics, transportation, healthcare, and other operations research problems.

Prof. Dr. Frank Werner
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.

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Keywords

  • linear and nonlinear programming
  • integer and mixed-integer programming
  • dynamic programming
  • combinatorial optimization
  • semi-infinite programming
  • semidefinite programming
  • global optimization
  • stochastic optimization
  • robust optimization
  • multi-criteria optimization problems
  • operations research problems
  • optimization on graphs and networks
  • scheduling
  • optimization in logistics
  • optimization of manufacturing processes
  • vehicle routing and other transportation problems
  • healthcare problems
  • control-theoretic problems
  • exact solution algorithms
  • advanced heuristics and metaheuristics
  • machine-learning
  • complexity issues

Published Papers (5 papers)

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Research

33 pages, 824 KiB  
Article
Optimizing Retaining Walls through Reinforcement Learning Approaches and Metaheuristic Techniques
Mathematics 2023, 11(9), 2104; https://doi.org/10.3390/math11092104 - 28 Apr 2023
Cited by 1 | Viewed by 1783
Abstract
The structural design of civil works is closely tied to empirical knowledge and the design professional’s experience. Based on this, adequate designs are generated in terms of strength, operability, and durability. However, such designs can be optimized to reduce conditions associated with the [...] Read more.
The structural design of civil works is closely tied to empirical knowledge and the design professional’s experience. Based on this, adequate designs are generated in terms of strength, operability, and durability. However, such designs can be optimized to reduce conditions associated with the structure’s design and execution, such as costs, CO2 emissions, and related earthworks. In this study, a new discretization technique based on reinforcement learning and transfer functions is developed. The application of metaheuristic techniques to the retaining wall problem is examined, defining two objective functions: cost and CO2 emissions. An extensive comparison is made with various metaheuristics and brute force methods, where the results show that the S-shaped transfer functions consistently yield more robust outcomes. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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24 pages, 2041 KiB  
Article
A Modified q-BFGS Algorithm for Unconstrained Optimization
Mathematics 2023, 11(6), 1420; https://doi.org/10.3390/math11061420 - 15 Mar 2023
Cited by 2 | Viewed by 1753
Abstract
This paper presents a modification of the q-BFGS method for nonlinear unconstrained optimization problems. For this modification, we use a simple symmetric positive definite matrix and propose a new q-quasi-Newton equation, which is close to the ordinary q-quasi-Newton equation in [...] Read more.
This paper presents a modification of the q-BFGS method for nonlinear unconstrained optimization problems. For this modification, we use a simple symmetric positive definite matrix and propose a new q-quasi-Newton equation, which is close to the ordinary q-quasi-Newton equation in the limiting case. This method uses only first order q-derivatives to build an approximate q-Hessian over a number of iterations. The q-Armijo-Wolfe line search condition is used to calculate step length, which guarantees that the objective function value is decreasing. This modified q-BFGS method preserves the global convergence properties of the q-BFGS method, without the convexity assumption on the objective function. Numerical results on some test problems are presented, which show that an improvement has been achieved. Moreover, we depict the numerical results through the performance profiles. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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25 pages, 2399 KiB  
Article
A Distributed Blocking Flowshop Scheduling with Setup Times Using Multi-Factory Collaboration Iterated Greedy Algorithm
Mathematics 2023, 11(3), 581; https://doi.org/10.3390/math11030581 - 22 Jan 2023
Cited by 3 | Viewed by 1254
Abstract
As multi-factory production models are more widespread in modern manufacturing systems, a distributed blocking flowshop scheduling problem (DBFSP) is studied in which no buffer between adjacent machines and setup time constraints are considered. To address the above problem, a mixed integer linear programming [...] Read more.
As multi-factory production models are more widespread in modern manufacturing systems, a distributed blocking flowshop scheduling problem (DBFSP) is studied in which no buffer between adjacent machines and setup time constraints are considered. To address the above problem, a mixed integer linear programming (MILP) model is first constructed, and its correctness is verified. Then, an iterated greedy-algorithm-blending multi-factory collaboration mechanism (mIG) is presented to optimize the makespan criterion. In the mIG algorithm, a rapid evaluation method is designed to reduce the time complexity, and two different iterative processes are selected by a certain probability. In addition, collaborative interactions between cross-factory and inner-factory are considered to further improve the exploitation and exploration of mIG. Finally, the 270 tests showed that the average makespan and RPI values of mIG are 1.93% and 78.35% better than the five comparison algorithms on average, respectively. Therefore, mIG is more suitable to solve the studied DBFSP_SDST. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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13 pages, 333 KiB  
Article
Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model
Mathematics 2022, 10(24), 4767; https://doi.org/10.3390/math10244767 - 15 Dec 2022
Cited by 2 | Viewed by 1680
Abstract
This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this [...] Read more.
This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers’ wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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27 pages, 2251 KiB  
Article
An Improved Arithmetic Optimization Algorithm for Numerical Optimization Problems
Mathematics 2022, 10(12), 2152; https://doi.org/10.3390/math10122152 - 20 Jun 2022
Cited by 12 | Viewed by 2184
Abstract
The arithmetic optimization algorithm is a recently proposed metaheuristic algorithm. In this paper, an improved arithmetic optimization algorithm (IAOA) based on the population control strategy is introduced to solve numerical optimization problems. By classifying the population and adaptively controlling the number of individuals [...] Read more.
The arithmetic optimization algorithm is a recently proposed metaheuristic algorithm. In this paper, an improved arithmetic optimization algorithm (IAOA) based on the population control strategy is introduced to solve numerical optimization problems. By classifying the population and adaptively controlling the number of individuals in the subpopulation, the information of each individual can be used effectively, which speeds up the algorithm to find the optimal value, avoids falling into local optimum, and improves the accuracy of the solution. The performance of the proposed IAOA algorithm is evaluated on six systems of nonlinear equations, ten integrations, and engineering problems. The results show that the proposed algorithm outperforms other algorithms in terms of convergence speed, convergence accuracy, stability, and robustness. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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