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Mathematics
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The Application of Optimization Algorithm in Mathematical Model
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The Application of Optimization Algorithm in Mathematical Model

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

Deadline for manuscript submissions: closed (30 August 2024) | Viewed by 2857

Special Issue Editor

Prof. Dr. Li-Ning Xing

E-Mail Website
Guest Editor
School of Electronic Engineering, Xidian University, Xi’an 710126, China
Interests: management decision; simulation optimization; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Optimization technologies occupy a very important position in decision analysis, and mathematical models dominate optimization technologies. As the system becomes more and more complex, the mathematical model becomes more and more complex also. How to solve complex mathematical models is an important problem that we need to solve urgently. Intelligent optimization technology provides a feasible path for solving complex mathematical models. For this reason, we plan to organize one Special Issue. This Special Issue will focus on new developments and advances in the application of optimization algorithms in mathematical models, including the theory and applications to the fields of engineering, scientific computing, and computer science.

Prof. Dr. Li-Ning Xing
Guest Editor

Manuscript Submission Information

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Keywords

  • optimization algorithm
  • mathematical model
  • genetic algorithm
  • ant colony optimization
  • particle swarm optimization
  • tabu search
  • simulated annealing

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Published Papers (2 papers)

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22 pages, 2753 KiB  
Article
Two-Stage Satellite Combined-Task Scheduling Based on Task Merging Mechanism
by Jing Yu, Jiawei Guo, Lining Xing, Yanjie Song and Zhaohui Liu
Mathematics 2024, 12(19), 3107; https://doi.org/10.3390/math12193107 - 4 Oct 2024
Viewed by 992
Abstract
Satellites adopt a single-task observation mode in traditional patterns. Although this mode boasts high imaging accuracy, it is accompanied by a limited number of observed tasks and a low utilization rate of satellite resources. This limitation becomes particularly pronounced when dealing with extensive [...] Read more.
Satellites adopt a single-task observation mode in traditional patterns. Although this mode boasts high imaging accuracy, it is accompanied by a limited number of observed tasks and a low utilization rate of satellite resources. This limitation becomes particularly pronounced when dealing with extensive and densely populated observation task sets because the inherent mobility of satellites often leads to conflicts among numerous tasks. To address this issue, this paper introduces a novel multi-task merging mechanism aimed at enhancing the observation rate of satellites by resolving task conflicts. Initially, this paper presents a task merging method based on the proposed multitask merging mechanism, referred to as the constrained graph (CG) task merging approach. This method can merge tasks while adhering to the minimal requirements specified by users. Subsequently, a multi-satellite merging scheduling model is established based on the combined task set. Considering the satellite combined-task scheduling problem (SCTSP), an enhanced fireworks algorithm (EFWA) is proposed that incorporates the CG task synthesis mechanism. This algorithm incorporates local search strategies and a population disturbance mechanism to enhance both the solution quality and convergence speed. Finally, the efficacy of the CG algorithm was validated through a multitude of simulation experiments. Moreover, the effectiveness of the EFWA is confirmed via extensive comparisons with other algorithms, including the basic ant colony optimization (ACO) algorithm, enhanced ant colony optimization (EACO) algorithm, fireworks algorithm (FWA), and EFWA. When the number of tasks in the observation area are dense, such as in the case where the number of tasks is 700, the CG + EFWA (CG is adopted in the task merging stage and EFWA is adopted in the satellite combined-task scheduling stage) method improves observation benefits by 70.35% (compared to CG + EACO, CG is adopted in the task merging stage and EACO is adopted in the satellite combined-task scheduling stage), 78.93% (compared to MS + EFWA, MS is adopted in the task merging stage and EFWA is adopted in the satellite combined-task scheduling stage), and 39.03% (compared to MS + EACO, MS is adopted in the task merging stage and EACO is adopted in the satellite combined-task scheduling stage). Full article
(This article belongs to the Special Issue The Application of Optimization Algorithm in Mathematical Model)
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19 pages, 7314 KiB  
Article
Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques
by Longhui Meng, Liang Ding, Aqib Mashood Khan, Ray Tahir Mushtaq and Mohammed Alkahtani
Mathematics 2024, 12(17), 2670; https://doi.org/10.3390/math12172670 - 28 Aug 2024
Cited by 1 | Viewed by 1138
Abstract
This research introduces the Iterative Overlap Optimization Placement (IOOP) method, a novel approach designed to enhance the efficiency of irregular pattern packing by dynamically optimizing overlap ratios and pattern placements. Utilizing a modified genetic algorithm, IOOP addresses the complexities of arranging irregular patterns [...] Read more.
This research introduces the Iterative Overlap Optimization Placement (IOOP) method, a novel approach designed to enhance the efficiency of irregular pattern packing by dynamically optimizing overlap ratios and pattern placements. Utilizing a modified genetic algorithm, IOOP addresses the complexities of arranging irregular patterns in a given space, focusing on improving spatial and material efficiency. This study demonstrates the method’s superiority over the traditional Size-First Non-Iterative Overlap Optimization Placement technique through comparative analysis, highlighting significant improvements in spatial utilization, flexibility, and material conservation. The effectiveness of IOOP is further validated by its robustness in handling diverse pattern groups and its adaptability in adjusting pattern placements iteratively. This research not only showcases the potential of IOOP in manufacturing and design processes requiring precise spatial planning but also opens avenues for its application across various industries, underscoring the need for further exploration into advanced technological integrations for tackling complex spatial optimization challenges. Full article
(This article belongs to the Special Issue The Application of Optimization Algorithm in Mathematical Model)
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