Mathematical Optimizations and Operations Research

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

Deadline for manuscript submissions: 20 February 2025 | Viewed by 1297

Special Issue Editors


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Guest Editor
School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Interests: optimization method and its applications; stochasitic programming; robust optimization

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China
Interests: stochasitic programming; robust optimization; reinforcement learning

Special Issue Information

Dear Colleagues,

The importance of optimization is increasing in addressing complex, real-world problems across various industries and disciplines. As the world becomes more interconnected and data-driven, the need for efficient decision-making processes that leverage mathematical optimization techniques becomes paramount.

The development of mathematical optimization has been marked by significant advancements in theoretical research and practical applications, such as nonconvex optimization algorithms, stochastic optimization, distributionally robust optimization, discrete optimization, optimization theory, and applications in artificial intelligence, transportation, and finance. However, designing efficient algorithms and applying these novel approaches to real problems is still an open issue—particularly for nonconvex optimization, nonsmooth optimization, large-scale optimization, integer programs, and optimization under uncertainty.

This Special Issue invites researchers to report their latest research on developing all aspects of mathematical optimization and new applications in operations research. The scope includes but is not limited to convex and nonconvex optimization, nonsmooth optimization, large-scale optimization, integer program, stochastic optimization, robust optimization, computational methods, and applications of optimization techniques in various domains such as finance, logistics, energy, healthcare, transportation, and manufacturing.

Dr. Shen Peng
Dr. Jia Liu
Guest Editors

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Keywords

  • convex and nonconvex optimization
  • nonsmooth optimization
  • large-scale optimization
  • integer program
  • stochastic optimization
  • robust optimization
  • distributionally robust optimization
  • artificial intelligence
  • operations research

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Published Papers (1 paper)

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Research

33 pages, 53062 KiB  
Article
An Improved MOEA/D with an Auction-Based Matching Mechanism
by Guangjian Li, Mingfa Zheng, Guangjun He, Yu Mei, Gaoji Sun and Haitao Zhong
Axioms 2024, 13(9), 644; https://doi.org/10.3390/axioms13090644 - 20 Sep 2024
Viewed by 890
Abstract
Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing [...] Read more.
Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
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