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Axioms
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Dynamic Optimization, Optimal Control and Machine Learning
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Dynamic Optimization, Optimal Control and Machine Learning

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 2812

Special Issue Editor

Prof. Dr. Jiawei Chen

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Interests: robust optimization; sparse optimization; vector optimization theory and algorithms; bilevel programs; vector variational inequalities; eco-chain industry; image space analysis

Special Issue Information

Dear Colleagues,

This Special Issue focuses on current advances in “Dynamic Optimization, Optimal Control and Machine Learning” and includes novel research on the theory and algorithms of dynamic optimization, optimal control, and machine learning, in addition to their applications using deterministic methods, evolutionary algorithms, and new optimization methods as well as algorithms. Contributions focusing on novel mathematical modeling, applications, or both are encouraged.

Potential topics include, but are not limited to, the following:

  • Sparse optimization;
  • Dynamical system;
  • Multiobjective optimization;
  • Multiobjective optimal control;
  • Bilevel programs;
  • Minimax problem;
  • Variational inequality;
  • Supervised learning;
  • Meta learning;
  • Support vector machine;
  • Iterative algorithms;
  • Numerical optimization;
  • Evolutionary algorithms;
  • Optimality conditions.

Prof. Dr. Jiawei Chen
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

  • sparse optimization
  • dynamical system
  • optimality conditions
  • multiobjective optimization
  • variational inequality
  • iterative algorithms
  • bilevel programs
  • minimax problem
  • optimal control
  • multiobjective optimal control

Published Papers (2 papers)

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Research

16 pages, 1655 KiB  
Article
Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty
by Xinya Li, Yan Sun, Jinfeng Qi and Danzhu Wang
Axioms 2024, 13(3), 200; https://doi.org/10.3390/axioms13030200 - 16 Mar 2024
Cited by 1 | Viewed by 1033
Abstract
This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing [...] Read more.
This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model. Full article
(This article belongs to the Special Issue Dynamic Optimization, Optimal Control and Machine Learning)
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16 pages, 459 KiB  
Article
An Intelligent Technique for Initial Distribution of Genetic Algorithms
by Vasileios Charilogis, Ioannis G. Tsoulos and V. N. Stavrou
Axioms 2023, 12(10), 980; https://doi.org/10.3390/axioms12100980 - 17 Oct 2023
Viewed by 1334
Abstract
The need to find the global minimum in multivariable functions is a critical problem in many fields of science and technology. Effectively solving this problem requires the creation of initial solution estimates, which are subsequently used by the optimization algorithm to search for [...] Read more.
The need to find the global minimum in multivariable functions is a critical problem in many fields of science and technology. Effectively solving this problem requires the creation of initial solution estimates, which are subsequently used by the optimization algorithm to search for the best solution in the solution space. In the context of this article, a novel approach to generating the initial solution distribution is presented, which is applied to a genetic optimization algorithm. Using the k-means clustering algorithm, a distribution based on data similarity is created. This helps in generating initial estimates that may be more tailored to the problem. Additionally, the proposed method employs a rejection sampling algorithm to discard samples that do not yield better solution estimates in the optimization process. This allows the algorithm to focus on potentially optimal solutions, thus improving its performance. Finally, the article presents experimental results from the application of this approach to various optimization problems, providing the scientific community with a new method for addressing this significant problem. Full article
(This article belongs to the Special Issue Dynamic Optimization, Optimal Control and Machine Learning)
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