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Mathematics
Special Issues
Modeling and Optimization of Complex Systems
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Modeling and Optimization of Complex Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C4: Complex Analysis".

Deadline for manuscript submissions: 20 December 2026 | Viewed by 1397

Special Issue Editor

Dr. Smain Femmam

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Guest Editor
Networks & Communication Department, University Haute Alsace (UHA), Mulhouse, France
Interests: computational modeling and simulation of complex systems; applications of modeling and optimization in manufacturing logistics and communication systems; interdisciplinary applications of applied mathematics in engineering and computer science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex systems are present in a wide range of domains, including manufacturing, transportation, communication networks, energy systems, logistics, biological processes, and socio-economic systems. These systems are often characterized by large scale, dynamic behavior, interdependencies, and uncertainty, making their modeling, analysis, and optimization particularly challenging.

The aim of this Special Issue is to bring together recent advances in mathematical modeling, simulation, and optimization of complex systems, with an emphasis on approaches that can address real-world complexity and support decision-making. Contributions may focus on the development of novel mathematical frameworks, computational techniques, and optimization strategies, as well as on innovative applications in engineering, industry, and science.

We welcome original research articles, review papers, and short communications that contribute to advancing the theory, methodology, and applications of modeling and optimization for complex systems. Applications across engineering, transportation, logistics, energy, telecommunications, and interdisciplinary domains are particularly encouraged.

Dr. Smain Femmam
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 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • complex systems
  • mathematical modeling
  • discrete-event systems
  • hybrid systems
  • system optimization
  • simulation and analysis
  • computational methods
  • scheduling and resource allocation
  • control and decision-making
  • performance evaluation

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Published Papers (2 papers)

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Research

27 pages, 610 KB  
Article
Supervisor Design for Minimal Event Observation in Discrete Event Systems: A Linear Programming Approach
by Menghuan Hu and Yufeng Chen
Mathematics 2026, 14(6), 1058; https://doi.org/10.3390/math14061058 - 20 Mar 2026
Viewed by 304
Abstract
This paper studies the supervisory control of discrete event systems (DESs) from an event observation perspective and addresses the problem of supervisor design with minimal observation. In supervisory control, a supervisor enables or disables controllable events based on its observation of the system [...] Read more.
This paper studies the supervisory control of discrete event systems (DESs) from an event observation perspective and addresses the problem of supervisor design with minimal observation. In supervisory control, a supervisor enables or disables controllable events based on its observation of the system trajectory to guarantee controllability and nonblocking behavior with respect to a given specification, while the number of observed events critically affects the implementation complexity and cost of the control logic. Rather than minimizing the state space of the supervisor, which is the focus of classical supervisor reduction, this paper is dedicated to the minimization of observable events. Specifically, it aims to reduce the observation alphabet while preserving control equivalence with the original supremal supervisor. By analyzing the consistency of disabling decisions between event-enabled and event-disabled states, necessary and sufficient distinguishability conditions are derived and represented using Parikh vectors, which enables their formulation as linear separation constraints. In addition, event-enabled circles are introduced to capture intrinsic structural observability requirements induced by cyclic behaviors of the supervisor. These results lead to a mixed-integer linear programming (MILP) formulation that minimizes the observation alphabet while preserving control equivalence with the original supremal supervisor, together with an E-closure-based construction that synthesizes an executable event-minimal supervisor. Illustrative examples demonstrate that the proposed method can significantly reduce observation requirements even when state-minimal supervisors are already available, thereby improving implementation efficiency in resource-constrained DES applications. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Systems)
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28 pages, 3093 KB  
Article
Rank-Based Copula-Adjusted Mann–Kendall (R-CaMK)—A Copula–Vine Framework for Trend Detection and Sensor Selection in Spatially Dependent Environmental Networks
by Khaled Haddad
Mathematics 2025, 13(23), 3762; https://doi.org/10.3390/math13233762 - 24 Nov 2025
Cited by 1 | Viewed by 704
Abstract
A Rank-Based Copula-Adjusted Mann–Kendall (R-CaMK) is proposed, with an end-to-end mathematical and computational framework that integrates rank-based multivariate dependence modelling (regular vines where data permit, Gaussian copula fallback otherwise), parametric spatial bootstrap for calibrated Mann–Kendall inference, and integer programming for budgeted sensor selection. [...] Read more.
A Rank-Based Copula-Adjusted Mann–Kendall (R-CaMK) is proposed, with an end-to-end mathematical and computational framework that integrates rank-based multivariate dependence modelling (regular vines where data permit, Gaussian copula fallback otherwise), parametric spatial bootstrap for calibrated Mann–Kendall inference, and integer programming for budgeted sensor selection. At each site, the deterministic trend is removed, AR(1) margins are fitted, and residuals are transformed to ranks; the joint rank structure is modelled via R-vines or a Gaussian copula. Spatially coherent null series are simulated from the fitted model to estimate VarS for the Mann–Kendall S-statistic and to compute empirical p-values. A detection score  wj is defined and an integer linear programme (ILP) is solved to select sensors under cost/budget constraints. Simulation experiments show improved Type-I control and realistic power estimation relative to standard corrections; an application to seven long annual maximum flow sites in New South Wales demonstrates calibrated inference and operational selection decisions. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Systems)
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