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Mathematics
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Algorithm Engineering for Complex Optimization Problems: Theory and Applications
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Algorithm Engineering for Complex Optimization Problems: Theory and Applications

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 2017

Special Issue Editor

Dr. Asma Ladj

E-Mail Website
Guest Editor
Railenium Research and Technology Institute, 59540 Valenciennes, France
Interests: optimization problems; scheduling problems; metaheuristics; predictive maintenance; machine learning

Special Issue Information

Dear Colleagues,

Optimization offers a robust set of tools and methodologies for resolving problems in science, engineering, and industry. Despite improvements in their convergence speed, traditional optimization methods often struggle with complex, high-dimensional problems, particularly those involving large and non-convex search spaces. The aim of this Special Issue is to explore the engineering of algorithms specifically developed to handle this complexity, effectively bridging the gap between theoretical knowledge and practical application.

This call for papers seeks high-quality research that explores the design principles, theoretical analysis, and empirical validation of optimization algorithms. We encourage submissions that cover a broad range of methodologies, including, but not limited to, evolutionary algorithms, swarm intelligence, hyper-heuristics, machine learning-based methods, and hybrid techniques. Submissions should place a strong emphasis on algorithmic novelty, demonstrable scalability, robustness across diverse instances of a problem, and the ability to adapt effectively to the challenges posed by complex problems.

We warmly invite researchers, academics, and industry experts to submit original, unpublished research papers to this Special Issue. Should you require additional time or have any questions regarding the Special Issue, please do not hesitate to get in touch by replying to this email.

Dr. Asma Ladj
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 optimization problems
  • evolutionary algorithms
  • swarm intelligence
  • heuristics, metaheuristics, hyper-heuristics, and hybrid algorithms
  • adaptive, robust, and scalable algorithms
  • machine learning for optimization
  • high-dimensional optimization
  • multi-objective optimization
  • stochastic optimization
  • optimization under uncertainty
  • algorithm design, analysis, tuning, and benchmarking

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

39 pages, 40860 KB  
Article
Cultural History Optimization Based on Film and Television Strategy and Multi-Strategy Improvements for Global Optimization and Engineering Problems
by Yajie Chen and Meng Wang
Mathematics 2026, 14(5), 925; https://doi.org/10.3390/math14050925 - 9 Mar 2026
Viewed by 384
Abstract
Wireless sensor network (WSN) coverage optimization is a critical factor in improving network service quality, yet it faces challenges such as deployment uniformity, high-dimensional optimization, and the balance between exploration and exploitation under limited node resources. To address the shortcomings of the cultural [...] Read more.
Wireless sensor network (WSN) coverage optimization is a critical factor in improving network service quality, yet it faces challenges such as deployment uniformity, high-dimensional optimization, and the balance between exploration and exploitation under limited node resources. To address the shortcomings of the cultural historical optimization algorithm (CHOA), including insufficient global exploration, lack of dynamic regulation, and limited local exploitation accuracy, this paper proposes a film and television strategy-based multi-strategy cultural historical optimization algorithm (FTSCHOA). The proposed algorithm enhances performance through three synergistic mechanisms: a DE-style evolutionary operator that strengthens global exploration and population diversity; a film-and-television strategy that balances exploration and exploitation via random perturbations and adaptive parameter regulation; and a memory-based neighborhood local search that performs refined exploitation around high-quality solution sets to improve local optimization accuracy. Extensive experiments conducted on the CEC2017 and CEC2022 benchmark suites with dimensions of 10, 20, 30, and 50 demonstrate that FTSCHOA outperforms comparative algorithms in terms of optimization accuracy, convergence speed, and stability. The Friedman mean rank test indicates that FTSCHOA consistently achieves the best average ranking, while the Wilcoxon rank-sum test confirms that its performance differences with respect to competing algorithms are statistically significant (p<0.05). When applied to WSN coverage optimization in a 100 m×100 m monitoring region, FTSCHOA achieves coverage rates of 0.9351 and 0.9738 with 25 and 30 sensor nodes, respectively, which are significantly higher than those obtained by PSO, GWO, CHOA, and other algorithms. Moreover, the resulting node deployments exhibit greater uniformity, fewer coverage holes, and lower redundancy. The experimental results demonstrate that FTSCHOA effectively overcomes the limitations of traditional algorithms and provides an efficient and practical solution for WSN node deployment optimization, with strong potential for application in real-world scenarios such as environmental monitoring and smart agriculture. Full article
(This article belongs to the Special Issue Algorithm Engineering for Complex Optimization Problems: Theory and Applications)
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35 pages, 1334 KB  
Article
Advanced Optimization of Flowshop Scheduling with Maintenance, Learning and Deteriorating Effects Leveraging Surrogate Modeling Approaches
by Nesrine Touafek, Fatima Benbouzid-Si Tayeb, Asma Ladj and Riyadh Baghdadi
Mathematics 2025, 13(15), 2381; https://doi.org/10.3390/math13152381 - 24 Jul 2025
Cited by 1 | Viewed by 1182
Abstract
Metaheuristics are powerful optimization techniques that are well-suited for addressing complex combinatorial problems across diverse scientific and industrial domains. However, their application to computationally expensive problems remains challenging due to the high cost and significant number of fitness evaluations required during the search [...] Read more.
Metaheuristics are powerful optimization techniques that are well-suited for addressing complex combinatorial problems across diverse scientific and industrial domains. However, their application to computationally expensive problems remains challenging due to the high cost and significant number of fitness evaluations required during the search process. Surrogate modeling has recently emerged as an effective solution to reduce these computational demands by approximating the true, time-intensive fitness function. While surrogate-assisted metaheuristics have gained attention in recent years, their application to complex scheduling problems such as the Permutation Flowshop Scheduling Problem (PFSP) under learning, deterioration, and maintenance effects remains largely unexplored. To the best of our knowledge, this study is the first to investigate the integration of surrogate modeling within the artificial bee colony (ABC) framework specifically tailored to this problem context. We develop and evaluate two distinct strategies for integrating surrogate modeling into the optimization process, leveraging the ABC algorithm. The first strategy uses a Kriging model to dynamically guide the selection of the most effective search operator at each stage of the employed bee phase. The second strategy introduces three variants, each incorporating a Q-learning-based operator in the selection mechanism and a different evolution control mechanism, where the Kriging model is employed to approximate the fitness of generated offspring. Through extensive computational experiments and performance analysis, using Taillard’s well-known standard benchmarks, we assess solution quality, convergence, and the number of exact fitness evaluations, demonstrating that these approaches achieve competitive results. Full article
(This article belongs to the Special Issue Algorithm Engineering for Complex Optimization Problems: Theory and Applications)
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