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Mathematics
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New Advances in Combinatorial Multi-Objective Optimization and Computational Intelligence
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New Advances in Combinatorial Multi-Objective Optimization and Computational Intelligence

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (25 July 2025) | Viewed by 1969

Special Issue Editors

Prof. Dr. Han Huang

E-Mail Website
Guest Editor
School of Software, South China University of Technology, Guangzhou 510641, China
Interests: evolutionary computation; image matting; optimization; algorithm
Dr. Yi Xiang

E-Mail Website
Guest Editor
School of Software, South China University of Technology, Guangzhou 510641, China
Interests: computational intelligence; machine learning; multi-objective optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Multi-objective combinatorial optimization (MOCO) involves resolving problems characterized by multiple conflicting objectives within a finite discrete solution space. MOCO is prevalent in various domains such as logistics, telecommunications, finance, and engineering. However, finding all the exact Pareto-optimal solutions for a MOCO problem is highly challenging. Consequently, computational intelligence methods have been developed to identify a manageable number of approximated Pareto solutions within a reasonable computational budget. Despite the advancements achieved, these methods may still struggle with the complexity and trade-offs inherent in MOCO, particularly in complex real-world applications. Therefore, innovative algorithms and methodologies for efficiently addressing MOCO are crucial.
The title of this Special Issue not only reflects the subject of the Special Issue itself but also provides a direct link to the 2025 IEEE Congress on Evolutionary Computation (IEEE CEC)(https://www.cec2025.org/index/page.html?id=1391), held in Hangzhou, China, Jun 8-12, 2025. The IEEE CEC conference is a central event in the field of evolutionary computation.

This Special Issue invites submissions from conference participants. Authors of papers presented at the conference—especially those from the "Multimodal Data-Driven Optimization (MMDD)" workshop—are encouraged to submit extended or enhanced versions of their work.
The publications resulting from the event are usually turned into one or more Special Issues in selected journals known for post-conference publications, such as this very Special Issue. We also welcome submissions from researchers worldwide, regardless of conference attendance. Topics of interest include (but are not limited to) the following:

  • Multi-objective optimization;
  • Computational intelligence;
  • Combinatorial optimization;
  • Evolutionary computation;
  • Optimization methods and algorithms;
  • Trade-off analysis;
  • Algorithm design and analysis;
  • Optimization models and algorithms in real-world applications;
  • Multimodal optimization and clustering;
  • Data-driven calibration and wearable technologies;
  • Evolutionary computation and optimization;
  • Large language models in industry applications;
  • Mathematical methods in image and signal processing.

Prof. Dr. Han Huang
Dr. Yi Xiang
Guest Editors

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. 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

  • multi-objective optimization
  • computational intelligence
  • combinatorial optimization
  • evolutionary computation
  • optimization methods and algorithms
  • trade-off analysis
  • algorithm design and analysis
  • optimization models and algorithms in real-world applications
  • multimodal optimization and clustering
  • data-driven calibration and wearable technologies
  • evolutionary computation and optimization
  • large language models in industry applications
  • mathematical methods in image and signal processing

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

Published Papers (4 papers)

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18 pages, 1227 KB  
Article
Tensorized Multi-View Subspace Clustering via Tensor Nuclear Norm and Block Diagonal Representation
by Gan-Yi Tang, Gui-Fu Lu, Yong Wang and Li-Li Fan
Mathematics 2025, 13(17), 2710; https://doi.org/10.3390/math13172710 - 22 Aug 2025
Viewed by 295
Abstract
Recently, a growing number of researchers have focused on multi-view subspace clustering (MSC) due to its potential for integrating heterogeneous data. However, current MSC methods remain challenged by limited robustness and insufficient exploitation of cross-view high-order latent information for clustering advancement. To address [...] Read more.
Recently, a growing number of researchers have focused on multi-view subspace clustering (MSC) due to its potential for integrating heterogeneous data. However, current MSC methods remain challenged by limited robustness and insufficient exploitation of cross-view high-order latent information for clustering advancement. To address these challenges, we develop a novel MSC framework termed TMSC-TNNBDR, a tensorized MSC framework that leverages t-SVD based tensor nuclear norm (TNN) regularization and block diagonal representation (BDR) learning to unify view consistency and structural sparsity. Specifically, each subspace representation matrix is constrained by a block diagonal regularizer to enforce cluster structure, while all matrices are aggregated into a tensor to capture high-order interactions. To efficiently optimize the model, we developed an optimization algorithm based on the inexact augmented Lagrange multiplier (ALM). The TMSC-TNNBDR exhibits both optimized block-diagonal structure and low-rank properties, thereby enabling enhanced mining of latent higher-order inter-view correlations while demonstrating greater resilience to noise. To investigate the capability of TMSC-TNNBDR, we conducted several experiments on certain datasets. Benchmarking on circumscribed datasets demonstrates our method’s superior clustering performance over comparative algorithms while maintaining competitive computational overhead. Full article
(This article belongs to the Special Issue New Advances in Combinatorial Multi-Objective Optimization and Computational Intelligence)
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19 pages, 1196 KB  
Article
A Hybrid Harmony Search Algorithm for Distributed Permutation Flowshop Scheduling with Multimodal Optimization
by Hong Shen, Yuwei Cheng and Yazhi Li
Mathematics 2025, 13(16), 2640; https://doi.org/10.3390/math13162640 - 17 Aug 2025
Viewed by 333
Abstract
Distributed permutation flowshop scheduling is an NP-hard problem that has become a hot research topic in the fields of optimization and manufacturing in recent years. Multimodal optimization finds multiple global and local optimal solutions of a function. This study proposes a harmony search [...] Read more.
Distributed permutation flowshop scheduling is an NP-hard problem that has become a hot research topic in the fields of optimization and manufacturing in recent years. Multimodal optimization finds multiple global and local optimal solutions of a function. This study proposes a harmony search algorithm with iterative optimization operators to solve the NP-hard problem for multimodal optimization with the objective of makespan minimization. First, the initial solution set is constructed by using a distributed NEH operator. Second, after generating new candidate solutions, efficient iterative optimization operations are applied to optimize these solutions, and the worst solutions in the harmony memory (HM) are replaced. Finally, the solutions that satisfy multimodal optimization of the harmony memory are obtained when the stopping condition of the algorithm is met. The constructed algorithm is compared with three meta-heuristics: the iterative greedy meta-heuristic algorithm with a bounded search strategy, the improved Jaya algorithm, and the novel evolutionary algorithm, on 600 newly generated datasets. The results show that the proposed method outperforms the three compared algorithms and is applicable to solving distributed permutation flowshop scheduling problems in practice. Full article
(This article belongs to the Special Issue New Advances in Combinatorial Multi-Objective Optimization and Computational Intelligence)
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28 pages, 2335 KB  
Article
Fine-Tuning Pre-Trained Large Language Models for Price Prediction on Network Freight Platforms
by Pengfei Lu, Ping Zhang, Jun Wu, Xia Wu, Yunsheng Mao and Tao Liu
Mathematics 2025, 13(15), 2504; https://doi.org/10.3390/math13152504 - 4 Aug 2025
Viewed by 530
Abstract
Various factors influence the formation and adjustment of network freight prices, including transportation costs, cargo characteristics, and policies and regulations. The interaction of these factors increases the difficulty of accurately predicting network freight prices through regressions or other machine learning models, especially when [...] Read more.
Various factors influence the formation and adjustment of network freight prices, including transportation costs, cargo characteristics, and policies and regulations. The interaction of these factors increases the difficulty of accurately predicting network freight prices through regressions or other machine learning models, especially when the amount and quality of training data are limited. This paper introduces large language models (LLMs) to predict network freight prices using their inherent prior knowledge. Different data sorting methods and serialization strategies are employed to construct the corpora of LLMs, which are then tested on multiple base models. A few-shot sample dataset is constructed to test the performance of models under insufficient information. The Chain of Thought (CoT) is employed to construct a corpus that demonstrates the reasoning process in freight price prediction. Cross entropy loss with LoRA fine-tuning and cosine annealing learning rate adjustment, and Mean Absolute Error (MAE) loss with full fine-tuning and OneCycle learning rate adjustment to train the models, respectively, are used. The experimental results demonstrate that LLMs are better than or competitive with the best comparison model. Tests on a few-shot dataset demonstrate that LLMs outperform most comparison models in performance. This method provides a new reference for predicting network freight prices. Full article
(This article belongs to the Special Issue New Advances in Combinatorial Multi-Objective Optimization and Computational Intelligence)
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34 pages, 2223 KB  
Article
A Local Pareto Front Guided Microscale Search Algorithm for Multi-Modal Multi-Objective Optimization
by Yinghan Hong, Xiaohui Zheng, Fangqing Liu, Chunyun Li, Guizhen Mai, Dan Xiang and Cai Guo
Mathematics 2025, 13(13), 2160; https://doi.org/10.3390/math13132160 - 1 Jul 2025
Viewed by 411
Abstract
Multimodal multiobjective optimization problems, characterized by multiple solutions mapping to identical objective vectors, are ubiquitous in real-world applications. Despite their prevalence, most existing multimodal multiobjective evolutionary algorithms (MMOEAs) predominantly focus on identifying global Pareto sets, often overlooking the equally significant local Pareto sets. [...] Read more.
Multimodal multiobjective optimization problems, characterized by multiple solutions mapping to identical objective vectors, are ubiquitous in real-world applications. Despite their prevalence, most existing multimodal multiobjective evolutionary algorithms (MMOEAs) predominantly focus on identifying global Pareto sets, often overlooking the equally significant local Pareto sets. While some algorithms attempt to address local Pareto sets, their performance in the objective space remains suboptimal. The inherent challenge lies in the fact that a single strategy cannot effectively tackle problems with and without local Pareto fronts. This study proposes a novel approach that first detects the presence of local Pareto fronts using a neural network, thereby enabling adaptive adjustments to the algorithm’s selection strategy and search scope. Based on this detection mechanism, we design a microscale searching multimodal multiobjective evolutionary algorithm (MMOEA_MS). Through extensive experiments on twenty-two benchmark problems, MMOEA_MS demonstrates superior performance in identifying local Pareto fronts and outperforms existing algorithms in the objective space. This study highlights the effectiveness of MMOEA_MS in solving multimodal multiobjective optimization problems with diverse Pareto front characteristics, thereby addressing key limitations of current methodologies. Full article
(This article belongs to the Special Issue New Advances in Combinatorial Multi-Objective Optimization and Computational Intelligence)
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