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Algorithms
Special Issues
Multi-Objective and Multi-Level Optimization: Algorithms and Applications (2nd Edition)
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Multi-Objective and Multi-Level Optimization: Algorithms and Applications (2nd Edition)

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Combinatorial Optimization, Graph, and Network Algorithms".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 513

Special Issue Editor

Prof. Dr. Massimiliano Caramia

E-Mail Website
Guest Editor
Department of Enterprise Engineering, University of Rome "Tor Vergata", 00133 Roma, Italy
Interests: scheduling; graph theory; optimization; mathematical modeling; supply chain optimization; logistics; transportation; production systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Decision-making in real-world applications often require the consideration of more than one objective to find an effective solution. When (conflicting) objectives are associated with either a single decision-maker or cooperative decision-makers, this typically leads to multi-objective optimization. Here, optional solutions do not have the same image value, as happens in single-objective optimization, but are non-dominated, equivalent, and allow the definition of the Pareto front. When objectives are associated with different non-cooperative decision-makers, we fall into the game theory arena; furthermore, when objectives and/or decision-makers have a hierarchy among them, this asks to cope with nested optimization problems and, therefore, multi-level optimization.

All these problems are computationally difficult to solve, and their resolution typically involves reformulating the latter into several single-objective problems or one single-objective problem by introducing additional (non-linear) constraints. Moreover, to limit the computational burden, before their resolution, it is worthwhile to reduce the number of objectives to a very limited (significative) number by applying proper methodologies.

The aim of this Special Issue is to collect original manuscripts dealing with multi-objective and multi-level optimization; we sought original papers presenting innovative applications and/or contributing to the theory.

Prof. Dr. Massimiliano Caramia
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. Algorithms 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 1600 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
  • multi-level optimization
  • decision-making

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Related Special Issue

Published Papers (2 papers)

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Research

29 pages, 666 KiB  
Article
Hestenes–Stiefel-Type Conjugate Direction Algorithm for Interval-Valued Multiobjective Optimization Problems
by Rupesh Krishna Pandey, Balendu Bhooshan Upadhyay, Subham Poddar and Ioan Stancu-Minasian
Algorithms 2025, 18(7), 381; https://doi.org/10.3390/a18070381 - 23 Jun 2025
Viewed by 152
Abstract
This article investigates a class of interval-valued multiobjective optimization problems (IVMOPs). We define the Hestenes–Stiefel (HS)-type direction for the objective function of IVMOPs and establish that it has a descent property at noncritical points. An Armijo-like line search is employed to determine an [...] Read more.
This article investigates a class of interval-valued multiobjective optimization problems (IVMOPs). We define the Hestenes–Stiefel (HS)-type direction for the objective function of IVMOPs and establish that it has a descent property at noncritical points. An Armijo-like line search is employed to determine an appropriate step size. We present an HS-type conjugate direction algorithm for IVMOPs and establish the convergence of the sequence generated by the algorithm. We deduce that the proposed algorithm exhibits a linear order of convergence under appropriate assumptions. Moreover, we investigate the worst-case complexity of the sequence generated by the proposed algorithm. Furthermore, we furnish several numerical examples, including a large-scale IVMOP, to demonstrate the effectiveness of our proposed algorithm and solve them by employing MATLAB. To the best of our knowledge, the HS-type conjugate direction method has not yet been explored for the class of IVMOPs. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications (2nd Edition))
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18 pages, 984 KiB  
Article
A Linear Regression Prediction-Based Dynamic Multi-Objective Evolutionary Algorithm with Correlations of Pareto Front Points
by Junxia Ma, Yongxuan Sang, Yaoli Xu and Bo Wang
Algorithms 2025, 18(6), 372; https://doi.org/10.3390/a18060372 - 19 Jun 2025
Viewed by 145
Abstract
The Dynamic Multi-objective Optimization Problem (DMOP) is one of the common problem types in academia and industry. The Dynamic Multi-Objective Evolutionary Algorithm (DMOEA) is an effective way for solving DMOPs. Despite the existence of many research works proposing a variety of DMOEAs, the [...] Read more.
The Dynamic Multi-objective Optimization Problem (DMOP) is one of the common problem types in academia and industry. The Dynamic Multi-Objective Evolutionary Algorithm (DMOEA) is an effective way for solving DMOPs. Despite the existence of many research works proposing a variety of DMOEAs, the demand for efficient solutions to DMOPs in drastically changing scenarios is still not well met. To this end, this paper is oriented towards DMOEA and innovatively proposes to explore the correlation between different points of the optimal frontier (PF) to improve the accuracy of predicting new PFs for new environments, which is the first attempt, to our best knowledge. Specifically, when the DMOP environment changes, this paper first constructs a spatio-temporal correlation model between various key points of the PF based on the linear regression algorithm; then, based on the constructed model, predicts a new location for each key point in the new environment; subsequently, constructs a sub-population by introducing the Gaussian noise into the predicted location to improve the generalization ability; and then, utilizes the idea of NSGA-II-B to construct another sub-population to further improve the population diversity; finally, combining the previous two sub-populations, re-initializing a new population to adapt to the new environment through a random replacement strategy. The proposed method was evaluated by experiments on the CEC 2018 test suite, and the experimental results show that the proposed method can obtain the optimal MIGD value on six DMOPs and the optimal MHVD value on five DMOPs, compared with six recent research results. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications (2nd Edition))
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