Multi-Objective Optimization Based on Artificial Intelligence and Evolutionary Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 14 June 2026 | Viewed by 155

Special Issue Editor


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Guest Editor
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Interests: computational intelligence; robotics; embodied intelligence

Special Issue Information

Dear Colleagues, 

Complex real-world challenges increasingly demand the integration of artificial intelligence (AI) and evolutionary algorithms (EAs) to address multi-objective optimization problems. These approaches synergize computational intelligence (including population-based heuristics), data-driven learning, and multi-criteria decision-making techniques to navigate high-dimensional, dynamic, and uncertain design spaces. The rapid evolution of AI-enhanced EAs—evidenced by surging publications and open-source tools—has reshaped fields from sustainable engineering to fintech. To harness this momentum, we invite contributions bridging AI, EAs, and decision-making to pioneer next-generation optimization frameworks. 

This Special Issue aims to unite researchers exploring AI–EA fusion for multi-objective optimization. We seek to foster cross-disciplinary dialogue between AI, evolutionary computation, and decision-making communities; accelerate the translation of theoretical advances into practical solutions; and highlight emerging applications requiring AI–EA hybridization. 

We welcome original research articles, reviews, and case studies on the following topics:

  • AI-Driven Optimization: Neural networks, reinforcement learning, transformers, and deep learning for surrogate modeling or adaptive operators;
  • Evolutionary and Swarm Intelligence: Novel EA variants (e.g., NSGA-III, MOEA/D), particle swarm, ant colony, or co-evolutionary algorithms;
  • Hybrid AI-EA Frameworks: Integration of machine learning with EAs for constraint handling, convergence acceleration, or preference articulation;
  • Large-Scale and Many-Objective Optimization: Scalable algorithms for >3 objectives, dimensionality reduction, and explainable Pareto fronts;
  • Constrained Multi-Objective Optimization: Novel constraint handling techniques for multi-objective optimization problems with constraints;
  • Uncertainty-Aware Optimization: Robustness under noise, fuzzy logic, Bayesian optimization, and stochastic environments;
  • Real-World Applications: Sustainable systems, Industrial 4.0, biomedicine, smart cities, climate modeling, financial portfolio optimization, and risk management.

Dr. Zhizhong Liu
Guest Editor

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Keywords

  • multi-objective evolutionary algorithms (MOEAs)
  • swarm intelligence
  • explainable AI in decision-making
  • constrained multi-objective optimization
  • high-dimensional Pareto fronts
  • data-driven surrogate modeling
  • robust optimization under uncertainty

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Published Papers (1 paper)

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43 pages, 7012 KB  
Article
Hybrid Mutation Mechanism-Based Moth–Flame Optimization with Improved Flame Update Mechanism for Multi-Objective Engineering Problems
by Zhifu Li, Ziyang Zheng, Haotong Huang, Haiming Liu, Peisheng Huang and Ge Ma
Mathematics 2026, 14(1), 134; https://doi.org/10.3390/math14010134 (registering DOI) - 29 Dec 2025
Abstract
Due to the complexity of multi-objective engineering problems, solutions obtained by many algorithms often exhibit poor distribution, and the algorithms tend to fall into local optima. To effectively alleviate these issues, an improved multi-objective moth–flame optimization algorithm (IETMFO) is proposed in this paper, [...] Read more.
Due to the complexity of multi-objective engineering problems, solutions obtained by many algorithms often exhibit poor distribution, and the algorithms tend to fall into local optima. To effectively alleviate these issues, an improved multi-objective moth–flame optimization algorithm (IETMFO) is proposed in this paper, with three core novelties: A hybrid mutation mechanism (integrating two mutation techniques) is first used to generate a new population, and then an indicator-based selection mechanism is adopted to produce a high-quality initial population, enhancing solution distribution. Enhanced Brownian motion is introduced as a local search strategy to reduce the risk of falling into local optima. An improved flame update mechanism is incorporated to maintain flame diversity, boosting the algorithm’s adaptability. The IETMFO is tested on 49 benchmark functions and 6 constrained engineering problems, and then compared with seven well-known algorithms (including NSGA-II, MOEA/D, and traditional MFO). The experimental results show the following: in benchmark function tests, IETMFO reduces the IGD value by an average of 32.7% and increases the HV value by an average of 28.5% compared with NSGA-II; on ZDT series functions, it outperforms the seven contrast algorithms in solution distribution uniformity; in the six engineering problems, its optimal solution proportion reaches 66.7%, and the risk of falling into local optima is reduced by 41.2%. These results demonstrate that the IETMFO achieves competitive performance in addressing multi-objective engineering problems. Full article
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