10.57647/fomj.2026.0701.04

An ABS-GA Algorithm for Solving Fuzzy Optimization Problems

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  • Ali Mehrabian1,
  • Reza Ghanbari*1,
  • Khatere Ghorbani-Moghadam2,
  1. Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
  2. Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran

Received: 2026-01-05

Revised: 2026-02-10

Accepted: 2026-03-27

Published in Issue 2026-03-30

Copyright (c) 2026 Ali Mehrabian, Reza Ghanbari, Khatere Ghorbani-Moghadam (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Mehrabian, A., Ghanbari, R., & Ghorbani-Moghadam, K. (2026). An ABS-GA Algorithm for Solving Fuzzy Optimization Problems. Fuzzy Optimization and Modeling Journal (FOMJ), 7(1). https://doi.org/10.57647/fomj.2026.0701.04
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Abstract

This paper presents a fuzzy programming model with LR fuzzy coefficients. To solve it efficiently, we propose a novel hybrid ABS-GA algorithm that synergistically combines the ABS algorithm for dimensionality reduction with a Genetic Algorithm (GA). First, ABS projects the original n-dimensional problem into a reduced (n−m)-dimensional subspace using the linear constraints Ax = b, ensuring feasibility and shrinking the search space. Then, a tailored GA optimizes within this reduced space, employing Ghanbari et al. [1] O(1) comparison formula for direct and efficient fuzzy number evaluation, and a novel tangent cone-based mutation operator for enhanced local exploration. Numerical experiments demonstrate that ABS-GA significantly outperforms existing methods in both solution quality and computational efficiency, validating the effectiveness of the integrated approach.

Keywords

  • Triangular intuitionistic fuzzy regression model (IFRM),
  • Full IFRM,
  • Triangular intuitionistic fuzzy numbers (TIFNs),
  • Intuitionistic fuzzy least absolute of discrepancies (IFLAD),
  • Homogeneity principleFuzzy optimization,
  • Hybrid ABS-GA algorithm,
  • Fuzzy comparison,
  • LR fuzzy numbers,
  • Genetic algorithm
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