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RESEARCH ARTICLE

A new bio-inspired metaheuristic optimization algorithm for solving an optimal control problem based on type 2 diabetes mellitus

Amin Jajarmi1 ,  Raheleh Khanduzi2* ,  Seyed Reza Khandoozi3 ,  Asiyeh Ebrahimzadeh4
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1 Department of Electrical Engineering, University of Bojnord, Bojnord , Iran
2 Department of Mathematics and Statistics, Gonbad Kavous University, Gonbad Kavous , Iran
3 Cancer Research Center, Faculty of Medicine, Golestan University of Medical Sciences, Gorgan , Iran
4 Department of Mathematics Education, Farhangian University, Tehran , Iran
IJOCTA, 026290161 https://doi.org/10.36922/IJOCTA026290161
Received: 14 July 2026 | Revised: 1 October 2026 | Accepted: 29 October 2026 | Published online: 9 November 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Type 2 diabetes mellitus (T2DM) remains one of the most challenging chronic diseases because of its complex progression, multiple complications, and substantial healthcare costs. Designing cost-effective intervention policies therefore requires robust mathematical models and efficient optimization techniques capable of solv optimal control problems (OCPs). In this paper, we propose a novel bio-inspired metaheuristic, called the type 2 diabetes optimization algorithm (T2DOA), inspired by the physiological mechanisms governing glucose-insulin regulation. The algorithm incorporates four biologically motivated search operators, namely insulin resistance, insulin compensation, beta-cell exhaustion, and glucose feedback regulation, to achieve an adaptive balance between global exploration and local exploitation. We develop a comprehensive optimal control model to describe the progression of T2DM through six interacting epidemiological compartments and an auxiliary cumulative mortality variable. The model integrates five time-dependent intervention strategies: media awareness campaigns, community-based education, lifestyle modification, medical treatment for patients without complications, and intensive treatment for patients with complications. We first discretize the resulting OCP using a collocation method based on Genocchi polynomials and then solve it using the proposed T2DOA, yielding a hybrid computational framework. In addition to the computational methodology, we rigorously establish the mathematical properties of the epidemiological model, including positivity, boundedness, existence and uniqueness of solutions, invariant regions, equilibrium analysis, the diabetes progression threshold, and local stability of both disease-free and endemic equilibria. Numerical experiments demonstrate that the proposed hybrid approach efficiently computes high-quality control policies while effectively reducing the prevalence of pre-diabetes, diabetes-related complications, cumulative mortality, and intervention costs. Comparative analyses indicate that the T2DOA-based framework provides competitive optimization performance and constitutes a promising decision-support tool for sustainable diabetes management and public health policy planning.

Graphical abstract
Keywords
Type 2 diabetes
Optimal control
Metaheuristic optimization algorithm
Collocation method
Genocchi polynomials
Funding
This work was supported by Iran National Science Foundation (INSF), 4039690.
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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