This paper presents an adaptive multi-tracker optimization algorithm (AMTOA) for global optimization problems with an emphasis on applications in chemical engineering. To obtain the AMTOA, first, several modifications are performed on the conventional multi-tracker optimization algorithm (MTOA). Then a number of its parameters are considered to be adaptive. The modifications include a novel way of determining the search radius of each global tracker (GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\text{T}}$$\end{document}), and introducing a more efficacious technique of searching for a new solution by GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\text{T}}$$\end{document}s. GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\text{T}}$$\end{document}s are the main components of the MTOA which look for the global optimal point (GOP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{GOP}}$$\end{document}). Additionally, the adaptation rules are employed for GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\text{T}}$$\end{document}s search radii and their searching parameters. These modifications lead to increasing the precision of the solution and reliability of the algorithm, both of which are the most important properties of an optimizer. Reducing the number of parameters of MTOA is another advantage of AMTOA. The results of applying this algorithm to several unconstrained and constrained general benchmarks along with several chemical engineering optimization problems reveal that AMTOA outperforms other well-known methods such as genetic algorithm (GA), particle swarm optimization (PSO), gray wolf optimizer (GWO), whale optimization algorithm (WOA), and conventional MTOA. Additionally, comparing the results of AMTOA to other advanced optimization algorithms such as LSHADE44, MA-ES, and IUDE show its superiority for chemical engineering optimization problems. Thus, the development of AMTOA could be advantageous to the area of chemical engineering.

中文翻译：

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全局优化问题的自适应多跟踪器优化算法：强调在化学工程中的应用

本文提出了一种用于全局优化问题的自适应多跟踪器优化算法 (AMTOA)，重点是在化学工程中的应用。为了获得 AMTOA，首先，对传统的多跟踪器优化算法 (MTOA) 进行了一些修改。然后它的一些参数被认为是自适应的。修改包括一种确定每个全局跟踪器搜索半径的新方法（GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\text{T}}$$\end{document}), GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} {-69pt} \begin{document}$$G_{\text{T}}$$\end{document} 是 MTOA 的主要组成部分，它寻找全局最优点 (GOP\documentclass[12pt]{minimal } \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document }$${\text{GOP}}$$\end{document}）。此外，适应规则适用于 GT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\text{T}}$$\end{document} 的搜索半径及其搜索参数。这些修改会提高解的精度和算法的可靠性，这两者都是优化器最重要的属性。减少 MTOA 的参数数量是 AMTOA 的另一个优点。将该算法应用于几个无约束和有约束的通用基准以及几个化学工程优化问题的结果表明 AMTOA 优于其他众所周知的方法，如遗传算法 (GA)、粒子群优化 (PSO)、灰狼优化器 (GWO)、鲸鱼优化算法 (WOA) 和传统的 MTOA。此外，将 AMTOA 的结果与 LSHADE44、MA-ES 和 IUDE 等其他高级优化算法的结果进行比较，显示了其在化学工程优化问题上的优越性。因此，AMTOA 的发展可能有利于化学工程领域。