## 1 Introduction
These advancements underline the significance of adopting multi-objective optimization strategies in hub location problems, particularly for dynamic and critical infrastructures like telecommunication systems. Building on this historical context, our study integrates environmental constraints and employs advanced algorithms, such as NSGA-II and MOPSO, to address the contemporary challenges of BTS site selection in telecommunication networks. This combination of classical principles and modern methodologies ensures a robust and comprehensive approach to solving this critical problem. This paper presents a novel hybrid approach that integrates the strengths of NSGA-II and MOPSO, providing a more efficient and scalable solution for dynamic telecommunications network planning, incorporating environmental constraints and uncertainty factors [28; 29; 30]. The objectives commonly considered in hub location problems are summarized below. Cost is one of the most common objectives in hub location problems [9]. Costs come in various types, divided into variable and fixed costs. Variable costs include installation expenses, while fixed costs include relocation expenses [19]. Typically, in hub location problems, a unified objective comprising all types of costs is considered. Another objective is coverage, which is used in maximal coverage problems. In this case, an objective is added to the model to maximize demand coverage. Other objectives exist in hub location problems, but we will not delve into them here. In this study, we aim to establish a balance between objectives such as maximizing demand coverage, minimizing costs, and maximizing greenness in the hub location. This article presents a multi-objective mathematical programming model in which the objectives of cost, demand coverage, and greenness of location are considered, aiming to address hub location under a comprehensive perspective to examine the optimality of the current facility locations and, if necessary, relocate existing facilities or locate new facilities. In order to find an effective and efficient solution, factors of uncertainty are also addressed. Given the nature of the problem under study and researchers' opinions, the hub location model is NP-hard. To validate the mathematical model, initially, the Pareto front of optimal solutions will be evaluated using an epsilon-constraint approach, and ultimately, to validate the model on larger scales, metaheuristic algorithms will be utilized. This article consists of five sections. The first section discusses the problem under study. The second section reviews the research literature, and the third section presents the mathematical model. The fourth section analyzes the mathematical model, and finally, conclusions and future research recommendations are provided. The increasing demand for efficient telecommunication networks, coupled with growing environmental concerns, has highlighted the need for sustainable solutions in network planning. This study addresses these challenges by integrating green supply chain principles into the optimization of BTS site selection, providing a novel approach to balancing cost efficiency, demand coverage, and environmental impact. \"This study makes several contributions to the field of telecommunication network optimization. First, it introduces a multi-objective mathematical programming model for green facility location problems. Second, the paper incorporates environmental constraints into the problem formulation, offering a novel perspective. Third, the comparative analysis of NSGA-II and MOPSO algorithms highlights their respective strengths and weaknesses for NP-hard problems. Finally, the practical implications of this research extend to improving telecommunication infrastructure sustainability and efficiency.\"  
These contributions underscore the novelty of this research and its relevance to the ongoing challenges of green supply chain optimization and telecommunication network planning. In comparison to prior works, this study offers several distinct contributions.