## 1 Introduction  
Underground engineering presents a series of unique challenges, particularly in the stabilization and deformation control of rock masses [1, 2, 3]. As mining depths increase, the complexity of managing rock mass behavior intensifies, primarily due to high-stress conditions, geological variability, and the influence of excavation methods [4, 5, 6]. This research addresses these challenges by focusing on the optimization of support systems and stress-relief measures within underground roadway, which is a critical issue in underground excavation projects [7, 8]. The control of surrounding rock in deep underground roadway is essential for maintaining structural integrity and ensuring operational safety [9, 10, 11, 12, 13]. One commonly employed method for mitigating stress and deformation is the implementation of stress-relief grooves [14, 15]. However, the effectiveness of these grooves, especially when considering various configurations and support conditions, remains a subject of ongoing investigation [16, 17]. Research on stress-relief grooves is relatively sparse, with most studies focusing on their field application rather than a systematic evaluation of different groove designs [14, 18]. This study aims to deepen the understanding of the impacts of different groove designs, particularly central and floor-side grooves, on the stability and deformation of rock masses [19]. Currently, artificial intelligence algorithms have a wide range of applications in various fields of mining engineering [20; 21; 22; 23; 24]. The Strengthened Elitist Genetic Algorithm (SEGA) was used to optimize machine learning models for predicting rock behavior [25; 26]. This approach not only enhances the accuracy of predictions but also promotes the effective application of multi-objective optimization techniques in geotechnical engineering [26; 27]. Building on this foundation, the study integrates multi-objective optimization techniques, specifically the Non-dominated Sorting Genetic Algorithm II (NSGA-II), to address complex optimization problems in geotechnical engineering. NSGA-II, as an advanced evolutionary algorithm, efficiently handles multiple performance metrics in multi-objective optimization, enabling the identification of Pareto optimal solutions [28; 29]. Despite being underutilized in geotechnical engineering, multi-objective optimization's capacity to simultaneously consider factors such as stress, deformation, and cost underscores its potential for optimizing complex engineering problems [30; 31; 32]. This research applies the NSGA-II algorithm to optimize the design of stress-relief grooves, significantly enhancing the overall performance and applicability of the solutions [29; 33]. Currently, in-depth research on floor grooving for stress relief is limited, and assessments of the optimal placement for floor grooving are mostly based on practical engineering conditions, lacking systematic theoretical support. Furthermore, there are few studies on the impact of floor grooving on the surrounding rock in deep mines. This paper aims to elucidate the effects of the grooving process on surrounding rock in deep mines, to assist onsite personnel in gaining a deeper understanding of the process and its rational application. This paper adopts a comprehensive approach to evaluate the performance of different groove parameters and develops new methods for monitoring stress and plastic zones to provide a detailed reflection of the rock mass state. Through feature engineering, key performance indicators are identified, and a thorough assessment of the impact of groove design on rock mass behavior is conducted. Concurrently, facing the conflicts in surrounding rock control caused by grooving for stress relief, this study proposes a multi-objective optimization approach combined with machine learning on small datasets to obtain optimal parameter solutions.