## 1 Introduction  
Real-world optimization problems are inherently complex, often comprising multiple interdependent sub-problems. Traditionally, researchers address these challenges by decomposing such complex problems into independent sub-problems, solving them separately without considering their interactions. However, this approach overlooks the interdependencies among these sub-problems, leading to sub-optimal solutions that do not necessarily translate to optimal solutions for the entire problem [1]. To address this issue and better understand real-world complexities, the Traveling Thief Problem (TTP) was introduced as a benchmark problem [2]. TTP is a combinatorial optimization problem that integrates the Traveling Salesman Problem (TSP) and the Knapsack Problem (KP). The unique aspect of TTP lies in its ability to simulate the interdependencies between these two sub-problems, capturing the essence of real-worldoptimization scenarios where decisions made in one aspect of the problem influence outcomes in another. By modeling such interactions, TTP provides a more holistic approach to solving complex problems, making it a significant tool for researchers aiming to develop optimization algorithms that are more applicable to real-world situations. In the context of TTP, two variants are commonly studied: the single-objective TTP and the bi-objective TTP (BITTP), which is the focus of this paper. The BITTP not only seeks to optimize the route and item selection to minimize travel time and maximize profit but also offers a framework for studying trade-offs between conflicting objectives, which is crucial for real-world decision-making processes. Numerous scholars have explored diverse methodologies to tackle the single-objective TTP, leveraging a spectrum of approaches ranging from heuristic algorithms [3; 4; 5; 6] to swarm intelligence optimization techniques [7; 8; 9; 10]. In recent years, the Bi-Objective Traveling Thief Problem (TTP) has garnered significant attention, with various approaches being developed to address its unique challenges. The complexity of TTP arises from the interdependence between the Traveling Salesman Problem and the Knapsack Problem, making traditional single-objective methods insufficient. To tackle these challenges, researchers have proposed a range of multi-objective evolutionary algorithms, hybrid approaches combining dynamic programming, and specialized metaheuristics. These methods aim to optimize both the journey time and the total value of collected items while addressing the interrelated nature of the sub-problems. For instance, several studies have focused on multi-objective evolutionary algorithms, such as NSGA-II and its variants, which demonstrate robust performance across various TTP instances [11]. Others have integrated dynamic programming within evolutionary frameworks, showing significant improvements in solution quality, particularly for large instances [12]. Additionally, adaptive and specialized algorithms tailored to the unique facets of TTP instances have been proposed [13], further enhancing the effectiveness of these methods. Metaheuristic approaches like Variable Neighbourhood Search [14] and weighted-sum methods [15] have also been explored, offering competitive results compared to traditional optimization techniques. Moreover, the application of Ant Colony Optimization (ACO) [16] and the Imperialist Competitive Algorithm (ICA) has shown promise in improving best-known solutions across different TTP instances [17]. The following Table 1 summarizes these recent advancements in solving the Bi-Objective TTP, categorizing the studies based on their research focus, methods, and key contributions.