## 2 Literature Review  
Our literature review focuses on two key aspects: the methodologies of bi-objective optimization and the applications of bi-objective optimization, providing readers with a thorough understanding of both theoretical frameworks and practical implementations of bi-objective optimization. The first research stream is related to the methodologies for solving bi-objective optimization problems, which are summarized in Table 1. A mainstream way of dealing with two objectives in the case that the unit of neither objective can easily be converted into the unit of the other objective is multi-objective optimization methods [10], such as the weighting method and the \(\epsilon\)-constraint method [11,12]. The weighting method, a classic approach for solving multi-objective optimization problems, involves assigning an appropriate weighting coefficient to each objective function and optimizing the linear combination of these weighted objectives [13,14]. Hence, the multiple objective functions are transformed into a single objective function. [PERSON] et al. [15] addressed a vehicle routing problem of a mixed fleet of conventional and electric vehicles, aiming to minimize total operational costs and time penalty costs. To solve this problem, a linear weighting method was adopted to transform the bi-objective programming model into a single-objective programming model. The weighting method, however, has several pitfalls. A major pitfall is that nonsupported efficient solutions, which are dominated by the convex combination of two or more other Pareto optimal solutions, are unable to be generated, even though these solutions are still Pareto optimal. Another pitfall of the weighting method is that the \"quality\" of the subset of Pareto optimal solutions generated is hard to control or quantify. In other words, whether the subset of Pareto optimal solutions generated is a \"good representation\" of the full set of Pareto optimal solutions is unknown. The \(\epsilon\)-constraint method is also a primary approach for solving multi-objective optimization problems. The fundamental principle of the \(\epsilon\)-constraint method is to optimize a single objective while transforming the remaining objectives into constraints by setting an upper bound for them [16]. [PERSON] et al. [17] focused on the optimization of the thresholds in the ship risk profile, which is a method used for quantifying ship risk. A bi-objective mixed-integer nonlinear model was formulated. To facilitate linearization, a big-M method was adopted to obtain a linear model. Additionally, an \(\epsilon\)-constraint method was implemented to obtain all Pareto optimal solutions. [PERSON] et al. [18] proposed an \(\epsilon\)-constrained multi-objective optimization model considering road network data, population density, and building characteristics to optimize transportation routes, thus reducing transportation risks and costs. [PERSON] et al. [19] focused on a location-routing problem for hazardous materials, and formulated a bi-objective optimization model aiming to minimize transportation costs and risks, which was solved by an augmented \(\epsilon\)-constraint method. A real-world case study indicated that the decrease in warehouse capacity led to more costs and higher risks. With the development of multi-objective optimization, several other well-known techniques, such as the lexicographic method [20] and the global criterion method [21], have been introduced and continuously improved. Interested readers can refer to [PERSON] et al. [22] and [PERSON] et al. [23] for a comprehensive understanding. Moreover, emerging technologies, such as machine learning, are increasingly applied to the field of multi-objective optimization in recent years [24]. The second research stream is relevant to the applications of bi-objective optimization. Bi-objective optimization has a wide range of applications. Readers can refer to [PERSON] and [PERSON] [1], [PERSON] et al. [25], and [PERSON] and [PERSON] [26] for a comprehensive overview.