## 2 Review of Related Works  
The foundational work on IVOPs is attributed to [PERSON] and [PERSON] [22], who investigated IVOPs by transforming them into corresponding deterministic MOPs. [PERSON] [23] derived optimality conditions for a class of constrained IVOPs, employing the notion of Hukuhara differentiability and assuming the convexity hypothesis on the objective and constraint functions. Moreover, [PERSON] [24] developed Karush-Kuhn-Tucker-type optimality conditions for IVOPs and derived strong duality theorems that connect the primal problems with their associated dual problems. [PERSON] and [PERSON] [25] explored IVOPs by defining interval-valued functions in parametric forms. More recently, [PERSON] et al. [26] proposed a gradient-based descent line search technique employing the notion of generalized Hukuhara (gH) differentiability to solve IVOPs. [PERSON] and [PERSON] [27] studied IVMOPs by transforming them into their corresponding deterministic MOPs and establishing the relationships between the solutions of IVMOPs and MOPs. [PERSON] et al. [28] introduced [PERSON]'s method for IVMOPs and established the quadratic convergence of the sequence generated by [PERSON]'s method under suitable assumptions. Subsequently, [PERSON] et al. [29] developed quasi-Newton methods for IVMOPs and demonstrated their efficacy in solving both convex and non-convex IVMOPs. For a more comprehensive and updated survey on IVMOPs, we refer [30; 31; 32; 33] and the references cited therein. The conjugate direction method was first introduced by [PERSON] and [PERSON] [17], who developed the conjugate gradient method to solve a system of linear equations. Subsequently, [PERSON] and [PERSON] [18] introduced the HS-type conjugate direction algorithm for MOPs by employing an inexact line search. [PERSON] et al. [34] introduced an HS-type conjugate direction algorithm for MOPs without employing line search techniques, and established the global convergence of the proposed method under suitable conditions. Recently, based on the memoryless Broyden-Fletcher-Goldfarb-Shanno update, [PERSON] and [PERSON] [35] presented a convex hybridization of the Hestenes-Stiefel and Dai-Yuan conjugate parameters. For a more detailed discussion on the conjugate direction method, we refer to [18; 36] and the references cited therein. From the above discussion, it is evident that HS-type conjugate direction methods have been developed to solve single-objective problems as well as MOPs. However, there is no research paper available in the literature that has explored the HS-type conjugate direction method for IVMOPs. The aim of this article is to fill the aforementioned research gaps by developing the HS-type conjugate direction method for a class of IVMOPs. Motivated by the works of [17; 18; 34], in this paper, we investigate a class of IVMOPs and define the HS-type direction for the objective function of IVMOPs. A descent direction property of the HS-type direction is established at noncritical points. To determine an appropriate step size, we employ an Armijo-like line search. Moreover, an HS-type conjugate direction algorithm for IVMOPs is presented, and the convergence of this algorithm is established. Furthermore, under appropriate assumptions, we deduce that the proposed algorithm exhibits a linear order of convergence. In addition to this, the order of complexity of the proposed algorithm is investigated. Finally, the efficiency of the proposed method is demonstrated by solving various numerical problems employing MATLAB. The primary contribution and novel aspects of the present article are as follows:  
* The results presented in this paper generalize several significant results from the existing literature. Specifically, we generalize the results established by [PERSON] and [PERSON] [18] on the HS-type method from MOPs to a more general class of optimization problems, namely, IVMOPs. * The algorithm introduced in this paper is more general than the steepest descent algorithm introduced by [PERSON] and [PERSON] [5].