## 7 Conclusions and Future Research Directions  
In this article, we have developed an HS-type conjugate direction algorithm to solve a class of IVMOPs. We have performed the convergence analysis, discussed the convergence rate, and investigated the worst-case complexity of the sequence generated by the proposed algorithm. The results established in this article have generalized several significant results existing in the literature. Specifically, we have extended the work of [PERSON] and [PERSON] [18] on the HS-type conjugate direction method for MOPs to a more general class of optimization problems, namely, IVMOPs. Moreover, it is worth noting that, if the conjugate parameter is set to zero and if every component of the objective function of the IVMOP is a real-valued function rather than an interval-valued function, then the proposed algorithm reduces to the steepest descent algorithm for MOPs, as introduced by [PERSON] and [PERSON] [5]. Furthermore, it is imperative to note that [PERSON]'s and quasi-Newton methods (see [PERSON] et al. [28; 29]) can be applied to solve certain classes of IVMOPs in which \begin{table}
\begin{tabular}{c c c} \hline \hline \(n\) & **Number of Iterations** & **Computation Times (in Seconds)** \\ \hline
100 & 4498 & 414.3 \\
120 & 4336 & 436.7 \\
140 & 4641 & 468.8 \\
160 & 4895 & 525.6 \\
180 & 4880 & 586.8 \\
200 & 4619 & 628.2 \\
220 & 4886 & 727.7 \\
240 & 4686 & 810.5 \\
260 & 4707 & 896.6 \\
280 & 5000 & 1044.4 \\
300 & 5000 & 1148.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The numerical results of Algorithm 1 for the problem (P3). the components of the objective function are twice continuously gH-differentiable as well as strongly convex. However, the HS-type conjugate direction algorithm proposed in this paper only requires the continuously gH-differentiability assumptions on the components of the objective function. In view of this fact, Algorithm 1 could be applied to solve a broader class of IVMOPs compared to the algorithms proposed by [PERSON] et al. [28; 29]. It has been observed that all objective functions in the considered IVMOP are assumed to be continuously gH-differentiable. Consequently, the findings of this paper are not applicable when the objective functions involved do not satisfy this requirement, which can be considered as a limitation of this paper. The results presented in this article leave numerous avenues for future research works. An important direction for future research is the exploration of hybrid approaches for IVMOPs that integrate a convex hybridization of different conjugate direction methods, following the methodology of [35]. Another key direction is investigating the conjugate direction method for IVMOP without employing any line search techniques, following the methodology of [42]. Moreover, in view of the works in [43; 44; 45], it would be interesting to develop a Hestenes-Stiefel-type conjugate direction algorithm to train neural networks under uncertainty, where intervals represent the model parameters or data, and to study the robustness of Algorithm 1 in the presence of noisy data. Conceptualization, B.B.U. and R.K.P. ; methodology, B.B.U. and R.K.P. ; validation, B.B.U., R.K.P., S.P., and I.S.-M.; formal analysis, B.B.U., R.K.P., and S.P. ; writing--review and editing, B.B.U., R.K.P., and S.P. ; supervision, B.B.U. All authors have read and agreed to the published version of the manuscript  
The first author would like to thank the University Grants Commission, New Delhi, India, for the received financial support (UGC-Ref. No. : 1213/(CSIR-UGC NET DEC 2017)). The third author extends their gratitude to the Ministry of Education, Government of India, for their financial support through the Prime Minister Research Fellowship (PMRF), granted under PMRF ID-2703573. No new data were created or analyzed in this study. Data sharing is not applicable to this article. The authors would like to thank the anonymous reviewers for their constructive suggestions, which have substantially improved the paper in its present form.