## 6 Experiments and Discussion
To generate an approximate locally weak effective solution set, we employ a multi-start approach, and \(|\alpha(\mathbf{u}^{(s)})|<\epsilon=10^{-4}\) or a maximum of \(1000\) iterations as the stopping criteria. Specifically, we generate \(100\) uniformly distributed random initial points and subsequently execute Algorithm 1 starting from each of these points. In view of the above fact, in Example 1 we generate a set of approximate locally weak effective solutions by selecting \(100\) uniformly distributed random initial points in the domain \([0,10]\times[0,10]\) using the \"rand\" function of MATLAB. The sequences generated from these points are illustrated in \[D_{gH}\mathcal{H}_{k}(u^{(s)},\mathfrak{o})+\frac{1}{2}\Big{[} \|\mathfrak{v}\|^{2},\|\mathfrak{v}\|^{2}\Big{]}\leq_{LU}[\alpha,\alpha],\]1  
**Remark 10**. : _It is worth noting that the objective function of problem (P1), presented in Example 1, is twice continuously gH-differentiable but not convex. Moreover, in view of the fact that [PERSON]'s and quasi-Newton methods for IVMOPs introduced by [PERSON] et al. [28; 29] are applicable to solve certain classes of IVMOPs in which the objective functions are strongly convex and twice continuously gH-differentiable, [PERSON]'s and quasi-Newton methods could not be applied to solve \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{s}\) & \(\mathbf{u}^{(\mathbf{s})}\) & \(\mathbf{w}^{(\mathbf{s})}\) & \(\boldsymbol{\eta}^{(\mathbf{s})}\) & \(|\boldsymbol{\alpha}(\mathbf{u}^{(\mathbf{s})})|\) \\ \hline
0 & \((-4,12)\) & \((10,-22)\) & \(0.125\) & \(292\) \\
1 & \((-2.75,9.25)\) & \((7.5,-16.5)\) & \(0.25\) & \(164.25\) \\
2 & \((-0.875,5.125)\) & \((3.75,-8.25)\) & \(0.5\) & \(41.062\) \\
3 & \((1,1)\) & \((-0.00099217,-0.00099217)\) & \(0\) & \(1.2\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sequence generated by Algorithm 1 for the problem (P1). Figure 1: Approximate locally weak effective solutions generated from 100 uniformly distributed random initial points. the problem (P1) presented in Example 1. Nevertheless, it has been demonstrated in Example 1 that our proposed algorithm, that is, Algorithm 1, effectively solves the problem (P1)._  
Moreover, in view of the works of [PERSON] et al. [28; 29], it can be observed that [PERSON]'s and quasi-Newton methods are applicable to solve certain classes of IVMOPs in which the objective functions of IVMOPs are twice continuously gH-differentiable as well as strongly convex. In contrast, our proposed algorithm only requires the continuously gH-differentiability 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]. To demonstrate this, we consider an IVMOP where the first component of the objective function is continuously gH-differentiable but not twice continuously gH-differentiable. **Example 2**. : _Consider the following problem (P2) which belongs to the class of IVMOPs._  
\[ \begin{array}{ll}\text{(P2)}&\text{Minimize}&(\mathcal{H}_{1}(\text{u}_{1 },\text{u}_{2}),\ \mathcal{H}_{2}(\text{u}_{1},\text{u}_{2})),\\ &\text{subject to}&(\text{u}_{1},\text{u}_{2})\in\mathbb{R}^{2},\end{array} \]  
_where \(\mathcal{H}_{1}:\mathbb{R}^{2}\to\mathfrak{C}(\mathbb{R})\) and \(\mathcal{H}_{2}:\mathbb{R}^{2}\to\mathfrak{C}(\mathbb{R})\) are defined as follows:_  
\[\mathcal{H}_{1}(\text{u}_{1},\text{u}_{2}):= \begin{cases}\Big{\{}\frac{(\text{ u}_{1}-3)^{2}}{2}+\text{u}_{1}\vee\frac{(\text{u}_{1}-3)^{2}}{2}+\text{u}_{1}+ \text{u}_{2}^{2}\Big{\}},&\text{if }\text{u}_{1}\geq 3,\\ \Big{\{}\frac{\text{u}_{1}^{2}}{4}-\frac{\text{u}_{1}}{2}+\frac{9}{4}\vee \frac{\text{u}_{1}^{2}}{4}-\frac{\text{u}_{1}}{2}+\frac{9}{4}+\text{u}_{2}^{ 2}\Big{\}},&\text{if }\text{u}_{1}<3,\end{cases}