## 2 Related Work  
MTO aims to conduct multiple tasks simultaneously through the use of knowledge transfer among different tasks. Supposing that there are \(K\) tasks to be completed and all of them are minimization problems. The \(j\)th task can be denoted as \(T_{j}\) with objective function \(f_{j}:\,X_{j}\longrightarrow\mathbb{R}\), in space \(X_{j}\). MTO aims to find a set of global optimal solutions \(\{x_{1}^{*},x_{2}^{*},\ldots,x_{k}^{*}\}\) which can satisfy  
\[x_{i}^{*}\;=\;\underset{x}{\text{argmin}}f_{i}(x),\,i\,\in\,\{1,2,\,\ldots,K\} \tag{1}\]  
MTO can solve multiple optimization tasks in a unified space and utilize similarities among different tasks to accelerate an optimization process, while single-task optimization just focuses on solving one task in one search space and finding the global optimal solution through vertical evolution. MFEA can transfer knowledge among different tasks by the interactions of genetic and cultural factors. During its operation, offspring not only inherit genetic factors, but also are influenced by habits and preferences of parents belonging to different tasks. To ensure different tasks can share useful optimization knowledge, it creates a unified search space for MTO problems. We first introduce some definitions related to individuals in MFEA [21]. Factorial Cost:The factorial cost of candidate \(p_{i}\) for a given task \(T_{j}\) can be given as \(\Psi_{j}^{i}=\Lambda\cdot\delta_{j}^{i}+f_{j}^{i}\), where \(\Lambda\) is a penalizing multiplier, \(f_{j}^{i}\) is an objective function value, and \(\delta_{j}^{i}\) represents the total constraint violation. Factorial Rank:The factorial rank \(r_{j}^{i}\) of individual \(p_{i}\) on task \(T_{j}\) is its index in the list of population members sorted in ascending order with respect to \(\Psi_{j}\). Scalar Fitness:The scalar fitness is calculated via the list of factorial ranks \(\{r_{1}^{i},\,r_{2}^{i},\,\ldots,r_{K}^{i}\}\), and \(\varphi_{i}=1/\min_{\{1,2,\ldots,K\}}\{r_{j}^{i}\}\). Skill Factor:The skill factor \(\tau_{i}\) is a task whose individual \(p_{i}\) performs the best, i.e., \(\tau_{i}=\operatorname*{argmin}_{j}\{r_{j}^{i}\}\), where \(j\ \ \{1,2,\ldots,K\}\). Since the appearance of the MFO [21], many improvements have been made. Considering that knowledge transfer of different optimization tasks is sensitive to negative inter-task interactions, [PERSON] et al. [34] proposed a novel evolutionary computation framework named MFAE-II. It can achieve online learning and explore similarities among distinct tasks. Based on MFAE-II, they further proposed a cognizant evolutionary multitasking approach called MO-MFEA-II to solve MOO problems [35]. [PERSON] et al. [23] proposed a self-regulated evolutionary multi-task optimization (SREMTO) that used an ability vector to reflect an individual's solving ability for solving each task. It can automatically adapt the intensity of cross-task knowledge transfer to different and varying degrees of relatedness among different tasks. [PERSON] et al. [36] proposed a surrogate-assisted multi-tasking memetic algorithm (SaM-MA) that used a surrogate model to assist an evolution procedure. [PERSON] et al. proposed an enhanced MTO framework named LDA-MFEA that derived linear transformations among solution spaces of component tasks [37]. Existing MTO algorithms only focus on solving a small number of tasks at the same time. If many tasks need to be solved, they would become ineffective in such complex multi-task environment. To handle many-tasking problems, [PERSON] et al. proposed a group-based MFAE to group similar tasks, such that the genetic information interaction could occur with the same group. To strengthen its effectiveness and efficiency, they further developed a new selection criterion and mating selection mechanism [38]. [PERSON] et al. proposed a framework named multisource selective transfer optimization that can choose source tasks well.