## 2 Related Work
### Multifactorial Evolutionary Algorithm  
As mentioned in Section 2.2, we need a strategy for optimizing population that not only addresses multiple goals simultaneously, user preference surrogate models, but also transfers information between models during the evolution of the population. It is worth noting that finding satisfactory items for each dimension of preferences can provide a wider choice of perspectives, which can likewise improve the diversity of recommendations. Considering an optimization task of each preference model as a unit of work, the multifactorial evolutionary algorithm (MFEA) [16] capable of optimizing multiple related tasks simultaneously is a natural selection. Optimization of multiple tasks differs from optimization of multiple objectives [35] in that the former aims to find the optimal solution for each task, whereas the latter seeks to discover a set of Pareto solutions. MFEA is structured similarly to a classical evolutionary algorithm, making it more economical to find new items for each preference by migrating the features of different tasks in each population iteration. In the case of related problems, transferring knowledge between different problem solutions will improve performance over solving problems in isolation [36; 37; 38].  
MFEA is a classic algorithm in the field of evolutionary multitasking, as described in Algorithm 1. One of the most essential innovations in MFEA is the skill factor \((\tau)\), which represents the task to which an individual is most suited to solve among all the tasks. Each task is a unique factor that affects the evolution of a single population of individuals, so the population is implicitly divided into multiple skill groups by skill factors, each of which is good at solving corresponding tasks. Two components of MFEA control the inter-tasks (different skill groups) and intra-tasks (identical skill groups) knowledge transfer for the population: assortative mating and vertical cultural transmission, as shown in Steps i and ii of Algorithm 1. Assortative mating controls two randomly selected parental candidates to perform the crossover. Two candidates with the same skill factor can mate directly. Conversely, crossovers are performed between candidates with different skill factors if the random mating probability \((rmp)\) condition is satisfied; otherwise, mutation is performed.  
Vertical cultural transmission means that individuals of the offspring randomly inherit the skill factors from their parents and evaluate only the task corresponding to the skill factor.  
```
1:Generate an initial population of individuals and store it in current-pop(P).
2:Evaluate every individual with respect to every optimization task in the multitasking environment.
3:Compute the skill factor \((\tau)\) of each individual.
4:while stopping conditions are not satisfied do
5: i. Apply genetic operators on current-pop to generate an offspring-pop(C). (Assortative Mating)
6: ii. Evaluate the individuals in offspring-pop for selected optimization tasks only. (Vertical Cultural Transmission)
7: iii. Concatenate offspring-pop and current-pop to form an intermediate-pop (P \(\cup\) C).
8: iv. Update the scalar fitness \((\varphi)\) and skill factor \((\tau)\) of every individual in intermediate-pop.
9: v. Select the fittest individuals from intermediate-pop to form the next current-pop(P).
10:endwhile
```  
**Algorithm 1** Basic structure of the multifactorial evolutionary algorithm  
Since MFEA is effective at solving multiple tasks and has not been extended to IEAD-based personalized recommendation, it is necessary to carry out a corresponding study to improve further the IEAs performance in optimizing personalized recommendation. Using the useful knowledge implied between preferences, knowledge migration is performed by gene selection, crossover, and mutation at the chromosome level. This is carried out to mine further desired items of the user under every preference.