# A Multi-Objective Evolutionary Algorithm Model for Product Form Design Based on Improved SPEA2  
[PERSON]  
1 School of Mechatronics Engineering, Nanchang University, Nanchang 330031, China 12 School of Art and Design, Nanchang University, Nanchang 330031, China 2 [EMAIL_ADDRESS]  
[PERSON]  
1 School of Mechatronics Engineering, Nanchang University, Nanchang 330031, China  
apply aggregation on the objectives to transform multiple objectives into a single objective rather than directly using MOEA in the MOO module [4]. [PERSON] and [PERSON] [5] integrated the multiple objectives into a single value by using the linear weighting method, and then adopted a genetic algorithm (GA) to get the optimal product form based on the prediction model constructed by a fuzzy neural network (FNN). [PERSON] et al. [6] also integrated multiple objectives into a single objective by using the linear weighting method, and obtained the optimal design by employing GA on the basis of the prediction model established by using a back propagation neural network (BPNN). This kind of study is simple and easy to implement, but because it limits the search space and excludes the consideration of all possible solutions, it has limited practical value for designers and consumers [7]. The second kind of study is to use MOEA directly in the MOO module. Although the application is more complicated, it has become a mainstream trend because it can better meet the performance requirements of PFDMOEM. [PERSON] [8] proposed a PFDMOEAM with a non-dominated sorting genetic algorithm II (NSGA-II) as MOEA in the MOO module, and used support vector regression (SVR) to provide multi-objective fitness functions required by NSGA-II. [PERSON] et al. [9] also constructed a PFDMOEAM with NSGA-II as MOEA. The difference is that fuzzy neural network (FNN) is used to provide fitness functions for NSGA II. [PERSON] et al. [10] also adopted NSGA-II as MOEA and combined with quantification theory type I as the prediction model, based on which a PFDMOEAM was established. As a widely used second-generation classical MOEA, NSGA-II has less time complexity and better convergence. However, because the diversity it provides is not the best compared with other MOEAs [11], this algorithm is not an ideal MOEA for PFDMOEAM with innovation as its key performance. In addition to the algorithm, as a renowned second generation classical MOEA, strength Pareto evolutionary algorithm 2 (SPEA2) has been used in PFDMOEAM recently. [PERSON] et al. [12] proposed a PFDMOEAM using SPEA2 as the MOEA in the MOO module. [PERSON] et al. [7] completed the comparative study of MOEAs which are most suitable for PFDMOEAM. The study systematically compared the performance of three classical MOEAs represented by SPEA2, NSGA II, and another MOEA, and proved that SPEA2, which provides designers with the most diverse product forms, is the best MOEA for PFDMOEAM. This conclusion provides a reference for the selection of MOEA of the model proposed in this paper. However, the convergence of SPEA2 is insufficient [7], and due to the fixed evolutionary mechanism, SPEA2 cannot make full use of the search space and is easy to fall into a local optimum [13]. To fully exploit SPEA2's diversity and avoid its deficiencies, this paper proposes a novel improved SPEA2 (ISPEA2) algorithm and uses it as the MOEA in the MOO module of PFDMOEAM. In addition to MOEA, the PFIA method in the DA module is also crucial to the model's performance. However, the traditional PFIA methods have obvious limitations and deficiencies in the refinement of product morphological features and the comprehensive recognition of key perceptual images [14]. As such, we proposed an elliptical Fourier analysis (EFA) method that can improve the traditional PFIA methods effectively, and proved its feasibility and effectiveness [14].