# A Multi-Objective Evolutionary Algorithm Model for Product Form Design Based on Improved SPEA2
## 5 Conclusions  
To overcome the major obstacle that restricts the performance of traditional PFDMOEAMs, we have proposed a novel ISPEA2 algorithm. Taking ISPEA2 as the core and combining the EFA and entropy-TOPSIS methods, we have further constructed a novel PFDMOEAM and developed its simulation system in this paper. The simulation results verify the feasibility and effectiveness of the model.  
(1) Since MOEA is the key to determining the performance of PFDMOEAM, we have proposed a novel ISPEA2 algorithm based on the SPEA2 algorithm selected from the renowned second generation classical MOEAs. In addition to improving the original operators in SPEA2, the MO operator was introduced for the first time to optimize the performance of ISPEA2. Through these operators, ISPEA2 is superior to SPEA2 in convergence and diversity, which lays a solid foundation for improving the comprehensive performance of the model.  
(2) For a better complete model, we have further constructed a novel PFDMOEAM that combines ISPEA2, EFA and entropy-TOPSIS. It makes full use of the superiorities of these methods to maximize its comprehensive performance, which are the excellent convergence and diversity of ISPEA2 as MOEA algorithm, the high accuracy and degree of multi-method integration of EFA as PFIA method, and the good objectivity and operability of entropy-TOPSIS as the MADM method. Therefore, the model exhibits excellent comprehensive performance in multi-objective evolutionary design of product form.  
(3) A case study of car form design has been used to elaborate the process of the proposed model, and its simulation system has been developed. The simulation results demonstrate that the model can generate a variety of new car profiles that meet the multi-image objective, offer powerful support for the scientific MADM of car form optimization, and provide a universal and effective design tool for designers. Although this study takes car form as an example, the model is also applicable to the form design of other products.  
It is acknowledged that the proposed model needs to integrate many different methods, which makes the debugging process a bit complicated. However, this problem has been properly implemented in practice. In addition, this model is only used in the design of a 2D product profile. Further exploring  
Figure 12: Automatic simulation system of the proposed PFDMOEAM.  
the application of the model in 3D product form design and combining the model with product color design will be the focus of future research.  
The following are available online at [[http://www.mdpi.com/2076-3417/9/14/2944/s1](http://www.mdpi.com/2076-3417/9/14/2944/s1)]([http://www.mdpi.com/2076-3417/9/14/2944/s1](http://www.mdpi.com/2076-3417/9/14/2944/s1)).  
[PERSON], [PERSON] and [PERSON] conceived of and designed the study. [PERSON] and [PERSON] performed the experiments and analyzed the data. [PERSON] wrote the manuscript. [PERSON], [PERSON] and [PERSON] revised and polished the manuscript. All authors have read and approved the final manuscript.  
This work is supported by the National Natural Science Council of the Republic of China under Grant No. 71661023.  
The authors would like to thank all of the anonymous referees for the comments and suggestions, which have helped to improve the paper. In addition, the authors would like to thank the National Natural Science Council of the Republic of China for financially supporting this research.  
The authors declare no conflict of interest.