dynamic model with a large amount of computation。 Finally, DOE was combined with genetic algorithm to obtain the suspension system which had the optimal performance。

Based on the above analysis, the toe-in curve of the vehicle was optimized to research the influence with the change of drag link ball joint coordinates on the dynamic force of the  vehicle

suspension under pavement displacement excitation。 The variables were the y and z  coordinates

of the 2 ball joints。 Their positions are as shown in Fig。 4。 To ensure the static ride comfort of the

suspension, the sum of the error square for the solver toe-in angle and the objective toe-in angle of the vehicle was set as the constraint, and it was less than 30。 The optimization target was that the dynamic load acting on jounce bumper of suspension was minimal [14, 15]。

Fig。 8。 Finite element model of jounce bumper

In this paper, the genetic algorithm was used to optimize and design the suspension system, and its necessity can be explained from the following aspects。

1) The traditional genetic algorithm was easy to be premature, and the local optimization ability was poor。 In addition, the accuracy of results was not high。 Although the results can quickly reach about 90 % of the optimal solution, it often required a lot of time to reach the optimal solution。 This will undoubtedly increase the computational cost and reduce the computational efficiency。 The improved genetic algorithm was proposed based on DOE method in this paper。 This method was realized by adding DOE method into the iterative process, and it can quickly determine the design variable value and range。 As a result, it made inpiduals of the population continue to mutate according to the required direction, which effectively improved the searching ability of genetic algorithm。 Finally, it can accelerate the convergence speed and improve the computational efficiency。

2) If optimization design was directly conducted based on the suspension multi-body dynamic model, the iteration process will take a relatively long time and require higher computational cost due to the complexity of the multi-body dynamic model。 The improved genetic algorithm proposed based on DOE method can not only quickly determine the design variables during the iterative process, but also obtain the approximate model to replace the multi-body dynamics model。 As a result, the iterative process will be simple。 There were a lot of papers to combine DEO method with genetic algorithm。

3) The research in this paper was based on Hyperstudy which was the commercial software。 Genetic algorithm and DOE method were integrated into this software。 When we wanted to use the improved genetic algorithm, only some parameters of this software should be modified, and it will not take a relatively long time to design a new program for optimization。 As a result, it will obviously improve the computational efficiency, and it has been widely used。

The improved genetic algorithm was used to optimize the suspension system, and the corresponding flow was shown in Fig。 9。

The detailed description of the optimization flow was as follows。

1) Chromosome coding。 Each parameter of the suspension system was identified by DOE method and then the final design variable was obtained before searching。 Finally, the target

function was encoded into a binary string, and these strings were called as chromosome。 The different combinations of these strings were the different search points of the search space。

2) Generation of the initial population。 The initial population size was set to be 40。

3) Computing fitness。 Fitness will directly affect the accuracy of the computational results。 The objective function of the suspension system was taken as fitness value。