Optimizing the color spraying sequence of auto parts can help enterprises to further reduce the production costs. However, there is no research proposing specific mathematical models and solutions for this type of problems. Considering the fact that each auto part must be sprayed and sprayed only once, which has the basic characteristics of the Traveling Salesman Problem (TSP), a modeling method of TSP transformation was proposed and the Genetic Algorithm (GA) with strong parallelism and robustness was selected to solve it. Firstly, the auto parts were defined as the TSP vertices, and the distance between the vertices and production constraints were defined according to the color and category requirements of the auto parts, so as to construct a 0-1 planning model for minimizing the number of color switching of the spraying sequence. Secondly, the color and category constraints of the auto parts were transformed into penalty factors, so as to construct the fitness function of the genetic algorithm. And, based on the championship selection strategy, the mutation strategies of copying, swapping, flipping, and sliding were comprehensively designed. Finally, three sets of data with 64, 93, 293 auto parts and 5, 7, 10 colors were constructed for simulation experiments. The proposed algorithm can obtain the accurate optimal solutions 5, 7, 10 for all three sets of data. With repeatedly running the algorithm, the average values of the approximate optimal solution are 5.63, 7.37, 11.49. Experimental results show that the established mathematical model is accurate to describe the auto part spraying sequence problem, and the designed genetic algorithm is efficient and practical, both of them can be applied to other similar production and processing problems.

Current Discounted {0-1} Knapsack Problem (D{0-1}KP) model takes the discounted relationship as a new individual, so the repair method must be adopted in the solving process to repair the individual coding, making the model have less solving methods. In order to solve the problem of single solving method, by changing the binary code expression in the model, an expression method with discounted relationship out of individual code was proposed. Firstly, if and only if each involved individual encoding value was one (which means the product was one), the discounted relationship was established. According to this setting, a Simplified Discounted {0-1} Knapsack Problem (SD{0-1}KP) model was established. Then, an improved genetic algorithm-FG (First Gentic algorithm) was proposed based on Elitist Reservation Strategy (EGA) and GREedy strategy (GRE) for SD{0-1}KP model. Finally, combining penalty function method, a high precision penalty function method-SG (Second Genetic algorithm) for SD{0-1}KP was proposed. The results show that the SD{0-1}KP model can fully cover the problem domain of D{0-1}KP. Compared with FirEGA (First Elitist reservation strategy Genetic Algorithm), the two algorithms proposed have obvious advantages in solving speed. And SG algorithm introduces the penalty function method for the first time, which enriches the solving methods of the problem.