Optimization analysis of gear profile modification based on genetic algorithm

In engineering design, there are many very complex optimization problems, which are often difficult to find the optimal solution by traditional optimization methods. Holland of the University of Michigan in the 1960s Professor et al. Established genetic algorithm by studying the adaptive behavior of natural and artificial systems, simulating the evolutionary view of population genetic selection and natural elimination. The great potential of genetic algorithm in solving complex optimization problems and its successful application in engineering design make it widely used in reliability design, group technology, plate layout, equipment layout and distribution Part structure optimization and other important engineering optimization fields. Genetic algorithm is a practical, efficient and robust optimization technology, which provides a general framework for solving complex system optimization problems such as non-linear, multi-model and multi-objective.

Genetic algorithm is a kind of adaptive global optimization probability search algorithm, which is formed by simulating the genetic and evolutionary process of living things in the natural environment. Its optimization process is the imitation of the evolution mechanism of living things. Its basic idea is derived from the natural law of biological genetics and survival of the fittest, and it is a search algorithm with the iterative process of “survival + detection”. First, the problem to be solved is represented as binary code or digital string, and the initial population (pulate) is generated.

The evolution of organisms is based on groups, so the operation object of the corresponding genetic algorithm is a set of m individuals called populations. Every individual in the population is a solution to the problem, which is called chromosome. It is similar to the natural evolution process of biological generation by generation. The operation process of genetic algorithm is also an iterative process. The chromosome is placed in the solution environment of the problem. According to the survival principle of the fittest, the fitness is used to determine the quality of the chromosome in each generation and generate The next generation of chromosomes is called offspring. The offspring is formed by the previous generation of chromosomes through selection, crossover and mutation. In the process of the formation of the new generation, selection is based on the individual’s adaptability. The higher the adaptability, the higher the chance of being selected, and the lower the adaptability, the lower the chance of being selected. The initial data can form a relatively optimized group through such a selection process, and then the selected individuals enter the cross operation process.

General genetic algorithm has a parameter of hybridization rate, which is generally 0.6 ~ 1. This hybridization rate reflects the probability of two selected individuals to carry out hybridization. Every two individuals produce two new individuals by crossing instead of the original ones, while the individuals without crossing remain unchanged, and their crossing positions are randomly generated. The next step is mutation, through which new offspring are produced. Generally, genetic algorithm has a fixed mutation constant, usually 0.01 or less, which represents the probability of mutation. According to this probability, the random mutation of a new individual’s chromosome is usually to change one byte of the chromosome (0 to 1, or 1 to 0). Through this series of processes (selection, hybridization and mutation), the new generation of individuals is different from the original generation, and the generation by generation develops towards the direction of increasing the overall adaptability, because the best individuals are always more selected to produce the next generation, while the ones with low adaptability are gradually eliminated. In this way, after several generations, the algorithm converges to the best chromosome, and it reaches or approaches the optimal solution of the problem. Its working principle is shown in the figure.