In computer science and operations research, genetic algorithm (GA) is a method inspired by the natural selection process and belongs to a larger class of evolutionary algorithms (EA). Genetic algorithms are often used to generate high-quality solutions for optimization and search problems by relying on bio-inspired operators such as mutation, crossover, and selection [11] . In genetic algorithms, a set of candidate solutions to optimization problems (called individual, creatures or phenotypic) evolve into a better solution. Each candidate solution has a set of attributes that can be mutated and changed (its chromosome or genotype). Traditionally, solutions are represented as strings in binary form, but other encodings are also possible. The implementation of genetic algorithms begins with a set of typical random chromosomes. These structures are then evaluated and assigned reproductive opportunities, providing better chromosomes with more reproductive opportunities than the chromosomes of poor solutions [12] .

Evolution usually begins with a randomly generated set of individuals and is an iterative process called generations. In each generation, assess the fitness of every individual in the population. Adaptability is usually the value of the objective function that solves the optimization problem. More suitable individuals are randomly selected from the current population, and each individual’s genome is modified (recombinant and possibly randomly mutated) to form a new generation. Then use the next generation of candidate solutions in the next iteration of the algorithm. Typically, the algorithm terminates when it produces the maximum generations or meets a satisfactory level of fitness.

The first step of genetic algorithm is population initialization. Since the genetic algorithm cannot directly deal with the parameters of problem, the feasible solution to the problem to be solved must be represented as a chromosome or an individual in the genetic space through coding. Common coding methods are grey coding, real coding, and structural coding. The real number coding does not have to be converted numerically, and the genetic algorithm operation can be performed directly on the expression of the solution. This article uses real coding to define each chromosome as real variable. Secondly, the fitness function is criterion to distinguish individual good from bad in a group, and is the only basis for natural selection. Generally, it is obtained by transforming an objective function. This article is to find the maximum value of the function as the individual fitness value. The larger the value of individual function is, the better the fitness is. Thirdly, the selection operation is to select a good individual from the old group with a certain probability to form a new group to multiply next generation of individuals. The probability that the individual is selected is related to the fitness value. The higher the individual fitness is, the greater the probability of being selected is. There are various methods for selecting the genetic algorithm, such as roulette method and competition game method. In this paper, the roulette method is adopted. Fourthly, cross operation refers to randomly selecting two individuals from population and transferring excellent genetic characteristics to substrings through the exchange combination of two chromosomes to generate new excellent individuals. Since individuals use real numbers, the crossover method uses real number method. Finally, the last step of genetic algorithm is mutation operation. The purpose of the mutation operation is to maintain the diversity of the population. The mutation operation selects one individual from the population and mutates to produce a better individual.

In this paper, a specific case is analyzed, we need to choose a shortest path that goes through all the points which are showed in Figure 1. There are five factors (the number of population, the number of generations, cross possibility, mutation possibility and generation gap) affecting the optimization performance of genetic algorithm. From Figure 2, we can see that as the value of population increases, the optimal results decrease and there will be some fluctuations in this process, indicating that the results are closer to optimal solution, so we can increase the value of population to improve the optimized performance. From Figure 3, we can see that as the value of generations increases, the optimal results decrease, indicating that the results are closer to optimal solution. Therefore, the performance of optimization can be improved by increasing the value of generations. From Figure 4, we can see that when the cross possibility is 0.5, the algorithm works best, and other values will reduce the optimization performance. From Figure 5, we can see that when the mutation possibility is 0.05, the

algorithm works best, and other values will reduce the optimized performance. From Figure 6, it can be seen that as the generation gap increases, the results continuously decrease, indicating that the results at this time are closer to the optimal solution. Therefore, the performance of optimization can be improved by increasing the value of generation gap.

Particle swarm optimization (PSO) originated from simulating the social behavior of birds, which was developed by Kennedy and Eberhart. In particle swarm optimization algorithm, each particle flies in the search space, and its speed is adjusted by its own flight memory and companion’s flight experience. All particles have fitness value determined by fitness function [13] . The main idea of the hybrid particle swarm algorithm is to integrate the genetic algorithm (GA) with the particle swarm algorithm (PSO). It consists of three major operators: enhancement, crossover and mutation. The first operator is enhancement. The enhancement operation attempts to simulate the maturation in the natural world, and the individuals become more suitable for the environment after changing. In addition, by using these enhanced elites as parents, the offspring will develop better than the original elite. In the PSO, the same generation promotes themselves based on their own private perceptions and social interactions. The second operator is crossover. In order to cultivate outstanding individuals, parents are selected from among the elites in the crossover operation. The adoption of crossover can be seen as an elite crossover to improve search capabilities. In hybrid particle swarm algorithm, in the case of the same generation of work, the crossover operation introduces the concept of evolutionary evolution and the survival of the social adaptation test. The third operator is mutation. In hybrid particle swarm optimization, mutations occur in crossover operations. Thus, mutation is operator in which genes are randomly altered so that new genes can be introduced into the population. However, we should use mutations with caution because it is random search operator. Uniform mutations are used here, which is randomly selected mutated genes from the corresponding search interval [14] .

In this paper, a specific case is analyzed, we need to choose a shortest path that goes through all the points which are showed in Figure 1. There are two factors (the number of generations and the number of individuals) affecting the optimization performance of hybrid particle swarm algorithm. From Figure 7, we can see that as the value of generations increases, the optimal results decrease rapidly at the initial stage and slowly at the latter stage. This indicates that the results are closer to the optimal solution. Therefore, with the value of generations increases, the optimized performance improves. From Figure 8, we can see that as the value of individuals increases, the optimized value decreases continuously, and it declines quickly in the early stage and slowly in the later stage. This shows that the results are closer to the optimal solution, so we can increase the value of individuals to improve the optimized performance.

The ant colony algorithm (ACO) is a method to simulate the behavior of ant foraging. It solves traveling salesman and quadratic distribution problems. Ants are social insects that behave more like group than individual [15] . The ant colony algorithm uses simple agent called ant to iteratively construct a solution to the optimization problem. Ant’s solution is guided by artificial pheromone trajectories and problem-specific heuristics. Basically, for optimization problem, the pheromone indicates the strength of the ant of the solution component, and the strength is determined based on the contribution of each solution component in the objective function. A single ant builds a complete solution by starting from an empty solution and adding components iteratively until a complete solution is built. After establishing a complete solution, each ant provides feedback on the solution by placing pheromones on each solution component. Typically, solution components are used as part of better solutions and ants are used in many iterations to get more pheromone, and they are more likely to be used in future iterations [16] . The ant colony algorithm mainly consists of the following four steps. The first step is initialization. Set the initial population of colonies

and pheromone trails. Randomly place the starting nodes of all ants. The second step is solution construction. Taking into account heuristic information dependence and problem path-tracking advantages, each ant chooses the next node that will not move with probability. Repeat this step until the solution building is complete. The third step is to update the path. The solution is evaluated according to the quality of the solution and stores the pheromone in the solution path. The better the solution is, the greater the amount of pheromone deposition is. The fourth step is the evaporation of pheromones. At the end of the iteration, in order to build a complete solution, the pheromone path is reduced by a constant factor [17] .

In this paper, a specific case is analyzed, we need to choose a shortest path that goes through all the points which are showed in Figure 1. There are six factors (the number of ants, the value of α, the value of β, the value of ρ, the value of Q, max iteration) affecting the optimization performance of ant colony algorithm. The value of α represents the importance factor of pheromone, the value of β represents the importance factor of heuristic function, the value of ρ is the pheromone evaporation coefficient, the value of Q is the factor of total pheromone release. From Figure 9, we can see that as the number of ants increases, the optimal results decrease, but there will be some fluctuations in the process, indicating that the results at this time are closer to the optimal solution. Therefore, increasing the number of ants can be used to improve optimized performance. From Figure 10, we can see that as the value of α increases, the optimal results keep rising and there will be some fluctuations in this process, which means that the results at this time are getting far away from the optimal solution. Therefore, the optimized performance can be improved by reducing the value of α. From Figure 11, we can see that with the increase of β, the optimization result decreases rapidly at the initial stage, and at this time, the optimal solution is continuously approached. When the value of β is close to 4, the optimal solution is obtained. As the value of β continues to increase, the optimal results will continue to increase, gradually deviating from the optimal solution. From Figure 12, we can see that as the value of ρ increases, the optimal results decrease rapidly at the initial stage, and at this point, the optimal solution is gradually approached. When the value of ρ is 0.3, the optimal solution is obtained. With the value of ρ continuing to increase, the optimal results will continue to increase, gradually deviating from the optimal solution. From Figure 13, we can see that with the increase of Q, the optimal results decline quickly at the initial stage, which are close to the optimal solution at this time. When the value of Q is 3, the optimal solution is obtained. As the value of Q increases, the optimal results will increase, gradually deviating from the optimal solution. From Figure 14, we can see that as the max iteration increases, the optimization results decrease rapidly

at an early stage, and then gradually tend to be flat. At this time, the optimal results are close to the optimal solution. Therefore, in order to obtain better optimal results, the max iteration should be increased.