Swarm intelligence algorithm (Swarm Intelligence Algorithm) belong to the new advanced heuristic algorithm, in 90 began to grow in the 20th century, there have been a mimic natural biological group behavior structure stochastic optimization algorithm. Typical methods mainly include the proposed ACO and PSO. Ant Colony Algorithm is a type of colony intelligence algorithm proposed by Dorigo in the 1990s and designed according to the principle of ant foraging. It is also the earliest form of ant colony algorithm. In the process of foraging, many ants have the behavior of setting and following trails [17]. The agent secretes a chemical pheromone from the route of the nest in the food source area, and other foragers will follow the pheromone path to search for food resources. Its principle is a system of positive feedback mechanism, which converges to the optimal path through constant updating of pheromones [18]. Therefore, ant colony algorithm is also a reinforcement learning method based on Monte Carlo. PSO is an intelligent simulation optimization process based on the foraging conduct of birds proposed by Kennedy and Eberhart in 1995. Due to its unpretentious concept and easy implementation, the algorithm has been rapidly developed in just a few years, and many improved particle swarm optimization algorithms have emerged. Baskar proposed his own collaborative PSO algorithm, and improved the particle swarm optimization by optimizing different dimensions of multiple particle swarm and collaborative optimization. Higashi proposed the self-mutation PSO algorithm, and enhanced its global search capability by introducing mutation operator to jump out of the attraction of local extreme point [19]. The multi-phasepso proposed by Al-Kazemi is that the individuals searching for the selected part of the particle population are constantly moving in the direction of global optimization, while the other individuals are constantly moving in the opposite direction, thus expanding the spatial scope of the search. Shelokar heterozygous PSO algorithm and ACO algorithm. Kao heterozygosity genetic algorithm and PSO algorithm. Brits applies PSO to search for multiple optimal values [20, 21]. Kiranyaz proposed a multidimensional space search method for PSO. Based on genetic algorithm and PSO, Cui Guangzhao proposed an improved PSO. Yu Xuejing set the sensitive particles and response threshold, and proposed the dynamic particle swarm optimization algorithm. Since Schmit combined mathematical programming theory with finite element method for solving the minimum weight design problem of elastic structures under various loading conditions, the new idea of structural optimization design quickly attracted the attention of structural design engineers. In the past few years, the structural optimization has become one of the hot research directions in structural engineering [22].
For truss structure, given the structure form, material, layout topology and shape, optimizing each member of the section size to make the structure the lightest or the most economical is called size optimization. The design variable in dimension optimization is the cross-sectional area of the member. For the optimal design of discrete variable structure, the algorithm usually determines the efficiency of calculation and the quality of results [23]. In the arena of structural optimization, traditional optimization algorithms, such as Optimization Criterion (OC) and Mathematical Programming (MP), have been widely used in the past decades. OC method is more effective for optimization problems with single constraints, it is easy to get iterative formula, and the convergence speed is fast. However, for optimization problems with multiple constraints, OC method is difficult to determine whether the constraints are effective or not. Different kinds of constraints, variables, objective functions and so on, are required for deriving different optimization criteria, so the generality is poor. The MP method can attain the global optimal solution of convex optimization and non-convex optimization problems [24]. It is a precise solution method and can be directly applied to continuous variable structure optimization. However, when MP is used to optimize large-scale structural systems, there are many times of structural reanalysis, which requires a large amount of storage space, a large amount of computation, and the algorithm is poor in generality. Any parameter change may cause the failure of the algorithm. Therefore, it is only suitable for the optimization of components, but not for the optimization of large structural systems. Recently, heuristic algorithms like GA and simulated annealing algorithm (SA) have emerged in the field of engineering structure optimization design [25]. GA has no requirement for continuous differentiability of the optimization model, and it can search the global optimum solution, so it has been widely used. However, GA mainly has some disadvantages, such as the difficulty in determining the population-size, cross-over, mutation rate, time-consuming, etc. However, when SA is used for structural optimization design, there are many times of structural reanalysis, large calculations, low efficacy and problematic determination of control parameters [26, 27].
PSO algorithm is a swarm intelligence algorithm based on stochastic optimization technology proposed by Eberhart and Kennedy under the stimulation of the social conduct of birds and fish. PSO shares many characteristics with GA, for example, the system is adjusted with a randomly distributed population, and the optimal solution is found by updating the evolutionary generation. Unlike GA, PSO has no evolutionary operators like cross-over and mutation. In the PSO algorithm, the possible solution called particle follows the current optimal particle to fly in the solution space, and each particle has an adaptive value and a velocity obtained according to the best experience of the group to adjust its flight direction in the multi-dimensional solution space to discover the global optimal solution [28]. Compared with traditional optimization algorithms and other evolutionary algorithms, PSO has some unique advantages: First, PSO has memory function, and each particle retains the optimal solution it has experienced; Secondly, in PSO, there are constructive operators among particles, that is, the information between particles is shared among the population. Third, the principle of PSO is simple, only a few parameters need to be adjusted, and it is easy to implement in the algorithm. As a novel evolutionary algorithm, PSO is getting more and more attention and application due to its simplicity, easy execution and fast convergence. In structural engineering, there are few literatures on PSO based on actual structural system optimization [29].
The innovation point of this paper: this paper applies PSO algorithm to the size optimization of truss structures, and evaluates the effect of using PSO algorithm to optimize the size of truss structures by solving typical illustrations and comparing with the results of relevant literatures.