Group Search Optimization for Applications in Structural Design

It is fairly accepted fact that one of the most important human activities is decision making. It does not matter what field of activity one belongs to. Whether it is political, military, economic or technological, decisions have a far reaching influence on our lives. Optimization techniques play an important role in structural design, the very purpose of which is to find the best ways so that a designer or a decision maker can derive a maximum benefit from the available resources. The methods of optimization can be divided into two category such as traditional optimization algorithms and modern optimization algorithms. The traditional optimization algorithms turn into an independent subject began in 1947 when Dantzig [1, 2] proposed the simplex method for solving general linear optimization problems. From then on, study on the optimization method is booming. Many methods of optimization are proposed [3] sequentially as follow: unconstrained optimization methods, large-scale unconstrained optimization methods, nonlinear least squares methods, linear constrained optimization methods, nonlinear constrained optimization methods and so on. These traditional mathematical gradient-based optimal techniques have been applied to the design of optimal structures [4]. While, many practical engineering optimal problems are very complex and hard to solve by traditional method [5].

In this chapter, we present an approach that integrates the finite element method (FEM) with a particle swarm optimization (PSO) algorithm to deal with structural optimization problems. The proposed methodology is concerned with two main aspects. First, the problem definition must be established, expressing an explicit relationship between design variables and objective functions as well as constraints. The second aspect is to resolve the minimization problem using the PSO technique, including the use of finite element method. In this chapter, particle swarm optimizer is extended to solve structural design optimization problems involving problem-specific constraints and mixed variables such as integer, binary, discrete and continuous variables. The standard PSO algorithm is very efficient to solve global optimization problems with continuous variables, especially the PSO is combined with the FEM to deal with the constraints related with the boundary conditions of structures controlled by stresses or displacements. The proposed algorithm has been successfully used to solve structure design problems. The calculation results show that the proposed algorithm is able to achieve better convergence performance and higher accuracy in comparison with other conventional optimization methods used in civil engineering.

This chapter introduces the application of an improved particle swarm algorithm to optimal structure design. The algorithm is named heuristic particle swarm optimization (HPSO). It is based on heuristic search schemes and the standard particle swarm algorithm. The efficiency of HPSO for pin connected structures with continuous variables and for pin connected structures and plates with discrete variables is compared with that of other intelligent algorithms, and the implementation of HPSO is presented in detail. An optimal result of a complex practical double-layer grid shell structure is presented to value the effectiveness of the HPSO.

This chapter introduces a novel optimization algorithm, group search optimizer (GSO) algorithm. The implementation method of this algorithm is presented in detail. The GSO was used to investigate the truss structures with continuous variables and was tested by five planar and space truss optimization problems. The efficiency of GSO for frame structure with discrete variables was valued by three frame structures. The optimization results were compared with that of the particle swarm optimizer (PSO), the particle swarm optimizer with passive congregation (PSOPC) and the heuristic particle swarm optimizer (HPSO), ant colony optimization algorithm (ACO) and genetic algorithms (GA). Results from the tested cases illustrate the competitive ability of the GSO to find the optimal results.

This chapter introduces the improvement and application of swarm algorithm named Group Search Optimizer (GSO) in civil structure optimization design. GSO is a new and robust stochastic searching optimizer, as it is based on PS (produce and scrounger) model and the animal scanning mechanisms. An improved group search optimizer named IGSO was presented based on harmony search mechanism and GSO. The implementation of IGSO for different optimal purposes is presented in detail, including the application of IGSO to truss structure shape optimal design, to truss structure dynamic optimal design, to truss structure topology optimization design. Different truss structures are used to test the GSO and IGSO in structural shape optimization, dynamic optimization and topology optimization.

Based on the basic principles of an optimization algorithm, group search optimization (GSO) algorithm, two improved GSO, named quick group search optimizer (QGSO) and quick group search optimizer with passive congregation (QGSOPC), are presented in this chapter to deal with structural optimization design tasks. The improvement of QGSO has three main aspects: first, increase the number of ‘ranger’ when the target stops going forward. Second, use the search strategy of particle swarm optimizer (PSO) by considering the best group member and the best personal member. Employ the step search strategy to replace the visual search strategy. Third, reproduce the ‘ranger’ with hybrid of the group best member and the personal best member. the QGSOPC is a hybrid QGSO with passive congregation. The QGSO is tested by planar and space truss structures with continuous variables and discrete variables. The QGSOPC is only tested by discrete variables. The calculation results of QGSO and QGSOPC are compared with that of the GSO and HPSO. The results show that the QGSO and QGSOPC algorithms can handle the constraint problems with discrete variables efficiently, and the QGSOPC has more efficient search ability, faster convergent rate and less iterative times to find out the optimum solution.

There are some problems in multi-objective optimization of engineering structures, such as, the difficulties in dealing with the constraints, the complexity of program and the low computational efficiency. To solve these problems, an improved group search optimizer, named Multi-objective Group Search Optimizer (MGSO), and combined with Pareto solutions theory is presented in this chapter. Different types of examples are employed to evaluate the performance of MGSO, including truss structures and frame structures with continuous variables or discrete variables. The calculation results show the feasibility, practicality and superiority of MGSO in structure optimal design. As a stochastic algorithm, MGSO has excellent performance in terms of convergence rate. Only the best individual is needed to be selected and partial constraints are needed to be checked to find the producer, thus a great deal of computational time is saved. The MGSO is of obvious advantages for complex engineering problems especially for high-dimensional ones.

As reviewed in previous chapters, there are only a few optimization algorithms inspired by animal behavior, including ACO, PSO and GSO. Although, PSO and GSO both are swarm intelligence (SI) optimization algorithms and draw inspiration from animal social forging behavior, both of them were initially proposed for continuous function optimization problems, then they were developed for discrete optimization problems, they have some obvious differences. It is not difficult to note from previous discussion that there are major difference between PSO and GSO. The first and the most fundamental one is that the PSO was originally developed from the models of coordinated animal motion. Animal swarm behavior, mainly bird flocking and fish schooling, serves as the metaphor for the design of PSO. The GSO was inspired by general animal searching behavior. A genetic social foraging model, e.g., PS model was employed as the framework to derive GSO. Secondly the producer of GSO is quite similar to the global best particle of PSO, the major difference is the producer performs producing, which is a search strategy that differs from the strategies performed by the scroungers and the dispersed members. While, in PSO each individual performs the same searching strategy. Thirdly, in GSO the producer remembers its head angle when it starts producing. In PSO each individual maintains memory to remember the best place it visited. Finally, unlike GSO, there is no dispersed group members that perform ranging strategy in PSO.