Truss topology optimization using an improved species-conserving genetic algorithm

Jian-Ping Li
2014 Engineering optimization (Print)  
The aim of this paper is to apply and improve the species conserving genetic algorithm (SCGA) to search in a single run multiple solutions of truss topology optimization problems. A species is defined as a group of individuals with similar characteristics and is dominated by its species seed. The solutions of an optimization problem will be selected from the found species. In order to improve the accuracy of solutions, a species mutation technique is introduced to improve the fitness of the
more » ... d species seeds and the combination of a neighbor mutation and a uniform mutation is applied to balance exploitation and exploration. A real-vector is used to represent the corresponding cross-sectional areas and a member is thought to be existent if its area is bigger than a critical area. A finite element analysis model has been developed to deal with more practical considerations in modeling, such as existences of members, kinematic stability analysis and the computation of stresses and displacements. Cross-sectional areas and node connections are decision variables and optimized simultaneously to minimize the total weight of trusses. Numerical results demonstrate that some truss topology optimization examples have many global and local solutions and different topologies can be found by using the proposed algorithm on a single run and some trusses have smaller weight than the solutions in the literature. Jian-Ping Li 1985; Hajela and Lee 1995), when a topology analysis is performed based on a ground structure, member cross-sectional areas and truss configurations are assumed to be fixed. Once a topology is found, the member areas and /or configuration of the obtained topology are optimized. It is obvious that such a method may not always provide a global solution. When genetic algorithms are used, the cross-sectional areas of members are represented by strings of some binary data. Grieson and Pak (1993) suggested the use of an extra bit to indicate the existence of a member. Ohsaki (1995) added a topological bit to the left of each string to indicate the existence of a member. Su et al. (1990) used two separate matrixes to present the cross-sectional areas and the existences of members. A random number is generated to decide the value of each topological bit in the individuals in the initial generation. Deb and Gulati (2001) introduced a new methodology to present the existences of members so that the cross-sectional areas and topologies can be optimized simultaneously. A real-vector is used to present the cross-sectional areas of a ground structure. When the cross-area of one member is bigger than a given critical number, which is the minimum cross area and a positive number, it is assumed that the corresponding element is existent; otherwise it is assumed to be absent. Generally, the lower limits of cross-sectional areas are less than the critical number. Since cross-sectional areas are real numbers, a real-coded genetic algorithm should be used. Deb and Gulati (2001) applied a simulated binary crossover (SBX) and a parameter-based mutation operator (Sue et al. 2009) to solve truss optimizations. Truss optimization is also complex, in which there are many constraints, such as stresses, displacements, and buckling (Rozvany 1996) . The number of stress constraints is dependent on the number of elements, and the number of displacement constraints is the function of nodes or dependent to requirements. Generally, when the cross sectional area of a bar member increases, the weight of the bar will increase and its stress will decrease. A solution should be located on boundaries of constraints. All intersectional points of constraints are potential solutions, therefore, a truss optimization may have multiple solutions and most of them are local optimal solutions. In order to search global solutions, the species conserving genetic algorithm (SCGA) (Li et al. 2002) is improved and applied in this paper to solve truss topology optimization problems. This paper is organized as follow: Section 2 describes the general forms of truss topology optimization problems. In Section 3, the strategies of improving the species conserving genetic algorithm (SCGA) are presented. In Section 4, a number of truss topology optimization problems from the literature are solved with the proposed algorithms. Finally, some conclusions are included in Section 5. Truss Topology Problems A truss structure is a collection of bar members. The end points of members (bars) are called nodes and a member is a connection of two nodes. Mathematically, a truss topology optimization problem can be formulated as a nonlinear programming problem (Deb and Gulati 2001):
doi:10.1080/0305215x.2013.875165 fatcat:hrlvih6ntfflhm6qm2kklmndtu