Hybrid OC-GA Method
2.1 Hybridization Strategy
In the proposed OC-GA method, a local search Optimality Criteria algorithm is incorporated into the GA process and thus called as an OC operator, which has the ability of performing element sizing optimization for a selected topology. The GA framework first starts with a randomly generated initial population and then produces new offspring designs with random changes in both the topology and element sizing by crossover and mutation. Unlike the genetic operators, the OC operator is a deterministic gradient based algorithm which improves a design with predefined topology subject to the specified structural design constraints. The OC technique is an efficient local search method which can resize rapidly the element sizes through the use of a recursive algorithm that satisfies a set of prescribed necessary optimality conditions. The balance between the global exploration of topology by the GA and the exploitation of efficient local element optimization by the OC is crucial to the success of achieving progressively improved designs whilst avoiding the occurrence of premature convergence. To achieve a satisfactory cooperation between GA and OC, the proposed hybridization strategy involves promoting frequent topology changes in the GA and precluding premature dominant designs generated by the OC at the early generations.
Figure 1. Schematic of the hybrid OC-GA method
An application of the OC operator can be illustrated in Fig.1. At the nth generation, child designs are first recombined by crossover and mutation from the parent population. The OC operator is then applied to a portion of the child designs stochastically to undertake the local search OC element sizing optimization. The rate of OC, poc, denoting the probability of a child design that takes on the OC
operation, is used to control the application of the local search operator. If a randomly generated real number ranging from 0 to 1 is found to be smaller than a prescribed value of poc, the OC operator will then be invoked. In theory, the OC operator may be applied to every child design (i. e. when poc.=1). However, it may become impractical to do so for realistic structures with a large population due to the excessive computation required. It is important that an appropriate value of the probability of OC be determined to strike a right balance between computational efficiency and the quality of the optimised designs. After the fitness of each design is evaluated, an enlarged sampling selection (Gen and Cheng, 1997) is employed such that the population size is temporarily enlarged to contain both the parent and offspring designs during the selection process. Based on their fitnesses, the offspring designs are set to compete with their parents and the surviving candidates then form the next parent population in the (n+1)th generation.