桁架优化遗传算法的若干改进

针对桁架优化问题研究二进制编码遗传算法，采用凝聚函数将约束优化问题转化为无约束优化问题，提出一种综合考虑约束值和适应度值的选择方法，保证了有潜力的设计被优先选择。并利用子代和父代之间的竞争使进化过程充分考虑以前最优值的遗传基因。算例表明，本文提出的方法是可行的，而且适应性更广。

IMPROVEMENTS ON GENETIC ALGORITHM FOR TRUSS STRUCTURAL OPTIMIZATION

A new algorithm--Genetic Algorithm (GA) is proposed for the design optimization of truss structures. GA has inherently better probability of searching the global optimum than the traditional gradient based optimization algorithms. The approach is ideally suited to minimizing or maximizing an unconstrained function; in general, its use to the constrained optimization problem is obtained through the use of the penalty function approach. A traditional penalty function formulation for treatment of nonlinear constrained optimization problems in genetic search has been shown to be extremely sensitive to user specified schedules of selecting penalty parameters. The sensitivity is manifested in biasing of the search toward suboptimal designs and a general increase in the number of function evaluations required obtaining a converged design. Handling constraints is motivated by the fact that both feasible and infeasible designs are generally present in population of designs at any generation. In this paper, surrogating function is adopted to convert constrained problems into unconstrained ones. It is differentiable and takes the maximum entropy theory as assistant rational rule. Previous reproduction is only based on fitness value, so it will result in failure of optimization if the selection of penalty parameters isn't suitable. To void the disadvantage, a new reproduction method considering both the fitness values and constraint values is proposed. Its basic idea is that it considers the design with the short distance from feasible domain and the design can enter the feasible domain by operating on the feasible design and potential design. This ensures potential designs to be chosen preferentially. Offspring and parent populations form an extent population, from which next generation population is chosen. This makes good individual not to be destroyed. Competing between offspring and parent takes into account the genetic inheritance of all the best individuals coming from previous generation. The two classical truss examples show that these methods are feasible, effective, and adaptive, and have improved the genetic algorithm. The method isn't sensitive to the selection of penalty parameter.