遗传算法在含连续/离散变量结构优化中的应用

Application of Genetic Algorithms to Structural Optimization with Mixed Continuous/Discrete Design Variables

传统的优化方法难于有效地处理含有连续／离散混合变量优化问题。本文探讨了如何将遗传算法应用于含连续／离散设计变量的结构优化问题。着重讨论了连续／离散混合变量的编码方法和减少适应度函数计算次数的ｍ ｉｃｒｏ ＧＡ 技术。将遗传算法应用于数学考题和十杆结构尺寸／材料混合变量优化问题。两个算例表明，遗传算法能比较有效地解决含连续／离散混合设计变量的优化问题。

Many engineering systems contain both continuous and discrete design variables. But the traditional optimization methods have difficulty to deal with the optimization problems with mixed continuous/discrete design variables. An application of genetic algorithms (GA) to the optimal design of a structural system with mixed continuous/discrete design variables is presented. The coding approach is proposed for such mixed design variables and a micro GA technique is utilized to reduce the computational load. Two examples are used to verify this method. The first one is a relatively simple problem which allows us to compare the GA with other methods in the context of convergent speed. The second optimization problem is a 10 bar truss structure with ten continuous design variables (cross sectional areas of each member) and ten discrete design variables (material type of each member). The results of the examples demonstrate that genetic algorithms may provide an efficient method for structural optimization with mixed continuous/discrete design variables.