离散变量结构优化设计的相对差商-遗传算法

将相对差商法(RDQA)和遗传算法(GA)结合起来,提出一个离散变量结构优化设计的有效解法———相对差商-遗传算法。3个算例结果显示出其优于相对差商法与遗传算法:(1)大大提高了遗传算法搜索全局最优解的能力及计算效率;(2)间接证明了相对差商法具有足够的逼近全局最优解的能力。

A relative difference quotient-genetic algorithm for discrete optimal designs of structures

The optimal designs of structures with discrete variables are very difficult problems.The existing methods have their own limitations.The relative difference quotient algorithm(RDQA) is an efficient method,which can find the local optimal solution.The main advantages of this method are: 1.There are no divergence and oscillation;2.It is not restricted to the scale of problems;3.The solution can be found quickly.It's weakness is that the ability to approach the global solution is not strong.The genetic algorithm(GA) has the advantage of finding the approximate global optimal solution,but consuming too much computing time is its weakness.In this paper,the RDQA is used at the first stage and the GA is used at the second stage in the whole procedure of optimization.At the first stage,a local optimal solution is obtained by the RDQA.And then the reduced allowable discrete sets e.i.S_i(i=1~n) of various variables are composed of the adjacent 4 or 8 elements at the two sides of the elements in S(the common allowable set for all variables),which are just those elements in the previous solution respectively.So the solution space of variables is greatly reduced from m~n(m-number of elements in S,n-number of variables) to 4~n or 8~n.At the second stage,the reduced sets S_i(i=1~n) are used in GA,and the computer time can be greatly saved.And the solutions obtained by this method and by the two original methods separately are compared with one another.It is shown that the combination of GA and RDQA is superior to each of the original two methods.This method will be more efficient for discrete optimum shape,topology and layout design of structures.