Discrete Optimization of Structures under Dynamic Loading by using Sequential and Parallel Evolution Strategies

Evolution Strategies in Engineering Optimization

“…(7). For structural optimization problems, according to our research [3], a suitable I value ranges from 8 to 12. The first line in Eq.…”

“…There are 6 geometrical variables: XI, x2 and x3 define the z-coordinates of three levels as shown in Figure 4; x4 is the distance AS, BS and CS in the x-y-plane at the level of the nodes 4, 5 and 6; similarly x, and x6 are the distances at the level of 7-8-9' and 10-11 -12, respectively. Moreover, five sizing variables are defined: x7 is the crosssectional area of the elements defined by the pairs of nodes (1,4), (2, 5) and (3,6); xg is the cross-sectional area of the elements defined by (4, 7), (5,8) and (6,9); x9 is the cross-sectional area of the elements defined by (7, lo), (8, I I) and (9, 12); xlo is the cross-sectional area of the elements defined by (10, 13), (1 1, 14) and (12, 15); x, is the crosssectional area of the remaining elements.…”

Advanced solution methods in structural optimization based on evolution strategies

“…This means that (n-l) components of the randomly changed vector Z (g) have zero value. The components of the randomly changed vector Z (g) have the form (Cai, 1995;Cai and Thierauf, 1993): 7where δx i is the current difference between two adjacent values in the discrete set and κ is a Poisson distributed integer random number with the following distribution 8in which γ is the deviation and the expectation of the random number κ. For a very small γ (say 0.001) the number κ takes the value zero with probability greater than 99 per cent, and for γ = 0.05 the number κ can take the value zero with probability of 95 per cent and the value one with probability of 5 per cent.…”

“…A uniformly distributed random choice decides which l components should be changed according to Equation (7). For structural optimization problems, according to our experience, a suitable l value ranges from 8 to 12 (Cai, 1995).…”

“…For discrete optimization the following termination criteria are suggested in (Cai, 1995;Thierauf and Cai, 1994), which can be used selectively:…”