Engineering Optimization: Theory and Practice, Fourth Edition

762 Practical Aspects of Optimization

Initialize node i

Data from the host node

Randomly perturb one variable out of S(i)

Change the design

Exchange updated information

from other nodes

All variable perturbed

out of S(i)?

Yes

No

No

Yes

Globally assemble all

updated design

variables

All cycles done?

Final design, stop

Figure 14.8 Flow diagram of parallel simulated annealing on a single node.S(i), set of design

variables assigned to nodei; nodei=processori.

FindX=















x 1

x 2

..

.

xn















(14.102)

which minimizesf 1 (X), f 2 ( X),... , fk(X) (14.103)

subject to

gj( X)≤ 0 , j= 1 , 2 ,... , m (14.104)

wherekdenotes the number of objective functions to be minimized. Any or all of the

functionsfi( andX) gj( may be nonlinear. The multiobjective optimization problemX)

is also known as avector minimization problem.