May 2015
Intermediate to advanced
466 pages
10h 33m
English
Content preview from Optimization
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208 Optimization: Algorithms and Applications
Let us check the performance of the weighted sum method for multiobjec-
tive problems that have a nonconvex Pareto front. Consider the following
multiobjective optimization problem:
Minimize
f
1
(x) = x
1
Minimize
f x x x
2 2
2
1 1
1 0 1 3( ) . sin( )x = + − − π
subject to
0 ≤ x
1
≤ 1, −2 ≤ x
2
≤ 2
On executing the modied SQP code for these functions, an incomplete
Pareto front is generated and is shown in Figure 7.4. The weighted sum
approach, though simple to implement, has difculty in locating the Pareto
front of the nonconvex type. Another disadvantage of the weighted sum
approach ...
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