Difference between revisions of "Optimization problem"
From BioUML platform
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[[File:optimization_formula_2.png]] | [[File:optimization_formula_2.png]] | ||
| + | In order to get solution situated inside ℱ, we minimize the penalty function | ||
| + | [[File:optimization_formula_3.png]] | ||
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| + | The problem could be solved by different optimization methods. We implemented the following of them in the BioUML software: | ||
==References== | ==References== | ||
# Runarsson T.P., Yao X. Stochastic ranking for constrained evolutionary optimization. ''IEEE Transactions on Evolutionary Computation''. 2000. 4(3):284–294 | # Runarsson T.P., Yao X. Stochastic ranking for constrained evolutionary optimization. ''IEEE Transactions on Evolutionary Computation''. 2000. 4(3):284–294 | ||
Revision as of 16:25, 12 March 2019
The general nonlinear optimization problem [1] can be formulated as follows: find a minimum of the objective function ϕ(x), where x lies in the intersection of the N-dimensional search space
and the admissible region ℱ ⊆ ℝN defined by a set of equality and/or inequality constraints on x. Since the equality gs(x) = 0 can be replaced by two inequalities gs(x) ≤ 0 and –gs(x) ≤ 0, the admissible region can be defined without loss of generality as
In order to get solution situated inside ℱ, we minimize the penalty function
The problem could be solved by different optimization methods. We implemented the following of them in the BioUML software:
References
- Runarsson T.P., Yao X. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation. 2000. 4(3):284–294
