Optimization problem

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 ⊆ ℝ^N defined by a set of equality and/or inequality constraints on x. Since the equality g_s(x) = 0 can be replaced by two inequalities g_s(x) ≤ 0 and –g_s(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:

stochastic ranking evolution strategy (SRES) [1];</li> cellular genetic algorithm MOCell [2]; particle swarm optimization (PSO) [Sierra and Coello, 2005]; deterministic method of global optimization glbSolve [Björkman and Holmström, 1999]; adaptive simulated annealing (ASA) [Ingber, 1996]

References

1. Runarsson T.P., Yao X. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation. 2000. 4(3):284–294