Optimization problem - Revision history

Elena.kutumova@biouml.org at 06:30, 3 September 2021

2021-09-03T06:30:58Z

Elena.kutumova@biouml.org at 06:54, 30 August 2021

2021-08-30T06:54:43Z

Elena.kutumova@biouml.org at 06:53, 30 August 2021

2021-08-30T06:53:31Z

Elena.kutumova@biouml.org at 06:52, 30 August 2021

2021-08-30T06:52:31Z

Elena.kutumova@biouml.org at 06:51, 30 August 2021

2021-08-30T06:51:32Z

Elena.kutumova@biouml.org at 06:49, 30 August 2021

2021-08-30T06:49:13Z

Elena.kutumova@biouml.org: /* Implementation of the parameter estimation process in BioUML */

2019-03-14T08:02:53Z

‎Implementation of the parameter estimation process in BioUML

Elena.kutumova@biouml.org at 08:01, 14 March 2019

2019-03-14T08:01:44Z

Elena.kutumova@biouml.org at 07:39, 14 March 2019

2019-03-14T07:39:48Z

Elena.kutumova@biouml.org at 14:02, 13 March 2019

2019-03-13T14:02:49Z

@@ Line 15: / Line 15: @@
 <ul>
-<li>Evolution strategy (SRES) [1];</li>
+<li>stochastic ranking evolution strategy (SRES) [1];</li>
-<li>Cellular genetic algorithm [2] - MOCell;</li>
+<li>cellular genetic algorithm MOCell [2];</li>
-<li>Particle swarm optimization [3] - PSO;</li>
+<li>particle swarm optimization (PSO) [3];</li>
-<li>GLBSOLVE [4];</li>
+<li>deterministic method of global optimization glbSolve [4];</li>
-<li>Adaptive simulated annealing [5] - ASA.</li>
+<li>adaptive simulated annealing (ASA) [5].</li>
 </ul>
-The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and GLBSOLVE run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in GLBSOLVE the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
+The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and glbSolve run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in glbSolve the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
 with the number ''k'' = 0,…, ''N<sub>it</sub>'' − 1. The method ASA considers sequentially generated guesses ''x<sup>k</sup>'' ∈ Ω, ''k'' ∈ ℕ<sup>+</sup>, and stops if distance between ''x<sup>k</sup>'' and ''x''<sup>''k''+1</sup> defined as Euclidean norm
@@ Line 31: / Line 31: @@
 [[File:optimization_table_1.png]]
-All methods, excepting GLBSOLVE, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method GLBSOLVE is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
+All methods, excepting glbSolve, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method glbSolve is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
 ==Application of non-linear optimization to systems biology==

@@ Line 16: / Line 16: @@
 <ul>
 <li>Evolution strategy (SRES) [1];</li>
-<li>Cellular genetic algorithm (MOCell) [2];</li>
+<li>Cellular genetic algorithm [2] - MOCell;</li>
-<li>Particle swarm optimization (PSO) [3];</li>
+<li>Particle swarm optimization [3] - PSO;</li>
-<li>glbSOLVE [4];</li>
+<li>GLBSOLVE [4];</li>
-<li>Adaptive simulated annealing (ASA) [5].</li>
+<li>Adaptive simulated annealing [5] - ASA.</li>
 </ul>
-The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and glbSOLVE run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in glbSOLVE the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
+The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and GLBSOLVE run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in GLBSOLVE the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
 with the number ''k'' = 0,…, ''N<sub>it</sub>'' − 1. The method ASA considers sequentially generated guesses ''x<sup>k</sup>'' ∈ Ω, ''k'' ∈ ℕ<sup>+</sup>, and stops if distance between ''x<sup>k</sup>'' and ''x''<sup>''k''+1</sup> defined as Euclidean norm
@@ Line 31: / Line 31: @@
 [[File:optimization_table_1.png]]
-All methods, excepting glbSOLVE, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method glbSOLVE is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
+All methods, excepting GLBSOLVE, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method GLBSOLVE is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
 ==Application of non-linear optimization to systems biology==

@@ Line 18: / Line 18: @@
 <li>Cellular genetic algorithm (MOCell) [2];</li>
 <li>Particle swarm optimization (PSO) [3];</li>
-<li>GLBSOLVE [4];</li>
+<li>glbSOLVE [4];</li>
 <li>Adaptive simulated annealing (ASA) [5].</li>
 </ul>
-The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and GLBSOLVE run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in GLBSOLVE the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
+The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and glbSOLVE run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in glbSOLVE the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
 with the number ''k'' = 0,…, ''N<sub>it</sub>'' − 1. The method ASA considers sequentially generated guesses ''x<sup>k</sup>'' ∈ Ω, ''k'' ∈ ℕ<sup>+</sup>, and stops if distance between ''x<sup>k</sup>'' and ''x''<sup>''k''+1</sup> defined as Euclidean norm
@@ Line 31: / Line 31: @@
 [[File:optimization_table_1.png]]
-All methods, excepting GLBSOLVE, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method GLBSOLVE is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
+All methods, excepting glbSOLVE, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method glbSOLVE is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
 ==Application of non-linear optimization to systems biology==

@@ Line 16: / Line 16: @@
 <ul>
 <li>Evolution strategy (SRES) [1];</li>
-<li>Cellular genetic algorithm [2];</li>
+<li>Cellular genetic algorithm (MOCell) [2];</li>
-<li>Particle swarm optimization [3];</li>
+<li>Particle swarm optimization (PSO) [3];</li>
 <li>GLBSOLVE [4];</li>
-<li>Adaptive simulated annealing [5].</li>
+<li>Adaptive simulated annealing (ASA) [5].</li>
 </ul>

@@ Line 22: / Line 22: @@
 </ul>
-The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and glbSolve run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in glbSolve the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
+The below table shows the generic scheme of the optimization process for these methods. SRES, MOCell, PSO and GLBSOLVE run a predefined number of iterations ''N<sub>it</sub>'' considering a sequence of sets (populations) ''P<sup>i</sup>'', ''i'' = 0,…,''N<sub>it</sub>'' − 1, of potential solutions (guesses). In the case of the first three methods, the size ''s'' ∈ ℕ<sup>+</sup> of the population is fixed, whereas in GLBSOLVE the initial population ''P''<sup>0</sup> consists of one guess, while the size ''s''<sub>''k''+ 1</sub> of the population ''P''<sup>''k''+1</sup> is found during the iteration
 with the number ''k'' = 0,…, ''N<sub>it</sub>'' − 1. The method ASA considers sequentially generated guesses ''x<sup>k</sup>'' ∈ Ω, ''k'' ∈ ℕ<sup>+</sup>, and stops if distance between ''x<sup>k</sup>'' and ''x''<sup>''k''+1</sup> defined as Euclidean norm
@@ Line 31: / Line 31: @@
 [[File:optimization_table_1.png]]
-All methods, excepting glbSolve, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method glbSolve is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
+All methods, excepting GLBSOLVE, are stochastic and seek global minimum of the function ϕ taking into account the admissible region ℱ. Thus, a guess ''x'' ∈ Ω is more preferable than a guess ''y'' ∈ Ω at some iteration of methods, if ψ(''x'') = 0 and ψ(''y'') ≠ 0 or ψ(''x'') < ψ(''y''). The method GLBSOLVE is suited to solve only the problems with Ω ⊆ ℱ. Values of the function ψ are calculated but do not affect on the generation of potential solutions.
 ==Application of non-linear optimization to systems biology==

@@ Line 78: / Line 78: @@
 [[BioUML]] allows performing parameter estimation by creation a special optimization document. For details about this document, see the section [[Optimization document]].
-Examples of the [[BioUML]] application for solving optimization problems is done in the section [[Optimization examples]]. You can also found more details in the article [7].
+Examples of the BioUML application for solving optimization problems is done in the section [[Optimization examples]]. You can also found more details in the article [7].
 ==References==

@@ Line 12: / Line 12: @@
 [[File:optimization_formula_3.png]]
-The problem could be solved by different optimization methods. We implemented the following of them in the BioUML software:
+The problem could be solved by different optimization methods. We implemented the following of them in the [[BioUML]] software:
 <ul>
@@ Line 77: / Line 77: @@
 ==Implementation of the parameter estimation process in BioUML==
-BioUML allows performing parameter estimation by creation a special optimization document. For details about this document, see the section [[Optimization document]].
+[[BioUML]] allows performing parameter estimation by creation a special optimization document. For details about this document, see the section [[Optimization document]].
-Examples of the BioUML application for solving optimization problems is done in the section [[Optimization examples]]. You can also found more details in the article [7].
+Examples of the [[BioUML]] application for solving optimization problems is done in the section [[Optimization examples]]. You can also found more details in the article [7].
 ==References==

@@ Line 49: / Line 49: @@
 where normalization factors ω<sub>min</sub>/ω<sub>''i''</sub> with ω<sub>min</sub> = min<sub>''i''</sub>ω<sub>''i''</sub> are used to make all concentration trajectories have similar
-importance. The weights ωi are calculated by one of the formulas on experimentally measured concentrations:
+importance. The weights ω<sub>''i''</sub> are calculated by one of the formulas on experimentally measured concentrations:
 [[File:optimization_formula_8.png]] (mean square value), [[File:optimization_formula_9.png]] (mean value), [[File:optimization_formula_10.png]] (standard deviation).