# Olympia Roeva Institute of Biophysics and Biomedical Engineering Bulgarian Academy of Sciences

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A Comparison of Simulated Annealing and Genetic Algorithm Approaches for Cultivation Model Identification. Olympia Roeva Institute of Biophysics and Biomedical Engineering Bulgarian Academy of Sciences E-mail: olympia@clbme.bas.bg. 1. Introduction 2. Outline of the GA 4. Test problem
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A Comparison of Simulated Annealing and Genetic Algorithm Approaches for Cultivation Model IdentificationOlympia RoevaInstitute of Biophysics and Biomedical Engineering Bulgarian Academy of SciencesE-mail: olympia@clbme.bas.bg1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• competing paradigms in the field of modern heuristicsGenetic AlgorithmSimulated Annealing Algorithmquite close relatives and much of their difference is superficialpopulation size → one population new solutionsby → a new solution by modifying only combining two different solutionsone solution with a local move (crossover and mutation) (only mutation)In this work, both GA and SA are applied and compared for a parameter identification of non-linear mathematical model of E. coli MC4110 fed-batch cultivation process. 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• A pseudo code of a GA is presented as: 1. Set generation number to zero (t = 0) 2. Initialise usually random population of individuals (P(0)) 3. Evaluate fitness of all initial individuals of population 4. Begin major generation loop in k: 4.1. Test for termination criterion 4.2. Increase the generation number 4.3. Select a sub-population for offspring reproduction (select P(i) from P(i – 1)) 4.4. Recombine the genes of selected parents (recombine P(i)) 4.5. Perturb the mated population stochastically (mutate P(i)) 4.6. Evaluate the new fitness (evaluate P(i)) 5. End major generation loop 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• Basic GA operators and parameters 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• A pseudo code of SA could be presented as: 1. Find initial solution (by generating it randomly) 2. Set initial value for the control parameter T = T0 3. Set a value for r, the rate of cooling parameterj = 0 Generate (at random) a new solution S’ Calculate the difference in cost:  = cost(S’) – cost(S) Examine the new solution and decide: accept or reject If accepted, it becomes the current solution; otherwise,keep the old one; j = j+1Reduce the temperature and generate a new solution 4. Until some stopping criterion applies 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• Boltzman distributionwith the probability of acceptance:Temperature update:T = T0 0.95rAnnealing parameters: 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• Parameter identification of E. coli MC4110 fed-batch cultivation modelReal experimental data of the E. coli MC4110 fed-batch cultivationare used. 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• A two stage parameter identification procedure is usedObjective function 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• GA max = 0.4796, kS = 0.0162, YS/X = 2.0137SA max = 0.4864, kS = 0.0150, YS/X = 1.9088Table 1. Results from parameter identification – second stepCurrent Best IndividualBest: 0.11025 Mean: 0.1160225150Best fitnessMean fitness2010015Current best individualFitness value1050500123020406080100Number of variables (3)GenerationBest, Worst, and Mean ScoresScore Histogram8004060030Number of individuals400202001000204060801000.110.120.130.140.15GenerationScore (range)
• 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• Best GA resultBest pointBest Function Value: 0.11041252520201515Function valueBest point1010550012301000200030004000Number of variables (3)IterationCurrent PointCurrent Function Value: 0.112072540203015Current pointFunction value20101050012301000200030004000Number of variables (3)Iteration
• 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• Best SA result 1. Introduction 2. Outline of the GA 4. Test problem
• 3. Outline of the SA5. Results and discussion
• Cultivation of E. coli MC411021.2GA modelSA model21Exp. data20.8Dissolved oxygen, [%]20.620.920.420.8520.820.220.7520.020.78.48.58.68.78.88.999.19.29.39.419.86789101112Time, [h]
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