Department of engineering control instrumentation

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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Schemes Several algorithms evaluated: Genetic algorithms (GA) Differential evolution (DE) Hybrid GA / Hybrid DE Dividing Rectangles (DIRECT)
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Scheme Genetic algorithms Search space Accuracy 1e-6 Chromosomes length 105 bits (5 genes) Initial population 50 Genetic operators Roulette selection 0.6 Single point crossover 0.9 Binary uniform mutation 0.00 5
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Scheme Genetic algorithms (cont.) Termination criteria improvement on the solution accuracy ≤ 1e-6 for a defined number of generations, fixed at 15 stop iteration Each trial gives different total number of simulations
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Scheme GA Results Slow convergence to global optimum No. of simulations very high (~5000) Computationally prohibitive – slow (~ 3-4 hours for each test point) [0.1000, 0.0750, 0.0500, 0.18309, 0.0500, 36.0908]
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Scheme Differential Evolution Random initialisation Mutation Crossover Evaluation and selection Termination criteria same as that of GA
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Scheme DE Results Better convergence to global optimum Reduced number of simulations (~3000) [0.1000, 0.0750, 0.0500, 0.18309, 0.0500, 36.0908]
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Global Optimisation Scheme Global optimisation comparison statistics Optimisation Trials Avg. Max. Min. Std. Dev. Prob. of success GA 100 4485 7500 2400 828.364 65% DE 100 3086 4176 1152 567.57 90% Trials Trials Trials Trials
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Hybrid Optimisation Scheme Hybrid global and local optimisation schemes Exploit the advantages of both schemes Question: When to switch between the schemes? Standard approach: run global algorithm, then run local algorithm We use a more sophisticated decision making scheme based on one proposed by Lobo and Goldberg, 1996
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar 2006 Hybrid Optimisation Scheme Probabilistic switching scheme Weighted reward for each algorithm Probability of algorithm being selected depends on improvement in cost function Initial probabilities selected to favour use of GA at beginning “fmincon” is the local algorithm (SQP) Termination criteria same as previous cases Hybrid genetic algorithm (HGA)
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  • Fall '19
  • Mathematical optimization, Evolution strategy, Control & Instrumentation Research Group

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