Lecture_1B - iologically Inspired Methods (7CEMM708)...

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Unformatted text preview: iologically Inspired Methods (7CEMM708) iologically Inspired Methods (7CEMM708) Introduction to Optimisation Introduction to Optimisation Dr. Lei Ren ivision of Engineering Kings College London Division of Engineering, King s College London, Strand, London, WC2R 2LS ail: lei ren@kcl ac uk E-mail: lei.ren@kcl.ac.uk Room 244, Strand Building, Strand Campus Definition Definition ptimisation ptimisation Finding the best solution ptimization is the process of adjusting the inputs to or characteristics Optimization is the process of adjusting the inputs to or characteristics of a device, mathematical process, or experiment to find the minimum or maximum output or result. Function, rocess or Input r Output r Process or Experiment or Variables or Cost Throughout this module, we address the optimisation problem and scheme as a minimisation problem. Definition Definition ptimisation ptimisation Categories of Optimisation trial & error ction static d y n a func a m i c OPTIMISATION d i m ntinuous i s c r e t e random inimum continuous minimum seeking Minimum Minimum-Seeking Algorithm Seeking Algorithm ptimisation ptimisation Exhaustive Search 1. Exhaustive Search his approach requires checking an extremely large but finite solution This approach requires checking an extremely large but finite solution space with the number of combinations of different variable values given by = var N i Q V 1 i V = number of different variable combinations N var = total number of different variables Q i = number of different values that variable i can attain Minimum Minimum-Seeking Algorithm Seeking Algorithm ptimisation ptimisation Exhaustive Search 1. Exhaustive Search Find the minimum of: f(x,y)= xsin(4x)+1.1ysin(2y) Subject to: x 10 and 0 y 10 j y Global minimum of -18.5547 at ( x,y ) = (0.9039, 0.8668) sampled at intervals of 0.1, requiring a total of 101 2 function evaluations Minimum Minimum-Seeking Algorithm Seeking Algorithm...
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Lecture_1B - iologically Inspired Methods (7CEMM708)...

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