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# Comparison of Optimization Algorithms [5 P]

Apply the four optimization algorithms gradient descent, genetic algorithms, simulated annealing, and particle swarm optimization to minimize each of the following four 2-dimensional functions;

1)
Rastrigin:

in the interval ,
2)
Rosenbrock:

in the interval ,
3)
Ackley:

in the interval ,
4)
Chasm:

in the interval
and compare their performance and run time.

a)

b)
Implement the particle swarm optimization algorithm. Complete the MATLAB function pso.m.

c)
Implement the gradient descent algorithm by estimating the gradient with finite differences as provided in the MATLAB function gradient.m.

d)
In order to carry out the optimization you can write your own MATLAB code or use the code template provided in compare.m. Missing code fragements that have to be completed are marked with "... HOMEWORK ...".

e)
Repeat the minimization for each of the four functions with each of the four algorithms 10 times and calculate the mean and the standard error of the mean (SEM) of the 20 resulting minimum function values and the corresponding run times.

f)
Compare the results obtained in e) and interpret possible strengths and weaknesses of each optimization algorithm with respect to the optimized functions. Hand in graphical illustrations of your results that support all your statements.

Present your results clearly, structured and legible. Document them in such a way that anybody can reproduce them effortless.

Next: Cart-Pole Controller Optimization [5 Up: MLB_Exercises_2010 Previous: Exercises
Haeusler Stefan 2011-01-25