Global optimisation with iTGO

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Global optimisation with iTGO

• (Iterative topographical global optimisation)

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Aims

• better then Pivot
• Pivot depends on constraints
• accuracy vs. efficiency
• preference is on accuracy

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The algorithm

• Aimo Törn Sami Viitanen (Åbo Akademi)
• For least square optimisation in PET
• topographical minimum point that is better than
  M neighbour points
• N units of pseudorandom points (solution
  candidates) are drawn in to the feasible region
• the distances between N points are saved in a
  triangular matrix

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The algorithm

• iterations
• to avoid large matrix
• On each round n topographical minima are saved
  and N-n new random points are created
• After iterations there are m topographical
  minimum
• A local optimisation algorithm Powell is started
  in these points
• The best point is selected to be the solution

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Testing and results

• Griewank
• 1 global minimum
• infinite number of local minima
• Branin
• 5 global minimum
• Shekel 10
• 1 global minimum in R4

• FLB data
• program fitglob.c
• results compared with test program mapmin.c
• no dependency on constraints

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http//users.utu.fi/kaelse/

• Masters thesis
• link to web version in my homepage