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Temperature Scheduling in Simulated Annealing (view source)
Revision as of 09:24, 20 December 2007
, 09:24, 20 December 2007→Size of the problem
The three cooling schedules featured in the ParSA Library are the SA_EasyScheduler, the SA_AartsScheduler and the SA_MIRScheduler. Each of these rely on different principles who's aim is to find the best solution in the least amount of time. The SA_EasyScheduler relies on many user set parameters that include the initial temperature, the initial chain length for temperature (equilibrium), the decrement factor, and the frozen factor. Cite the turkish paper here with concurrence for large problems and a constant cooling factor. Difficulty of determiing starting temperature difficult tho.The SA_Aarts Scheduler requires that the user set three parameters, epsilon, delta and omega that govern the temperature scheduling process. epsilon is the the frozen parameter. omega is the smoothing parameter. delta is the distance factor, which shows up in the temperature decrement calculator. its rough dependence is given in the graph at the left. [[Image:Temp_delta.jpg|thumb|A rough portrayal of the dependence of the next temperature step as a function of the delta parameter and the previous temperature's value]] The MIR scheduler, which stands for Multiple Independent runs is based off of the idea that runs of shorter chain lengths linked together will find a more accurate solution than one sequential run of the same lenght. the reason that this provides a more accurate search is that the search can span a larger area in the search space. Thus, with more space covered the the solution given is more likely to be closer to the global optimum.
The three cooling schedules featured in the ParSA Library are the SA_EasyScheduler, the SA_AartsScheduler and the SA_MIRScheduler. Each of these rely on different principles who's aim is to find the best solution in the least amount of time. The SA_EasyScheduler relies on many user set parameters that include the initial temperature, the initial chain length for temperature (equilibrium), the decrement factor, and the frozen factor. Cite the turkish paper here with concurrence for large problems and a constant cooling factor. Difficulty of determiing starting temperature difficult tho.The SA_Aarts Scheduler requires that the user set three parameters, epsilon, delta and omega that govern the temperature scheduling process. epsilon is the the frozen parameter. omega is the smoothing parameter. delta is the distance factor, which shows up in the temperature decrement calculator. its rough dependence is given in the graph at the left. [[Image:Temp_delta.jpg|thumb|A rough portrayal of the dependence of the next temperature step as a function of the delta parameter and the previous temperature's value]] The MIR scheduler, which stands for Multiple Independent runs is based off of the idea that runs of shorter chain lengths linked together will find a more accurate solution than one sequential run of the same lenght. the reason that this provides a more accurate search is that the search can span a larger area in the search space. Thus, with more space covered the the solution given is more likely to be closer to the global optimum.
==Size of the problem==
==Difficulty of the problem==
A solution in our search space corresponds to an ordered set of numbers that are determined by the order of the legendre polynomial for the phase and amplitude of the surface of the diamond in the simulated annealing run. We have three phases and two amplitudes (make a picture of the setup, with the diamond and reference labelled).
A solution in our search space corresponds to an ordered set of numbers that are determined by the order of the legendre polynomial for the phase and amplitude of the surface of the diamond in the simulated annealing run. We have three phases and two amplitudes (make a picture of the setup, with the diamond and reference labelled).
The size and ''terrain'' of a particular search space are two concepts that one should include when speaking of the difficulty of a search space. The computing time drastically increases with the size (or dimensionality) of search space [1]. However, it is still possible to have higher dimensional problems that are unimodal or have very few local minima. Thus, one must also take into account the shape of search space when contemplating the difficulty.
[1] Esin Onbasoglu and Ozdamar Yeditepe University, Istanbul, Turkey Journal of Global Optimization 2001
==Prospective strategies==
==Prospective strategies==
Each of the above cooling schedule classes have parameters that guide every portion of the cooling process. the warming up, the equilibrium determination, the cooling and the frozen.
Each of the above cooling schedule classes have parameters that guide every portion of the cooling process. the warming up, the equilibrium determination, the cooling and the frozen.