Question

Compare the different SA cooling schedule techniques (Linear, Geometric,Exponential, Logarithmic and Adaptive Schedule (Reversibility)). In terms of time complexity and optimality. Also, Advantage and disadvantage.?

Answer 1

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So let's start so from the question it ask what is SA cooling technique firstly we have know what is Simulated annealing

Simulated annealing:

Simulated annealing is a probabilistic search heuristic for global min/max.

It is often suitable for questions where the an approximate answer to the global min/max is ok. The algorithm will converge to the global min/max when the annealing schedule is run indefinitely, but in practice it is often a good technique to improve run-time at the expense of some solution accuracy.

Flowchart of ALGORITHM

different SA cooling schedule techniques :

Cooling Schedule: The cooling schedule is the procedure that decreases the temperature parameter. Bringing the temperature parameter from a large value to zero too quickly has some dramatic consequences on the quality of the solution.

Logarithmic Cooling Schedule:

T_{​​​​​​t}​​​​​= c/log(1+t)

where c is positive constant independent of t
but depending on the problem. Theoretically,
the logarithmic cooling schedule asymptotically
converges towards the global minimum. However, this scheme converges very slowly and requires a large computation time

Geometrical Cooling Schedule:

This type of cooling schedule is faster than
the logarithmic cooling scheme as it is decreasing geometrically.

Tt = Tinit α^{​​​​​​t}

^where alpha is constant between 0 and 1

Linear Cooling Schedule:

To have a slow decrease of temperature, it is necessary that the value of alpha is closer to 1.
The linear cooling schedule is defined as follows
Tt = Tinit − nt,

Adaptive Schedule (Reversibility):

This cooling schedule slightly differs from the geometric cooling schedule  It decreases the
temperature when the new average energy is less
than or equal to the previous average energy.

This schedule has two major drawbacks, namely
the constant a must be adjusted properly and it is very slow in practice.

Advantage :

Simulated annealing can deal with highly nonlinear models, chaotic and noisy data and many constraints. It is a robust and general technique.

The algorithm is quite versatile since it does not rely on any restrictive properties of the model.

Disadvantage:

Since SA is a metaheuristic, a lot of choices are required to turn it into an actual algorithm.
There is a clear tradeoff between the quality of the solutions and the time required to compute them.

The precision of the numbers used in implementation is of SA can have a significant effect upon the quality of the outcome.