Two Simulated Annealing Optimization Schemas for Rational Bézier Curve Fitting in the Presence of Noise

Algorithm 1

Simulated annealing.

Require: (Initial Parameters)

()    Initial Temperature

()    Schedule Criteria

()    Stopping Criteria SC

()    Neighbourhood function :

()    System Energy :

()    Cooling Schedule : (strictly decreasing function)

()                        ▹ Temperature initialization

()    Randomly select start state  

()    

() repeat                      ▹ External loop: stopping criteria

()  repeat                   ▹ Internal loop: thermal equilibrium

()                      ▹ New state generated

()                  ▹ Energy evaluation of current state

()                   ▹ Energy evaluation of new state

()   

()   if    then                           ▹ Acceptance criterion

()    

()   else

()    Randomly compute               ▹ Metropolis procedure

()    if    then                             ▹ Equation (6)

()     

()    end if

()   end if

()  until  

()                          ▹ Temperature update

() until  

() return                                ▹ Best final solution