Changes

Once a sufficient number of runs have been completed, the α and ''K'' factors will be known and can thereby be exploited to find the most effective chain length to run multiple independent Markov chains.  Given the potential size of the search space, one can muse that the α factor will most likely be closer to one rather than to zero, because with the multiple run strategy, faster cooling will result in a particular chain settling very quickly to a minimum (which may be a local minimum).  After settling, the cluster can then move on to a new chain to settle to another minima.  If this is repeated, the chances of finding the global minima among one of the solutions is much greater than if only one chain were used [[#References|[4]]].

Once a sufficient number of runs have been completed, the α and ''K'' factors will be known and can thereby be exploited to find the most effective chain length to run multiple independent Markov chains.  Given the potential size of the search space, one can muse that the α factor will most likely be closer to one rather than to zero, because with the multiple run strategy, faster cooling will result in a particular chain settling very quickly to a minimum (which may be a local minimum).  After settling, the cluster can then move on to a new chain to settle to another minima.  If this is repeated, the chances of finding the global minima among one of the solutions is much greater than if only one chain were used [[#References|[4]]].

[[Image:SA_perform_3.jpg|thumb|Figure 4: Another example of convergence for a Simulated Annealing Run]]

[[Image:SA_perform_3.jpg|thumb|Figure 4: Another example of convergence for a Simulated Annealing Run]]

The figures to the right represent convergence graphs of different optimization algorithms.  In figure 2 [[#References|[6]]], the lines with equilateral triangles dispersed throughout represent simulated annealing algorithms similar to ParSA.  The graph with the base of the triangle up represents adaptive simulated annealing, while the graph with the base of the triangles down represents non-adaptive simulated annealing.  In figures 3 and 4 [[#References|[5]]], the dotted line denoted by SA represents simulated annealing.

The figures to the right represent convergence graphs of different optimization algorithms.  In figure 2 [[#References|[6]]], the lines with equilateral triangles dispersed throughout represent simulated annealing algorithms similar to ParSA.  The graph with the base of the triangle up represents adaptive simulated annealing, while the graph with the base of the triangles down represents non-adaptive simulated annealing.  In figures 3 and 4 [[#References|[5]]], the dotted line denoted by SA represents simulated annealing.