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<math> P(\chi_n \notin Cost_{min}) \sim \left(\frac{K}{n}\right)^{\alpha} </math>
<math> P(\chi_n \notin Cost_{min}) \sim \left(\frac{K}{n}\right)^{\alpha} </math>
where ''P'' is the probability of non-convergence, <math>\chi_n</math> is a solution of a run of length ''n'', <math>Cost_{min}</math> is the minimum acceptable solution, and ''K'' and <math>\alpha</math> are problem specific parameters. ''K'' and <math>\alpha</math> can be determined by plotting the Bayesian estimator for ''P'' versus ''n'' on a log scale and determining the slope and y-intercept. The expression for the Bayesian
where ''P'' is the probability of non-convergence, <math>\chi_n</math> is a solution of a run of length ''n'', <math>Cost_{min}</math> is the minimum acceptable solution, and ''K'' and <math>\alpha</math> are problem specific parameters. ''K'' and <math>\alpha</math> can be determined by plotting the Bayesian estimator for ''P'' versus ''n'' on a log scale and determining the slope and y-intercept. The expression for the Bayesian estimator <math> \hat{p} </math> is given by
{|align=center
|<math> \hat{p} = \frac{n_f + 1}{N + 2} </math>
|}
where <math>n_f</math> is the number of runs whos cost function value is greater than <math>Cost_{min}</math> and ''N'' is the total number of runs.
{|align=center
{|align=center
''' ''alpha'' = 0.5 '''
''' ''alpha'' = 0.5 '''
Fig. 7 shows the log plot of probability of non-convergence versus run length. The
Fig. 7 shows the log plot of probability of non-convergence versus run length for a MIR run with the ''alpha'' cooling parameter set to 0.5. The slope and y-intercept of the linear least-squares fit are <math>-0.0273 \pm 0.0103</math> and <math>0.297 \pm 0.127</math> with a reduced <math>\chi^2</math> value of 1.0. ''K'' and <math>\alpha</math> were then determined to be <math>(5.31 \pm 2.4) \times 10^4</math> and <math>0.0273 \pm 0.0103</math>.
''' ''alpha'' = 0.9 '''
''' ''alpha'' = 0.9 '''
Fig. 8 shows the log plot for a MIR run with the cooling parameter ''alpha'' set to 0.9. The slope and y-intercept of the linear least-squares fit are <math>0.0047 \pm 0.0060</math> and <math>-0.070 \pm 0.074</math> with a reduced <math>\chi^2</math> value of 0.55. ''K'' and <math>\alpha</math> were then determined to be <math>(0.03 \pm 1.2) \times 10^8</math> and <math>-0.0047 \pm 0.0060</math>. Runs of greater lengths will be needed to determine these parameters for this value of ''alpha''.
=== Sequential Performance ===
=== Sequential Performance ===