Time to solve a math programming problem. IEEE Transactions presented a hybrid algorithm for solving a polynomial zero–one mathematical programming problem. The algorithm incorporates a mixture of pseudo- Boolean concepts and time-proven implicit enumeration procedures. Fifty-two random problems were solved by the hybrid algorithm; the times to solution (CPU time in seconds) are listed in the accompanying table and saved in the MATHCPU file.
a. Estimate, with 95% confidence, the mean solution time for the hybrid algorithm. Interpret the result.
b. How many problems must be solved to estimate the mean μ to within .25 second with 95% confidence?
c. Form a 95% confidence interval for the true standard deviation of the solution times for the hybrid algorithm. Interpret the result
.045 | 1.055 | .136 | 1.894 | .379 | .136 | .336 | .258 | 1.070 |
.506 | .088 | .242 | 1.639 | .912 | .412 | .361 | 8.788 | .579 |
1.267 | .567 | .182 | .036 | .394 | .209 | .445 | .179 | .118 |
.333 | .554 | .258 | .182 | .070 | 3.985 | .670 | 3.888 | .136 |
.091 | .600 | .291 | .327 | .130 | .145 | 4.170 | .227 | .064 |
.194 | .209 | .258 | 3.046 | .045 | .049 | .079 |
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Source: Snyder, W. S., and Chrissis, J. W. “A hybrid algorithm for solving zero– one mathematical programming problems.” IEEE Transactions, Vol. 22, No. 2, June 1990. Copyright © 1990. IEEE Reprinted with permission.
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