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Extra resources for A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs

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Examples very far from 5 1 1 are: 000011101, 000000000, 000001010 and 00001 0010. Contrasting these two sets of binary numbers it becomes apparent that the near maximum values of x are all instances of I I #######.

Generate an initial (g= 1) population of random binary strings of length zlk,where M is the number of unknowns and M 1, the length of binary k-1 string required by any unknown k. In general lk f 4; k f j . 2. Decode each individual, i, within the population to integers Zl,k and then to real numbers rl,k, to obtain the unknown parameters. 3. Test each individual in turn on the problem at hand and convert the objective function or performance, Sat, of each individual to a fitnessf;, where a better solution implies a higher fitness.

The only way to improve accuracy is either to reduce the size of the search space, or to increase the length of the strings used to represent the unknowns. It is possible to use different presentations that remove this problem [MI94]; however for most problems this proves unnecessary. By not making the search space larger than required and by choosing a suitable string length, the required accuracy can usually be maintained. ) For problems with a large n ~ b e of important to use the smallest possible string length for each parameter.

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A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs by Cheon M.

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