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Unformatted text preview: ld and Huang, 1977]. Lee and Woo developed an algorithm for ensuring the optimal selection among tolerances by exploiting the special structure of the constraints [Lee and Woo, 1989].
4.2. Problem solution method We hereby propose an efficient optimal method to the tolerance allocation problem stated in equation (11). It is sometimes called Dakin’s method. The method follows the optimal method framework presented in section 3.2, and consists of three main steps: (a) start with a relaxed LP, (b) branch on the binary variables by adding constraints, and (c) successively retrieve lower bounds by solving a series of ‘warm-started’ dual LPs until an optimal integer solution is found:
Set z* := +inf, the best solution found so far Solve the relaxed linear program P yielding a solution X Pick a variable xi in X that is not 0 or 1 Partition P into two sub-problems P1 and P2 by adding a constraint (xi = 0 for P1 or xi = 1 for P2) for P respectively 4. For each sub-problem Ps (s = 1,2), a. Calculate a lower bound zs to the optimal solution by solving the dual to Ps b. If Xs is pure binary and...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.
- Spring '10
- The Land