Research Article
An Exact Algorithm for Bilevel 0-1 Knapsack Problems
Algorithm 1
A polynomial time solution procedure for CBKP.
Let denote the optimal value of the leader objective function; | Let be an optimal solution of CBKP; | Initialization | Sort the variables and in decreasing order of the ratio for and | and for ; | Let | | be the optimal solution for the following problem: | ; | Let | | be the optimal solution for the following problem: | ; | /* The indexes and are respectively the indexes of the last | leader and follower variables with a positive value according | to the ordering */ | Let ; | ; ; | while and ) do | if then | ; ; ; | end | else if then | ; ; ; | end | else if then | ; ; ; ; | end | if then | ; ; | end | end |
|