A hybrid dynamic programming/branch-and-bound algorithm for the multiple-choice knapsack problem

Dynamic programming and branch-and-bound methodologies are combined to produce a hybrid algorithm for the multiple-choice knapsack problem. Lagrangian duality is used in a computationally efficient manner to compute tight bounds on every active node in the search tree. The use of Lagrangian duality also enables the use of a reduction procedure to reduce the size of the problem for the enumeration phase. Computational experience with up to 200 multiple-choice sets and 20000 zero-one variables is reported. The computational experience indicates that the resulting algorithm is faster than the best published algorithm and is simpler to code.