Two phases Method and Branch and Bound Procedures to Solve the Bi objective Knapsack Problem

The classical 0 1 knapsack problem is considered with two objectives. Two methods of the two phases type are developed to generate the set of efficient solutions. In the first phase, the set of supported efficient solutions is determined by optimizing a parameterized single-objective knapsack problem. Two versions are proposed for a second phase, determining the non supported efficient solutions: both versions are Branch and Bound approaches, but one is breadth first, while the other is depth first. Extensive numerical experiments have been realized to compare the results of both methods.