2-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 s et of efficient solutions. In the first phase, the set of supported ef ficient solutions is determined by optimizing a parameterized single-o bjective knapsack problem. Two versions are proposed for a second phas e, determining the non-supported efficient solutions: both versions ar e Branch and Bound approaches, but one is ''breadth first'', while the other is ''depth first''. Extensive numerical experiments have been r ealized to compare the results of both methods.