An Interactive Artificial Cutting Plane Method for Bicriterion Integer Programming Problems
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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This thesis develops an interactive solution method for bicriterion integer mathematical programming problems, called the Artificial Cutting Plane ACP method. This method consists of four major steps 1 Determine initial boundaries and the initial incumbent solution 2 Locate an associated frontier nondominated solution AFNs to the incumbent solution. If there is no AFNS in the remaining feasible area, the current incumbent solution is the best compromises solution and the algorithm terminates 3 Present the decision maker DM the incumbent solution and its AFNS, and update the boundaries based on which solution is preferred and 4 Let the preferred solution be the new incumbent, and return to step 2. The ACP method was tested and compared to Aksoys Interactive Branch and Bound method on the basis of four evaluation criteria. Both methods were applied to randomly generated solutions based on five different shapes of efficient frontiers. Four different utility functions, with three variations each, were used to simulate the responses of a DM. The ACP method generated very competitive results against Aksoys method.
- Operations Research