An improved interactive hybrid method for the linear multi-objective knapsack problem

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Abstract

In many situations, the knapsack problem in the presence of multiple, conflicting objectives frequently occurs in, for example, capital budgeting, project selection and capital investment, and budget control. Previous work was done to solve decision problems that had a weak point. An improved hybrid method is suggested to reduce the burden to the decision maker (DM) in selecting a solution and to obtain computational efficiency. In the method, bounding of the DM's utility value based on the revealed preference information is incorporated into a dynamic programming framework. In finding the most preferred solution (MPS), an implicit utility function is approximated by a linear function completely described by the scaling constants. The DM's partial preference expression is translated into a set of possible scaling constants [7]. In the stagewise solution process, an ideal objectives achievement of each partial solution is derived, and examined for whether it can give the highest utility value by comparing to the best-known objectives achievement. Elimination of partial solutions, which have proved not to lead to the MPS, is done to make the procedure more effective in finding the MPS. A suggested scheme based on the DM partial preference expression can give computational efficiency, which will be shown through computational experiments.

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K. I. Cho is an Assistant Professor of the School of Computer Science and Information Systems at Dongduk Women's University, Korea. He received his Ph.D. and M.S. in Industrial Engineering at KAIST, Korea, and a B.A. from Korea University, Korea. He has published articles on multi-criteria decision making, and decision support systems. His research areas are multi-criteria decision making, decision support systems, information systems, and CALS.

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S. H. Kim is a Professor of the Graduate School of Management at KAIST (Korea Advanced Institute of Science and Technology), Korea. He received his Ph.D. in Engineering-Economic Systems at the Stanford University, an M.S. in Industrial Engineering at the University of Missouri-Columbia, and a B.A. from Seoul National University. He has published numerous articles on decision analysis, multi-criteria decision making, decision support systems, expert systems, and groupware. He has been Vice Present of Korea Expert Systems Society, and also of Korea CALS/EC Association.

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