Abstract: "This paper presents a new approach to the exact solution of the 0-1 Knapsack Problem which combines dynamic programming and tight upper bounds into an overall robust algorithm. It is shown how additional constraints may be generated and surrogate relaxed. The solution of the relaxed...

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Bibliographic Details

Main Authors:	Martello, Silvano (Author), Pisinger, David (Author), Toth, Paolo (Author)
Format:	Book
Language:	English
Published:	København 1997
Series:	Datalogisk Institut <København>: DIKU-Rapport 1997,11
Subjects:	Combinatorial optimization Dynamic programming Operations research
Summary:	Abstract: "This paper presents a new approach to the exact solution of the 0-1 Knapsack Problem which combines dynamic programming and tight upper bounds into an overall robust algorithm. It is shown how additional constraints may be generated and surrogate relaxed. The solution of the relaxed problem gives a tight upper bound, and in many situations also an optimal lower bound. The enumeration is based on dynamic programming, which ensures pseudo-polynomial worst-case solution times. The algorithm does not use the classical approach to core problems. Instead of choosing a core as a collection of items with profit-to-weight ratios close to those of the break item, we use some heuristic rules to find a collection of items which fit well together. These are used as an initial core, which is gradually expanded according to some greedy principles. The algorithm has excellent solution times, being able to solve very large instances with bounded coefficients within less than one second. There is basically no difference in the solution times of 'easy' and 'hard' instances found in the literature."
Physical Description:	19 S.