Abstract: "We consider a variant of the 0-1 Knapsack Problem, where the profit of each item corresponds to its weight plus a fixed constant. These so-called Strongly Correlated Knapsack Problems have attained much interest due to their apparent hardness and wide applicability in several fixed-c...

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Bibliographische Detailangaben

1. Verfasser:	Pisinger, David (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	København 1996
Schriftenreihe:	Datalogisk Institut <København>: DIKU-Rapport 1996,29
Schlagworte:	Combinatorial analysis Dynamic programming Operations research Relaxation methods (Mathematics)
Zusammenfassung:	Abstract: "We consider a variant of the 0-1 Knapsack Problem, where the profit of each item corresponds to its weight plus a fixed constant. These so-called Strongly Correlated Knapsack Problems have attained much interest due to their apparent hardness and wide applicability in several fixed-charge problems. A specialized algorithm for the problem is presented, where the main approach is to derive an additional constraint from an extended cover. By surrogate relaxataion [sic] with optimal multipliers, we obtain a Subset-sum Problem defined in the profits of the items. It is proved that an optimal solution to the Subset-sum Problem is also an optimal solution to the original problem provided that the largest possible number of items is chosen. Based on this observation, a 2-optimal heuristic is derived which solves the problem to optimality for several large-sized problems. In those cases where the heuristic fails, we solve the problem to optimality by restricting the problem to a fixed number of chosen items [beta]. For each value of [beta] the problem is solved through dynamic programming. Extensive computational experiments are provided showing that we are able to solve strongly correlated instances faster than uncorrelated instances usually are solved. Thus problems with 100 000 [sic] items may be solved in less than 0.05 seconds."
Beschreibung:	18 S.