Average performance of greedy heuristics for the integer knapsack problem

Abstract This paper derives a lower bound on the average performance of a total-value greedy heuristic for the integer knapsack problem. This heuristic selects items in order of their maximum possible contribution to the solution value at each stage. We show that, as for the worst-case bound, the average performance bound for the total-value heuristic dominates the corresponding bound for the density-ordered greedy heuristic.

[1]  Hans Kellerer,et al.  Knapsack problems , 2004 .

[2]  Oj Onno Boxma,et al.  A probabilistic analysis of multiprocessor list scheduling : the Erlang case , 1985 .

[3]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[4]  Micha Hofri,et al.  A Stochastic Model of Bin-Packing , 1980, Inf. Control..

[5]  Rajeev Kohli,et al.  A total-value greedy heuristic for the integer knapsack problem , 1992, Oper. Res. Lett..

[6]  Alexander H. G. Rinnooy Kan,et al.  Asymptotic Properties of the Quadratic Assignment Problem , 1985, Math. Oper. Res..

[7]  M. L. Fisher,et al.  Probabilistic Analysis of the Planar k-Median Problem , 1980, Math. Oper. Res..

[8]  John L. Bruno,et al.  Probabilistic bounds for dual bin-packing , 1985, Acta Informatica.

[9]  P.W. Shor,et al.  The average-case analysis of some on-line algorithms for bin packing , 1984, Comb..

[10]  Paolo Toth,et al.  New trends in exact algorithms for the 0-1 knapsack problem , 2000, Eur. J. Oper. Res..

[11]  J. B. G. Frenk,et al.  A probabilistic analysis of the next fit decreasing bin packing heuristic , 1986 .

[12]  Sanjay V. Rajopadhye,et al.  Unbounded knapsack problem: Dynamic programming revisited , 2000, Eur. J. Oper. Res..

[13]  Richard M. Karp,et al.  Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane , 1977, Math. Oper. Res..

[14]  Rajeev Kohli,et al.  The Minimum Satisfiability Problem , 1994, SIAM J. Discret. Math..

[15]  G. S. Lueker,et al.  Asymptotic Methods in the Probabilistic Analysis of Sequencing and Packing Heuristics , 1988 .

[16]  John Franco,et al.  Probabilistic analysis of the Davis Putnam procedure for solving the satisfiability problem , 1983, Discret. Appl. Math..

[17]  Richard M. Karp,et al.  A probabilistic analysis of multidimensional bin packing problems , 1984, STOC '84.

[18]  Rajeev Kohli,et al.  Average Performance of Heuristics for Satisfiability , 1989, SIAM J. Discret. Math..

[19]  M. Fisher.  Worst-Case Analysis of Heuristic Algorithms , 1980 .

[20]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[21]  Rainer E. Burkard,et al.  Travelling Salesman and Assignment Problems: A Survey , 1979 .

[22]  Frank Thomson Leighton,et al.  Some unexpected expected behavior results for bin packing , 1984, STOC '84.