A fast algorithm for strongly correlated knapsack problems

David Pisinger
1998 Discrete Applied Mathematics  
We consider a variant of the O-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 fixedcharge 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 relaxation with optimal multipliers, we obtain
more » ... 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 8. For each value of b the problem is solved through dynamic programming. Extensive computational experiments are provided showing that we are able to solve strongly correlated instances faster than other algorithms solve uncorrelated instances. 0 1998 Elsevier Science B.V. All rights reserved.
doi:10.1016/s0166-218x(98)00127-9 fatcat:yzhqziok6vhfhd72dxzm2fkiv4