Federico Della Croce

Dynamic programming algorithms, efficient solution of the LP-relaxation and approximation schemes for the Penalized Knapsack Problem

  • Federico Della Croce
  • Ulrich Pferschy
  • Rosario Scatamacchia
    • Categories 0-1 Programming, Combinatorial Optimization, Dynamic Programming Tags , , ,

    We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an exact approach relying on a procedure which narrows the relevant range … Read more

    An exact approach for the 0–1 Knapsack Problem with Setups

  • Federico Della Croce
  • Rosario Scatamacchia
  • Fabio Salassa
    • Categories Combinatorial Optimization Tags ,

    We consider the 0–1 Knapsack Problem with Setups. We propose an exact approach which handles the structure of the ILP formulation of the problem. It relies on partitioning the variables set into two levels and exploiting this partitioning. The proposed approach favorably compares to the algorithms in literature and to solver CPLEX 12.5 applied to … Read more