Multiobjective 01 unidimensional knapsack problem (UKP)

Definition

The 01 unidimensional knapsack problem with $p$ linear objectives is defined as follow:

Max sum{j=1,…,n} c^k_j x_j      for k = 1,…,p
s/t sum{j=1,…,n} w_j x_j <= W
    x_j = 0 or 1                for j = 1,…,n

Datasets

• with 2 objectives:

  • Uncorrelated Instances
  • Instances with repeated costs
  • Instances with a positive correlation between weights and objective(s)
  • Instances with positively correlated objectives
  • Instances with negatively correlated objectives
  • Hansen instances

• with 3 objectives:

  • Uncorrelated Instances