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

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