A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

Figure 1

Relationship between distances on solution space and those on Lagrangian space (among randomly generated Lagrangian vectors). ^∗𝑥-axis: distance between Lagrangian vectors, 𝑦-axis: distance between binary solution vectors, and 𝜌: Pearson correlation coefficient.

(a) 5.100: 𝜌=0.44  

(b) 5.250: 𝜌=0.50

(c) 5.500: 𝜌=0.45

(d) 10.100: 𝜌=0.35

(e) 10.250: 𝜌=0.37

(f) 10.500: 𝜌=0.37

(g) 30.100: 𝜌=0.19

(h) 30.250: 𝜌=0.19

(i) 30.500: 𝜌=0.19