vOptLib
Library of numerical instances (MOMIP, MOLP, MOIP, MOCO)
UKP: class of uncorrelated instances
These are classical instances. The costs c1(i), c2(i) and the weights w(i) are generated independently following a uniform distribution in a given set. There is no correlation neither between the objective costs, nor between any objective cost and the weight.
Format
The format of all of these data files is:
number of variables (n)
number of objectives (p = 2)
number of constraints (k = 1)
cost of item i for objective 1 (i = 1,...,n)
cost of item i for objective 2 (i = 1,...,n)
weight of item i (i = 1,...,n)
total weight of the knapsack W
Lines of comments begin by #.
Instances:
Legend:
ID : instance’s name
: instance’s file
: report about the numerical characteristics
: set of non dominated points
: Maximum complete set of efficient solutions
Instances referenced 1A in [1]
The instances are denoted by 2KPn-c.dat where n is the size of the problem, and 0.c is the tightness ratio. The objective costs and the weights are generated according to a uniform distribution respectively in {30,…100} and in {20,…500}. There are 05 instances:
| ID | Available |
|---|---|
| 2KP50-11.dat | |
| 2KP50-50.dat | |
| 2KP50-92.dat | |
| 2KP100-50.dat | |
| 2KP500-41.dat | |
Files contain data from [1]:
[1] Xavier Gandibleux, Arnaud Freville. Tabu Search Based Procedure for Solving the 0-1 MultiObjective Knapsack Problem: the two objective case. Journal of Heuristics, 6 (3) 361-383, 2000.
Instances referenced 1B/A in [2]
The instances are denoted by 2KPn-1A.dat where n is the size of the problem. The objective costs and the weights are generated according to a uniform distribution in [1,…,100]. All instances have a tightness ratio W / (Sum{i=1,…n} w(i)) = 0.5. There are 10 instances:
| ID | Available |
|---|---|
| 2KP50-1A.dat | |
| 2KP100-1A.dat | |
| 2KP150-1A.dat | |
| 2KP200-1A.dat | |
| 2KP250-1A.dat | |
| 2KP300-1A.dat | |
| 2KP350-1A.dat | |
| 2KP400-1A.dat | |
| 2KP450-1A.dat | |
| 2KP500-1A.dat | |
Files contain data from [2]:
[2] M. Visée, J. Teghem, M. Pirlot and E. L. Ulungu. Two-phases Method and Branch and Bound Procedures to solve the Bi-objective Knapsack Problem. Journal of Global Optimization 12: 139–155 (1998).
Instances referenced 1B/B in [3]
The instances are denoted by 2KPn-1B.dat where n is the size of the problem. The first objective cost and the weights are generated according to a uniform distribution in [1,…,100]. The second objective is obtained by taking the objective cost of the first one in reverse order. All instances have a tightness ratio W / (Sum{i=1,…n} w(i)) = 0.5. There are 10 instances:
| ID | Available |
|---|---|
| 2KP50-1B.dat | |
| 2KP100-1B.dat | |
| 2KP150-1B.dat | |
| 2KP200-1B.dat | |
| 2KP250-1B.dat | |
| 2KP300-1B.dat | |
| 2KP350-1B.dat | |
| 2KP400-1B.dat | |
| 2KP450-1B.dat | |
| 2KP500-1B.dat | |
Files contain data from [3]:
[3] Fabien Degoutin and Xavier Gandibleux. Un retour d’expérience sur la résolution de problèmes combinatoires bi-objectifs. 5e journée du groupe de travail Programmation Mathématique MultiObjectif (PM20), Angers, France, 17 mai 2002.
Instances referenced 2/UNCOR [4]
The objective costs and the weights of the instances 2/UNCOR are both generated according to a uniform distribution in [1,…,300] or [1,…,1000]. All these instances have the same size n = 50. These instances are denoted by F5050Wx.dat (instances generated with numbers in [1,…,300]) or K5050Wx.dat (instances generated with numbers in [1,…,1000]), x denotes the number of the instance. All instances have a tightness ratio W / (Sum{i=1,…n} w(i)) = 0.5. There are 20 instances:
| ID | Available |
|---|---|
| F5050W01.dat | |
| F5050W02.dat | |
| F5050W03.dat | |
| F5050W04.dat | |
| F5050W05.dat | |
| F5050W06.dat | |
| F5050W07.dat | |
| F5050W08.dat | |
| F5050W09.dat | |
| F5050W10.dat | |
| K5050W01.dat | |
| K5050W02.dat | |
| K5050W03.dat | |
| K5050W04.dat | |
| K5050W05.dat | |
| K5050W06.dat | |
| K5050W07.dat | |
| K5050W08.dat | |
| K5050W09.dat | |
| K5050W10.dat | |
Files contain data from [4]:
[4] M. E. Captivo, J. Clímaco, J. Figueira, E. Martins and J. L. Santos. Solving bicriteria 0-1 knapsack problems using a labeling algorithm. Computers & Operations Research 30 (2003) 1865–1886.