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The paper consider 10 instances for the classical bi-objective linear assignment problem.
Instances are named Template_AP_n<n>.<raw/xml> where n is the size of the problem. The paper considers
instances of size 5-50; however, the instance set also contains 5 instances of size 60-100. Costs
are generated random in [0,30].
All instance files are given in both xml and raw format. The xml format is self explainable (see e.g. ex1).
We use the following parameter names:
-
$n$ = dimension/size -
$c^{k}_{r,c}$ =$k$ 'th cost of assigning row$r$ to column$c$ .
The instances have the following format:
n
c^{0}_{0,0}... c^{0}_{0,n-1}
c^{0}_{1,0}... c^{0}_{1,n-1}
...
c^{0}_{n-1,0}... c^{0}_{n-1,n-1}
c^{1}_{0,0}... c^{1}_{0,n-1}
c^{1}_{1,0}... c^{1}_{1,n-1}
...
c^{1}_{n-1,0}... c^{1}_{n-1,n-1}
That is, first the dimension, then the costs for the first criterion and next the cost for the second criterion.
The instances are contained in the sub folder MMAP. Instances are named
Template_MMAP_d<n>_e<I1>_c<I2>_m<M>_s<S>_<Y>.xml where Y is the instance number of a BiMMAP of
size I1 and cost range I2 using method M and shape S.
A total of 8000 instances are provided. That is, 100 instances of each of the following 80 possible configurations were generated:
- n: 4, 6, 8, 10.
- I1: 2-8 (not for method 2) and 10-30.
- I2: 0-500 and 0-10000.
- (M,S): (1, −60), (1,0), (1, 60), (2, 3), (2, 4), (3, 0).
Restults are given in the results folder using the json
format (see Step 3).