bts4-cta

decomposition numerics variable_bound mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Jordi Castro	75400	45350	8.53673e-05	hard	cta	67048.96566835219	bts4-cta.mps.gz

Set of MILP instances of the CTA (Controlled Tabular Adjustment) problem, a method to protect statistical tabular data, belonging to the field of SDC (Statistical Disclosure Control). Raw data of instances are real or pseudo-real, provided by several National Statistical Agencies. We generated the CTA problem for these data.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	75400	75399
Constraints	45350	45350
Binaries	2260	2260
Integers	0	0
Continuous	73140	73139
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	8.53673e-05	8.53678e-05
Nonzeroes	291904	291902

Constraint Classification Properties
	Original	Presolved
Total	45350	45350
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	9040	9040
Set Partitioning	0	0
Set Packing	0	0
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	36310	36310
General Linear	0	0
Indicator	0	0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	value	min	median	mean	max
Components	2.354108
Constraint %		0.0154355	0.444444	0.0352811	10.90630
Variable %		0.0185679	0.444444	0.0424409	9.49084
Score	0.955560

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID	Objective	Exact	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
2	67048.97	982568.3	6.3e-06	1.3e-06	0	Alex Fender, Alice Boucher, Akif Coerduek, Kumar Aatish, Nicolas Blin, Piotr Sielski	2025-01-10	Found with GPU-accelerated MIP heuristics in NVIDIA cuOpt. Proven via SCIP 9.0.1.
1	472243.42	525661.4	6.3e-06	1.0e-06	0	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to bts4-cta in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance	Status	Variables	Binaries	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
unitcal_7	easy	25755	2856	22899	48939	127595	R. O’Neill	–	19635558.244	benchmark benchmark_suitable precedence variable_bound mixed_binary general_linear
mod011	easy	10958	96	10862	4480	22254	MIPLIB submission pool	mod	-54558535.59	numerics aggregations variable_bound set_packing mixed_binary
a1c1s1	easy	3648	192	3456	3312	10178	M. Vyve, Y. Pochet	c1s1	11503.444125	benchmark_suitable aggregations variable_bound mixed_binary
a2c1s1	easy	3648	192	3456	3312	10178	M. Vyve, Y. Pochet	c1s1	10889.137625	benchmark_suitable aggregations variable_bound mixed_binary
dg012142	hard	2080	640	1440	6310	14795	A. Miller	–	2300867	aggregations precedence variable_bound mixed_binary

Reference

@ARTICLE{Castro2006,
  author =       {J. Castro},
  title =        {Minimum-distance controlled perturbation methods for large-scale tabular data protection},
  journal =      {European Journal of Operational Research},
  year =         {2006},
  volume =       {171},
  pages =        {39--52},
}
@ARTICLE{Castro2011,
  author =       {J. A. González, J. Castro},
  title =        {A heuristic block coordinate descent approach for controlled tabular adjustment},
  journal =      {Computers & Operations Research},
  year =         {2011},
  volume =       {38},
  pages =        {1826--1835},
}
@ARTICLE{Castro2012,
  author =       {J. Castro},
  title =        {Recent advances in optimization techniques for statistical tabular data protection},
  journal =      {European Journal of Operational Research},
  year =         {2012},
  volume =       {216},
  pages =        {257--269},
}

@ARTICLE{CastroFrangioniGentile2014,
  author =       {J. Castro, A. Frangioni, C. Gentile},
  title =        {Perspective reformulations of the CTA problem with L2 distances},
  journal =      {Operations Research},
  year =         {2014},
  volume =       {62},
  pages =        {891--909},
}

@ARTICLE{BaenaCastroGonzalez2015,
  author =       {D. Baena, J. Castro, J. A. González},
  title =        {Fix-and-relax approaches for controlled tabular adjustment},
  journal =      {Computers & Operations Research},
  year =         {2015},
  volume =       {58},
  pages =        {41--52},
}