berlin_5_8_0

precedence invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
G. Klau	1083	1532	2.71644e-03	easy	–	62	berlin_5_8_0.mps.gz

Railway optimization problems. The problem was solved using CPLEX 12.3 on a 32 core Sun Galaxy 4600 machine, equipped with eight Quad-Core AMD Opteron 8384 processors at 2.7 GHz and 512 GB RAM. It took approximately 9 hours. The problem was solved using CPLEX 12.4 in about 55 minutes (May 2014). Imported from MIPLIB2010.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	1083	1082
Constraints	1532	1531
Binaries	794	794
Integers	0	0
Continuous	289	288
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00271644	0.00272012
Nonzeroes	4507	4506

Constraint Classification Properties
	Original	Presolved
Total	1532	1531
Empty	0	0
Free	0	0
Singleton	1	0
Aggregations	0	0
Precedence	476	476
Variable Bound	0	0
Set Partitioning	0	0
Set Packing	0	0
Set Covering	309	0
Cardinality	0	0
Invariant Knapsack	0	309
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	746	746
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	0.4771212
Constraint %		39.6473	39.9086	39.9086	40.1698
Variable %		47.3684	47.7378	47.7378	48.1071
Score	0.4171230

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	62	62	0e+00	0	0	-	2018-10-11	Solution found during MIPLIB2017 problem selection.
1	62	62	1e-07	0	0	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to berlin_5_8_0 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
railway_8_1_0	easy	1796	1177	619	2527	7098	MIPLIB submission pool	–	400	benchmark_suitable precedence invariant_knapsack mixed_binary
usAbbrv-8-25_70	hard	2312	1681	631	3291	9628	publicly available	–	120	precedence invariant_knapsack knapsack mixed_binary
CMS750_4	easy	11697	7196	4501	16381	44903	MIPLIB submission pool	–	252	benchmark benchmark_suitable precedence invariant_knapsack mixed_binary
pigeon-16	easy	1072	928	144	2353	21104	Sam Allen	pigeon	-15000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-13	easy	754	637	117	1561	13871	Sam Allen	pigeon	-12000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary

Reference

@article{FischettiGloverLodi2005,
 author = {M. Fischetti and F. Glover and A. Lodi},
 journal = {Mathematical Programming},
 pages = {91--104},
 title = {The feasibility pump},
 volume = {104},
 year = {2005}
}