r4l4-02-tree-bounds-50

aggregations mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Christian Liebchen	11468	4768	3.48797e-04	open	–	499258899.0000008*	r4l4-02-tree-bounds-50.mps.gz

Periodic Event Scheduling Problem (PESP) Model for Timetable Optimization in Public Transport Data originating from (see additional file) https://lintim.math.uni-goettingen.de/ and https://num.math.uni-goettingen.de/~m.goerigk/pesplib/ Notation of the variables in the MIP model according to Sec. 9 in Liebchen (2006)

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	11468	9536
Constraints	4768	4768
Binaries	1938	7
Integers	2830	2830
Continuous	6700	6699
Implicit Integers	0	0
Fixed Variables	1932	0
Nonzero Density	0.000348797	0.000376312
Nonzeroes	19072	17110

Constraint Classification Properties
	Original	Presolved
Total	4768	4768
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	7
Precedence	0	0
Variable Bound	0	0
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	1938	1931
General Linear	2830	2830
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	2.025306
Constraint %		0.0209732	0.566675	0.0419463	24.3918
Variable %		0.0314597	0.753835	0.0734060	30.4320
Score	0.482416

Best Known Solution(s)

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

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion

ID	Objective	Exact	Obj. Viol	Submitter	Date	Description
3	499258899	499253949	0e+00	Edward Rothberg	2020-04-22	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	499722034		1e-07	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	503362120	503362120	0e+00	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to r4l4-02-tree-bounds-50 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
neos-4650160-yukon	easy	1412	624	788	1969	6416	Jeff Linderoth	neos-pseudoapplication-79	59.88499998695507	benchmark_suitable aggregations precedence variable_bound set_partitioning set_covering knapsack mixed_binary
bienst2	easy	505	35	470	576	2184	H. Mittelmann	–	54.59999999999996	decomposition benchmark_suitable precedence variable_bound cardinality mixed_binary
bienst1	easy	505	28	477	576	2184	MIPLIB submission pool	–	46.7499999999999	decomposition benchmark_suitable precedence variable_bound cardinality mixed_binary
newdano	easy	505	56	449	576	2184	Daniel Bienstock	dano	65.66666666	decomposition benchmark_suitable precedence variable_bound cardinality mixed_binary
uccase12	easy	62529	9072	53457	121161	419447	Daniel Espinoza	uccase	11507.4050616	benchmark benchmark_suitable aggregations precedence variable_bound mixed_binary

Reference

@article{GoerigkSchachtebeckSchoebel2013, author="M. Goerigk and M. Schachtebeck and A. Sch{\"o}bel", title="Evaluating line concepts using travel times and robustness", journal="Public Transport", volume="5", pages="267--284", year="2013", issue="3"}