control20-5-10-5

decomposition numerics variable_bound set_partitioning mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Qie He	1310	2430	4.62099e-03	easy	control	406205618311810	control20-5-10-5.mps.gz

Optimal control of a discrete-time switched system model Numerically challenging. Different solvers report this instance as solved to optimality, infeasible, or unbounded.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	1310	1300
Constraints	2430	2420
Binaries	100	100
Integers	0	0
Continuous	1210	1200
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00462099	0.00466942
Nonzeroes	14710	14690

Constraint Classification Properties
	Original	Presolved
Total	2430	2420
Empty	0	0
Free	0	0
Singleton	10	0
Aggregations	0	0
Precedence	0	0
Variable Bound	2000	2000
Set Partitioning	20	20
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	400	400
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	1.322219
Constraint %		4.58678	4.60744	4.58678	5.00000
Variable %		4.96183	4.96183	4.96183	4.96183
Score	0.875765

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
1	4.062056e+14	4.062056e+14	0	0.0599859	0	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to control20-5-10-5 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
control30-5-10-4	easy	1960	150	1810	3640	21460	Qie He	control	Infeasible	infeasible decomposition numerics variable_bound set_partitioning mixed_binary
control30-3-2-3	easy	332	90	242	512	1472	Qie He	control	-17.25658927192	decomposition numerics variable_bound set_partitioning mixed_binary
neos-799711	easy	41998	910	41088	59218	147164	NEOS Server Submission	neos-pseudoapplication-25	-11170211.734	numerics aggregations precedence variable_bound set_partitioning set_packing cardinality mixed_binary
rentacar	easy	9557	55	9502	6803	41842	MIPLIB submission pool	–	30356760.98379315	aggregations precedence variable_bound mixed_binary
neos-5078479-escaut	easy	3471	1330	2141	3442	9062	Jeff Linderoth	neos-pseudoapplication-35	9682.338178668055	benchmark_suitable aggregations variable_bound mixed_binary

Reference

@TECHREPORT{HeWu2017, 
author="Q. He and Z. Wu", 
title="Optimal control of a discrete-time switched system", 
INSTITUTION ={Department of Industrial and Systems Engineering, University of Minnesota},
month={February},
year="2017"}