comp07-2idx

benchmark decomposition benchmark_suitable precedence variable_bound set_packing cardinality invariant_knapsack mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Matias Sørensen	17264	21235	2.36161e-04	easy	coursetimetabling	6	comp07-2idx.mps.gz

Instances comp01-21 of curriculum based course timetabling from the International Timetabling Competition 2007. These are time-assignment models (Stage I of the decomposed model), which are smaller than the full model, but still hard to solve.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	17264	17187
Constraints	21235	21189
Binaries	17155	17078
Integers	109	109
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000236161	0.000237482
Nonzeroes	86577	86485

Constraint Classification Properties
	Original	Presolved
Total	21235	21189
Empty	0	0
Free	0	0
Singleton	46	0
Aggregations	0	0
Precedence	12028	12028
Variable Bound	6179	6179
Set Partitioning	0	0
Set Packing	0	1
Set Covering	187	0
Cardinality	131	131
Invariant Knapsack	839	2730
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	1716	11
General Linear	109	109
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	2.367356
Constraint %		0.0047200	0.372835	0.0047200	5.20081
Variable %		0.0116367	0.383058	0.0349101	5.14342
Score	0.838922

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	6	6	0	0	0	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to comp07-2idx 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	Integers	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
comp08-2idx	easy	11554	11487	67	0	12536	51608	Matias Sørensen	coursetimetabling	37	decomposition benchmark_suitable precedence variable_bound set_packing cardinality invariant_knapsack mixed_binary general_linear
comp21-2idx	easy	10863	10792	71	0	14038	57301	Matias Sørensen	coursetimetabling	74	benchmark decomposition benchmark_suitable precedence variable_bound set_partitioning cardinality invariant_knapsack mixed_binary general_linear
comp12-2idx	open	11863	11820	43	0	16803	73677	Matias Sørensen	coursetimetabling	291*	decomposition precedence variable_bound set_partitioning cardinality invariant_knapsack mixed_binary general_linear
neos-983171	easy	8965	6557	0	2408	6711	36691	NEOS Server Submission	neos-pseudoapplication-34	2360	benchmark_suitable precedence variable_bound set_packing invariant_knapsack integer_knapsack mixed_binary general_linear
neos-935769	easy	9799	7020	0	2779	6741	36447	NEOS Server Submission	neos-pseudoapplication-34	3010	decomposition benchmark_suitable precedence variable_bound set_packing invariant_knapsack integer_knapsack mixed_binary general_linear

Reference

ITC2007 webpage: www.cs.qub.ac.uk/itc2007/

Model reference: @Article{Lach2012,
author="Lach, Gerald
and L{\"u}bbecke, Marco E.",
title="Curriculum based course timetabling: new solutions to Udine benchmark instances",
journal="Annals of Operations Research",
year="2012",
volume="194",
number="1",
pages="255--272",
abstract="We present an integer programming approach to the university course timetabling problem, in which weekly lectures have to be scheduled and assigned to rooms. Students' curricula impose restrictions as to which courses may not be scheduled in parallel. Besides some hard constraints (no two courses in the same room at the same time, etc.), there are several soft constraints in practice which give a convenient structure to timetables; these should be met as well as possible.",
issn="1572-9338",
doi="10.1007/s10479-010-0700-7",
url="http://dx.doi.org/10.1007/s10479-010-0700-7"
}