tokyometro

aggregations precedence variable_bound set_partitioning equation_knapsack mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Hsiang-Yun WU	4537	7719	7.69764e-04	open	–	8263.099999999999*	tokyometro.mps.gz

The layout model for Tokyo Metro Map

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	4537	4157
Constraints	7719	7367
Binaries	2496	2148
Integers	2041	2009
Continuous	0	0
Implicit Integers	0	593
Fixed Variables	0	0
Nonzero Density	0.000769764	0.000822051
Nonzeroes	26958	25175

Constraint Classification Properties
	Original	Presolved
Total	7719	7367
Empty	0	0
Free	0	0
Singleton	28	0
Aggregations	150	289
Precedence	0	171
Variable Bound	622	488
Set Partitioning	386	265
Set Packing	0	0
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	3
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	0	2
General Linear	6533	6149
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	2.733197
Constraint %		0.0135740	0.0393647	0.0135740	0.814443
Variable %		0.0467181	0.0997950	0.0934361	0.607335
Score	0.212130

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	Submitter	Date	Description
4	8263.1	8263.1	Edward Rothberg	2022-07-12	Obtained with Gurobi 9.5 using the NoRel heuristic.
3	8329.4		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
2	8467.6		Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	8471.9	8471.9	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to tokyometro 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
lectsched-5-obj	easy	21805	21389	416	0	38884	239608	Harald Schilly	lectsched	24	benchmark benchmark_suitable aggregations precedence variable_bound set_covering invariant_knapsack integer_knapsack general_linear
allcolor10	hard	14872	476	13776	620	34014	89136	Domenico Salvagnin	allcolor	6	decomposition aggregations precedence variable_bound set_partitioning integer_knapsack general_linear
lectsched-4-obj	easy	7901	7665	236	0	14163	82428	Harald Schilly	lectsched	4	benchmark_suitable aggregations precedence variable_bound set_covering integer_knapsack general_linear
allcolor58	open	84376	2492	78288	3596	197154	515184	Domenico Salvagnin	allcolor	258.0*	decomposition aggregations precedence variable_bound set_partitioning integer_knapsack general_linear
neos-4165869-wannon	easy	31728	480	31248	0	85865	270474	Hans Mittelmann	neos-pseudoapplication-44	293	precedence variable_bound set_partitioning set_packing invariant_knapsack integer_knapsack general_linear

Reference

@Misc{TokyoMetro:17, 
  author = {H.-Y. Wu and S. Takahashi}, 
  title = {A MIP Dataset for the Layout of Tokyo Metro},
  Year = {2017}
}

@phdthesis{phdwu:13,
        author = {H.-Y. Wu},
        title = {Constrained Optimization Approaches to Customizing Layout and Annotation for Metro Maps},
        school = {The University of Tokyo},
        year = {2013},
        month = {March},
        address = {Chiba, Japan},
}