eva1aprime6x6opt

aggregations variable_bound set_packing mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Yoshihiro Kanno	3514	34872	1.31841e-03	open	evaprime	-18.100995280293*	eva1aprime6x6opt.mps.gz

MILP approach to generate structures with negative thermal expansion coefficients

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	3514	3514
Constraints	34872	34872
Binaries	836	836
Integers	0	0
Continuous	2678	2678
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00131841	0.00131841
Nonzeroes	161558	161558

Constraint Classification Properties
	Original	Presolved
Total	34872	34872
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	408	408
Precedence	0	0
Variable Bound	731	731
Set Partitioning	0	0
Set Packing	17155	17155
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	16578	16578
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	1.113943
Constraint %		0.0028700	4.37170	0.0573526	51.8840
Variable %		0.0569152	2.17226	0.2276610	23.7336
Score	0.401446

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	Int. Viol	Cons. Viol	Submitter	Date	Description
5	-18.100995	-18.100995	0e+00	0e+00	Peng Lin and Shaowei Cai	2024-09-29	PartiMIP Solver - A Dynamic Partitioning MIP Solver
4	-16.315283	-16.315283	0e+00	0e+00	Ed Rothberg	2023-05-19	Found with the NoRel heuristic.
3	-12.885929	-12.885691	2e-07	9e-07	Edward Rothberg	2020-09-14	Found with Gurobi
2	-11.618070		0e+00	0e+00	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-3.040871	-3.040871	0e+00	0e+00	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to eva1aprime6x6opt 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
eva1aprime5x5opt	open	1712	400	0	1312	11929	57162	Yoshihiro Kanno	evaprime	-17.94807560443689*	aggregations variable_bound set_packing mixed_binary
neos-3754224-navua	open	150228	3574	0	146654	232387	652974	Jeff Linderoth	neos-pseudoapplication-83	157909.0677610051*	numerics aggregations precedence variable_bound set_partitioning mixed_binary
neos-619167	easy	3452	400	0	3052	6800	20020	NEOS Server Submission	neos-pseudoapplication-83	1.664893618589958	decomposition numerics precedence variable_bound mixed_binary
neos-3594536-henty	open	22924	0	22924	0	21280	65712	Jeff Linderoth	neos-pseudoapplication-83	401223.0*	decomposition aggregations variable_bound general_linear
neos-5018451-chiese	easy	265713	1222	244	264247	170175	1249955	Jeff Linderoth	neos-pseudoapplication-69	-147988824.81	numerics aggregations variable_bound mixed_binary general_linear

Reference

@Article{HK15nte,
  author = "M.~Hirota, Y.~Kanno",
  title = "Optimal design of periodic frame structures with negative thermal expansion via mixed integer programming",
  journal = "Optimization and Engineering",
  volume = "16",
  pages = "767--809"
  year = "2015"
}