milo-v12-6-r1-75-1

decomposition aggregations precedence variable_bound mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Tamas Terlaky	5698	12243	4.61206e-04	open	milo	1153756.39820567*	milo-v12-6-r1-75-1.mps.gz

The models come from structural design optimization where the objective is to minimize the total weight of 2 and 3 dimensional cantilevers. The 2D examples are simpler, and GuRobi can solve the 40_1 and 58_1 instances, while struggles with 75_1. The 3D examples are more challenging. The x_0 and x_1 models are two different modeling of the same identical problems, so their optimal value is the same. The 1_x and 2_x problems are solved by GuRoBi, the 3_x and 4_x are not solved in reasonable time.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	5698	5698
Constraints	12243	11473
Binaries	1925	1925
Integers	0	385
Continuous	3773	3388
Implicit Integers	0	385
Fixed Variables	0	0
Nonzero Density	0.000461206	0.000480381
Nonzeroes	32174	31404

Constraint Classification Properties
	Original	Presolved
Total	12243	11473
Empty	0	0
Free	0	0
Singleton	770	0
Aggregations	391	391
Precedence	1540	1540
Variable Bound	4235	4235
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	5307	4922
General Linear	0	385
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	2.363612
Constraint %		0.235335	0.414432	0.235335	38.3160
Variable %		0.228150	0.434783	0.228150	38.5574
Score	0.802340

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
3	1153756	1153756	DeepMind	2020-10-07	Obtained with machine learning-based large neighborhood search.
2	1153880		Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	1154037	1154037	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to milo-v12-6-r1-75-1 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
milo-v12-6-r1-58-1	hard	4440	1500	2940	9540	25068	Tamas Terlaky	milo	634081.4112039516	decomposition aggregations precedence variable_bound mixed_binary general_linear
milo-v12-6-r2-40-1	easy	2688	840	1848	5628	14604	Tamas Terlaky	milo	326481.14282799	benchmark decomposition benchmark_suitable aggregations precedence variable_bound mixed_binary general_linear
milo-v13-4-3d-4-0	open	688	160	528	1328	3292	Tamas Terlaky	milo	358152.2621937089*	aggregations variable_bound mixed_binary general_linear
milo-v13-4-3d-3-0	hard	516	120	396	996	2456	Tamas Terlaky	milo	273238.08563337	aggregations variable_bound mixed_binary general_linear
neos-4292145-piako	open	32950	13370	19580	75834	190186	Jeff Linderoth	neos-pseudoapplication-57	29160.50026450142*	aggregations precedence variable_bound invariant_knapsack mixed_binary general_linear

Reference

No bibliographic information available