milo-v12-6-r1-58-1

decomposition aggregations precedence variable_bound mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Tamas Terlaky	4440	9540	5.91818e-04	hard	milo	634081.4112039516	milo-v12-6-r1-58-1.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	4440	4440
Constraints	9540	8940
Binaries	1500	1500
Integers	0	300
Continuous	2940	2640
Implicit Integers	0	300
Fixed Variables	0	0
Nonzero Density	0.000591818	0.000616422
Nonzeroes	25068	24468

Constraint Classification Properties
	Original	Presolved
Total	9540	8940
Empty	0	0
Free	0	0
Singleton	600	0
Aggregations	306	306
Precedence	1200	1200
Variable Bound	3300	3300
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	4134	3834
General Linear	0	300
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	2.255273
Constraint %		0.302013	0.532538	0.302013	38.5235
Variable %		0.292793	0.558659	0.292793	38.7613
Score	0.800440

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	634081.4	634081.4	Hans Mittelmann	2020-03-08	Solved with Gurobi 9.0 using 40 Threads within 16 hours
2	634081.4		Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	634205.2	634205.2	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to milo-v12-6-r1-58-1 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-r1-75-1	open	5698	1925	3773	12243	32174	Tamas Terlaky	milo	1153756.39820567*	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	19809.5007749*	aggregations precedence variable_bound invariant_knapsack mixed_binary general_linear

Reference

No bibliographic information available