dws008-03

decomposition precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Philipp Leise	32280	16344	3.13065e-04	hard	dws	62831.7633546923	dws008-03.mps.gz

MILP for designing a decentralized water supply system for drinking water in skyscrapers. The nonlinear characteristics of pumps are integrated with the help of an aggregated convex combination. The instances vary in the total number of floors and load scenarios for water demand. First stage variables represent the layout decisions, second stage variables represent the operational parameters, such as the continuous rotating speed of pumps or binary switching decisions.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	32280	32273
Constraints	16344	16272
Binaries	18928	18924
Integers	0	0
Continuous	13352	13349
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000313065	0.000314213
Nonzeroes	165168	165008

Constraint Classification Properties
	Original	Presolved
Total	16344	16272
Empty	0	0
Free	0	0
Singleton	52	0
Aggregations	0	0
Precedence	420	417
Variable Bound	1232	1223
Set Partitioning	280	280
Set Packing	28	28
Set Covering	84	0
Cardinality	0	0
Invariant Knapsack	0	84
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	14248	14240
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	2.404834
Constraint %		0.301131	0.352408	0.301131	13.27430
Variable %		0.374880	0.392122	0.374880	4.73712
Score	0.882460

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	Obj. Viol	Submitter	Date	Description
2	62831.76		0	0e+00	0	Robert Bixby	2020-02-10	Solved with Gurobi 9.0 within 7 hours
1	62831.76	62831.76	0	8e-07	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to dws008-03 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
dws012-02	open	51108	30096	21012	26382	261120	Philipp Leise	dws	126211.9341071*	aggregations precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary
dws012-03	open	76068	44616	31452	38484	389304	Philipp Leise	dws	140473.60932083728*	precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary
dws012-01	open	26148	15576	10572	14280	132936	Philipp Leise	dws	82030.55222223999*	decomposition precedence variable_bound set_partitioning set_packing mixed_binary
dws008-01	easy	11096	6608	4488	6064	56400	Philipp Leise	dws	37412.60458794508	benchmark decomposition benchmark_suitable precedence variable_bound set_partitioning set_packing mixed_binary
neos2	easy	2101	1040	1061	1103	7326	NEOS Server Submission	neos-pseudoapplication-93	454.86469703	decomposition benchmark_suitable precedence variable_bound set_partitioning mixed_binary

Reference

@inproceedings{AltherrPelzIREC2016, 
author = "Altherr, Lena C. and Wolf, Jan and Ederer, Thorsten and Leise, Philipp and Pelz, Peter F.", 
title="Algorithmic Design of an Optimal Water Supply System with TOR",
year="2016",
booktitle={3rd International Rotating Equipment Conference}
}