dws012-03

precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Philipp Leise	76068	38484	1.32986e-04	open	dws	140473.60932083728*	dws012-03.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	76068	76061
Constraints	38484	38362
Binaries	44616	44612
Integers	0	0
Continuous	31452	31449
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000132986	0.000133341
Nonzeroes	389304	389070

Constraint Classification Properties
	Original	Presolved
Total	38484	38362
Empty	0	0
Free	0	0
Singleton	102	0
Aggregations	0	0
Precedence	990	987
Variable Bound	2904	2895
Set Partitioning	660	660
Set Packing	66	66
Set Covering	198	0
Cardinality	0	0
Invariant Knapsack	0	198
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	33564	33556
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	2.127105
Constraint %		0.00261	0.0941957	0.0521349	0.187686
Variable %		0.00394	0.4553290	0.0170906	0.913692
Score	0.124156

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID	Objective	Exact	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
2	140473.6	140473.6	0e+00	1e-06	0	Edward Rothberg	2020-09-14	Found with Gurobi
1	148877.4	148877.4	3e-07	0e+00	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to dws012-03 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	121112.055928511*	aggregations precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary
dws008-03	hard	32280	18928	13352	16344	165168	Philipp Leise	dws	62831.7633546923	decomposition precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary
dws012-01	open	26148	15576	10572	14280	132936	Philipp Leise	dws	82030.53014261134*	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
uccase10	open	110818	16800	94018	196498	787045	Daniel Espinoza	uccase	39133.6229762502*	aggregations precedence variable_bound 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}
}