Inteligencia Artificial para

Optimizar el Uso del Agua

Ing. Wilmer Barreto

Introduction

Objective

To introduce a multi-tier multi-objective

approach to allocate funds in projects of

rehabilitation for drainage system networks.

Multi-objective approach

Funds Allocation for rehabilitation.

Optimal budget allocation

Preferences:

Urgent requirements

Better performance

Avoid or reduce flooding

Risk minimization

Stakeholder preferences

Multi Objective

Optimization approach

Sustainable Urban Drainage

(SUDS)

Sustainable

UDS

Technical Social

Environ. Economic

Local

Authorities

Engineers &

Developers

Public NGOs

& Pressure

groups

Rehabilitación del Drenaje

Drenaje Sostenible

Rehabilitación del Drenaje

Drenaje Sostenible (Green Roof)

Rehabilitación del Drenaje

Drenaje Sostenible

Multi-tier approach

Pareto Front

S

dssfObj )(1

2Obj

1ObjS

dssfObj )(2

Level of Service

Trade off Zone

Rehabilitation Phases

Initial Planning

Phase 1

Data Collection

Phase 2a

Assessing Structural

Condition

Phase 2b

Assessing Environmental

Condition

Phase 2c

Assessing Hydraulic

Performance

Phase 3

Developing the Drainage

Area Plan

Implementing

The Plan

Hydraulic modeling

Based on the UDS decomposition

(e.g., Djordjević 1999; Ole Mark 2004)

1D or 2D?

One o more

Objectives?

Hydraulic modeling

h

Minor system capacity - 1D

Major system capacity - 1D

Flooding - 2D

Sustainability Criteria Category

Primary Criteria

Technical and Scientific Performance

System performance (quantity and quality)

System reliability

System durability

System flexibility and adaptability

Environmental Impacts

Water volume impact

Water quality impact

Ecological impact

Resource use

Maintenance, service provision and responsibility

Social and Urban Community Benefits

Amenity, aesthetics, access, and community

benefits

Public information, education and awareness

Stakeholder acceptability, perception and attitude

to risk and benefits

Health and safety risks

Economic Costing

Financial risks

Affordability

Life cycle

Multi-tier approach

Objective functions

Multi-objective approach:

– Flooding damages:

– Rehabilitation costs (pipe renewal)

2

1

( * )n

i i

i

f Min L C

1 max

1 1

ncells nluk k

i i

i k

f fc C dep

Flood damage functions

)(VolumefCost flood

)*( CLfCostPipes

Volume Y(m) A m2 Cost

0.00 0.00 0.00 0.00

1500 1.25 320 12525.25

… … … …

L(m) D(m) Aging Cost

100 0.50 2 0.00

500 1.25 8 12525.25

… … … …

Above ground

Under ground

Optimization model structure

Preprocessor of the MOUSE data

Optimizer 1: NSGA-II

NSGA-II by Deb et al. (2002).

Pt

Qt

F1

F2

F3

Rt

Non-dominated

sorting

Crowding distance

sorting

} }

Rejected

P t+1

Optimizer 2: -MOEA (modification

to NSGA-II)

Laumanns and Deb (2002) introduced -domination

-dominated

dominated

Optimizer 2: -MOEA

Algorithm structure

Genetic Operation

Offspring Domination -domination

Population

Tournament

Archive

Software: Pareto layer generation

Algorithms’ performance: metrics

Metric Indicators (Zitzler 2002):

– Cardinality

– Number of function evaluations

– Time

– Hypervolume

– Epsilon Indicator

2

1

112

),(i

i

niAzBz z

zBAI MaxMinMax

Test Case

Test Case

Results

Test Case Best Results for NSGA-II and Epsilon-MOEA

NSGA -II -MOEA

Test Case

1

2

Parallel Computing

Cluster of computers: 1. Parallel Virtual Machine (PVM):

Heterogeneous Cluster Networks

Context management (virtual machine)

Fault tolerant

2. Message-Passing Interface (MPI):

Standard for Super Computers (MPP)

Commercial and free Implementations

Future of Parallel computations ?.

Parallel Computing

Serial approach:

Master/Slave

Master

Master

Slave 1

Slave 2

Slave 4

Slave 3

Serial Time

Parallel Time

Communication Time

Parallel Computing

A Parallel NSGA-II:

Random

Population

Population

Evaluation

Genetic

Operators

Init

End

Stop?

Parallel

evaluation

Master Slaves

Nsgas.exe

Ifacemouse.exe

Mouse.exe

Master: nsgam.exe

1. Start slaves

2. Send configuration command

3. Send Individual

4. Receive evaluated Individual

5. Go to step 3 until end

6. Send termination command

Nsgam.exe

Slave: nsgas.exe

1. Wait for master command

2. Select command:

Configuration

Evaluate Individual

Terminate

3. Go to step until end

Parallel Computing

The Cluster:

– 1 Cpu AMD Atholon 800Mhz. RAM 128MB HD 20GB. OS: LINUX Debian etch

– 4 Cpu’s Celeron 1.8GHz, RAM 128MB, HD 20GB, OS: WINDOWS 2000

– 4 Cpu’s Celeron 2.0GHz, RAM 128MB, HD 20GB, OS: WINDOWS 2000

– 2 Cpu’s P4 2.4GHz and 1.8GHz, RAM 256MB, HD 40GB, OS: WINDOWS 2000

Parallel Computing

Parallel Computing

Parallel Computing

Results after 5000 function evaluations:

1 Cpu = 12.8 hours

10 Cpu = 4.8 hours 62.5 % Reduction !!

Parallel Computing Pareto Front

Visualization

Results after 5000 function evaluations:

1 Cpu = 12.8 hours

10 Cpus = 4.8 hours 62.5 % Reduction !!

Study Case for parallel Bello Horizonte Network

• 168 Pipes

• 169 Nodes

• Hypothetical Rainfall

605000.0 606000.0 607000.0 608000.0 609000.0 610000.0

[m]

7806800.0

7807000.0

7807200.0

7807400.0

7807600.0

7807800.0

7808000.0

7808200.0

7808400.0

7808600.0

7808800.0

7809000.0

7809200.0

7809400.0

7809600.0

7809800.0

7810000.0

7810200.0

7810400.0

7810600.0

7810800.0

7811000.0

7811200.0

7811400.0

7811600.0

7811800.0

7812000.0

7812200.0

7812400.0

7812600.0

7812800.0

7813000.0

7813200.0

[m] Standard

Speed Up fo Bello Horizonte

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Processors

Sp

eed

Up

BelloHz Speed UP Theoretical Speed Up Test Case

OTROS PROYECTOS EN

CURSO

Optimización del uso del embalse Yacambú usando

algoritmos Genéticos

Estimación del almacenamiento Potencial de las Lagunas

en el Valle de Quibor mediante Redes Neuronales

Predicción de las Fallas en las Tuberías de

Abastecimiento de Agua Potable Mediante Minería de

Datos (Arboles de Decisión)

Gracias …

Cardinality

Higher cardinality

Lower cardinality

Back

Hypervolume 2 Objectives

Hypervolume 2

Hypervolume 1

Hypervolume 3 Objectives

1

2

3

z

y

x

1

3

2

Hypervolume Slices

c

b a

a

Back

Epsilon Indicator

Scaled Pareto Set

Original Pareto Set

I

Back