Transcript Final Presentation

A DATA MODEL FOR
VISUAL MOEA
Class: CEE 6110- Hydroinformatics
Date: 12/3/2013
Authors
 Caleb Buahin
 Tyler Stuart
 Miguel Leonardo
Introduction to Optimization
• Optimizing is an act, process, or methodology of making
something (as a design, system, or decision) as fully
perfect, functional, or effective as possible [MerriamWebster].
Components of an Optimization Model
• Classical optimization equation form:
• Minimize/Maximize F= [ f1(X), f2(X),....,fK(X)]
• Subject to the constraints G(X) = [g1(x), g2(x),..., gm(x)] <= 0
• Where k = number of objectives
• n = number of decision variables
• m = number of constraints
• Objective Function(s)
• Functions that operates on decision variables
• Could minimize some component of design
• Cost, Size, etc.
• Could maximize Benefits
• Profit
• Decision Variables
• Inputs that can be altered by operator or design X ={x1,x2,x3,…,xn}
• Constraints
• Limitations on Design
• Physical, Legal, etc.
Multi Objective Evolutionary Algorithms
• A class of optimization algorithms that attempt to mimic
the Darwinian theory of “survival of the fittest” to obtain
the best solutions for optimization problems with
competing objectives
• Evolutionary processes are modeled by MOEAs using
concepts of:
• Selection of good parents for mating
• Mating or cross over of parent genetic material to produce offspring
• Mutation of offspring's genes
• Truncation/trimming of the population to select fittest individuals
and genetic material to survive to the next level of evolution
Multi Objective Evolutionary Algorithms
• How do these biological concepts relate to a general
optimization problem ?
• Genes and chromosomes are represented by decision variables
• Individual/Person refers to a solution/model
• Population refers to a group of individuals
• Phenotypes represent objective function values from an
individual/person/solution/model
• Generation refers to a period at the end of which the best
solutions/individuals/models are selected to participate in the next
round of evolution
Pareto Optimality
• A single solution rarely optimizes all objective functions in an multi
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objective problem
Finding the “trade - offs” between objectives is therefore the goal of
an MOEA optimization.
Optimality within an MOEA is described using Pareto optimality
A solution/individual/model is said to be Pareto optimal in a
minimization problem if all of its objectives function values are at least
less than or equal to corresponding objectives in all other
individuals/solutions/models in a population. It must also have at least
one objective less than a corresponding objective in all other
individuals in a population. A solution with this characteristic is said to
be non-dominated belonging to the Pareto optimal set.
Objective values from the Pareto Optimal set form the Pareto Front
Provides a useful way of comparing individuals/solutions/models and
selecting best ones
Demonstration of how MOEAs find Pareto
Front
• Minimize F = {f1(X), f1(X)}
• f1 = (x1-5)2 + 5*(x2 - 2)2
• f2 = (x1-7)2 + 5*(x2 - 3)2
• X = {x1, x2}
• -5 <= x1 <= 5
• -5 <= x2 <= 5
Visual MOEA
• Originally developed to be used for calibration of
hydrologic models. Subsequently improved to be an all
purpose MOEA framework with tightly integrated reusable
components and a plugin architecture
• Motivation for development:
• Coupling with different models
• An object oriented modeling framework of reusable MOEA
components
• Strongly typed objects to ensure tight integration of reusable
components
• Plugin architecture where plugins supply their own editing, analysis
and visualization controls
• Serializable objects to simplify saving and managing of inputs and
ouputs
Visual MOEA Graphical User Interface
(Demo)
Visual MOEA Data Model
• Because of the large number of iterations that may be
needed to find the Pareto front, a lot of data will have to
be stored analyzed.
• Storing and managing data using files is difficult to
manage and keep track of.
• A relational data model has been designed on top of
Visual MOEA
• Microsoft's Entityframework model was used to achieve
O/R Mapping
Visual MOEA Core Data Model
MOEA Algorithm Types
Model Types
Model Variables
MOEA Objectives
Model Constraints
Stormwater Master Plan
• Three alternatives considered for managing stormwater in
the most recent study 2012:
• Alternative 1 - Continue to maintain the system as its currently
being done and no major infrastructure
• Alternative 2 - Bypass canal system entirely and transfer
stormwater through pipes, ponds and canals
• Alternative 3 – Reconstruct major parts of the canal system to
enable the system perform better against design storms.
• After considering costs, alternative 3 was the selected
alternative by the Logan City Council
Master Plan SWMM Model Alternative 3
Assumptions and Design
Stormwater link surcharging and node
flooding
Model Assessment
• Model divided into 172 watersheds covering an area of ~
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7239 ac
25 year 24 hour rainfall ~ 2.5 in used for modeling
Volume of node flooding ~116 ac-ft
Even with new design there are still areas with flooding
Especially the Logan Northwest Field Canal and Twins
Canals which pass directly through the city and are likely
to cause a lot of damage during flooding.
Optimizing Design For Flood Mitigation
• A node along Logan Northwest Field Canal at 800 N
showing significant flooding within a vulnerable part of the
city was selected to examine the tradeoffs between a
design to reduce the flooding and the costs of the design.
• Flooding volume at this node totaled 3.57 ac-ft
MOEA objectives
• SWMM Freeboard Objective
• This objective maximizes the freeboard in SWMM links
representing canals, culverts pipes etc. Logan City recommends
a 1ft freeboard.
• NL Variable Combination Objective
• Non linear combination of model variables for calculation of cost
based on depth, and size modifications
• Widths constrained to be between 8 to 15 ft
• SWMM Time Series Volume Objective
• This objective minimizes the volume of overflows/flooding on
SWMM model nodes including junctions, culverts, tanks etc.
MOEA objectives
MOEA objectives
SWMM Model Optimization Simulation
and Results
• 6187.999383
Conclusion
• A data model was designed to handle the onerous task of
managing files associated with MOEA
• All information related to an optimization simulation can
be visualized using Visual MOEA or directly queried within
the database to understand how MOEA’s evolve to find a
solution to a problem and understand the nature of a
problem being optimized
• Careful design of the Visual MOEA had to be undertaken
to ensure seamless object-relational mapping