Computational Intelligence For
Optimization
Deepak Sharma
Research Fellow
Department of Electrical and Computer Engineering
National University of Singapore
Email: [email protected]
Overview of Talk
Genetic Algorithm for Designing
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Introduction and Procedure of GA
Application in designing mechanism
Approach
Results and Discussion
Conclusions
M liA
Multi-Agent
Modeling
M d li for
f scheduling
h d li
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Introduction of MAS and Thermal generation scheduling
Problem formulation
Approach
Results and Discussion
Conclusions
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Borrowed from the lecture notes of
Dr Dipti Srinivasan @ NUS
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Genetic Algorithm for Designing
Introduction
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Computerized search and optimization technique
Based on Darwin’s principal of natural selection and genetics
inheritance
Works on the population
Does not require gradient information
Can avoid premature convergence to local optima
optima'ss
Suitable for complex problems
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Example: Mixed variables, continuous or discontinuous search space,
non-linearity, multiple objectives etc.
However, requires more computation time than point-by-point
search methods
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Procedure
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Initialize
Population
Population Based Meta-Heuristic Algorithm
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Initial random population of candidate
solutions
so
ut o s
Fitness evaluation of individuals, e.g., objective
and constraint violation calculations
Ranking: Assign rank to every individual in the
population based on fitness values
Selection: Survival of fittest by choosing good
solutions based on ranking
Elimination
Crossover: Create new individuals from the
selected parents
Mutation: Perturb the newly created individuals
Fitness evaluation of new population
Ranking of new population
Ranking
Elimination to propagate good individuals
Termination criterion
Report results
Fitness
evaluation
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Fitness
evaluation of
individuals
Ranking
Termination
criterion
met?
Parent
Population
p
No
Yes
Selection
Terminate
Report
results
Crossover
Mutation
Child
Population
Application in Designing
Goal: To design a mechanism
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Path ggeneratingg compliant
p
mechanism
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Advantage over traditional mechanism
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J
Joint-less
and monolithic structure
Less friction wear and noise
Light weight
Easy
asy to manufacture
a u actu e without
w t out assembly
asse b y
Applications
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One piece flexible elastic mechanism that has
to generate user defined path
Identifyy the locations where
material has to be filled optimally
Micro-actuators
Micro switches
Micro-switches
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Designing criterion in literature
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Minimizing the gap between actual and user
defined paths (single or multi-objective)
multi objective)
Limitation: Without limiting the gap, actual
and prescribed paths can be apart from
each other
Motivation
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Functionality of mechanism should be represented in terms of
constraints so that every feasible solution can be referred as path
generating compliant mechanism
Can solve the problem for optimal distribution of material in the
design domain
P
Proposed
d Approach
A
h
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Objective:
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Minimum weight
Constraints:
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Characteristics of ggiven designing
g g problem
p
•Discrete search space
•Mixed-variables
•Non-linear
•C t i d optimization
•Constrained
ti i ti problem
bl
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Multi Objectivization
Multi-Objectivization
Definition:
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Provide solution to single
g objective
j
optimization
p
byy addingg helper
p
objective(s) and deal with the problem as multi-objective optimization
Advantages
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Guide
G
id the
h searchh for
f evolutionary
l i
algorithms
l i h to avoid
id local
l l optima
i
Maintain the diversity in the population
Further Benefit
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Multiple optimal solutions
Bi-Objectives:
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Minimize weight of structure (Primary objective)
Minimize supplied input energy to structure (Secondary Objective)
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Customized Genetic Algorithm
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Structure
representation
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Domain specific initial
population
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Contd.
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Chromosome
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Shape
C diti
Conditions
Connectivity and repairing
techniques
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To connect topology
Single point connectivity
Floating element
2D crossover operator
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Finite element analysis
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Parallel Computing
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S
Stress
and
d deflection
d fl i analysis
l i
Master-Slave architecture
F reducing
For
d i th
the computation
t ti
time
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Contd.
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Local search: Post processing
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Mutation and hill
hill-climbing
climbing
Weighted sum method to reduce the bi-objective problem into
single objective
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Weights
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Results and Discussion
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Comparison
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Customized Initialization of structure shapes
Random Initialization of structure shapes
However, rest of the customized GA is same for both cases
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Contd.
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Performance test
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R indicator: Closeness to
R-indicator:
the reference Pareto-Optimal
front
H
Hypervolume-indicator:
l
i di
SSpread
d
and closeness
Path traced by solutions
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Contd.
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Shapes of structures
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Contd.
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Optimum conditions
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Main Findings
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Computation time
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Formulation that can
guarantee feasible designs
Multiple solutions for
decision
ec s o making
a g
Optimum set of conditions
Better performance of
customized GA against
random initialization based
GA
Customized schemes able
to generate practically
feasible designs
P ll l customized
Parallel
t i d GA
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Multi-Agent
Multi
Agent Modeling for Scheduling
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Multi-Agent System (MAS)
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Broadly classified approaches for exploiting MAS
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Building flexible-robust-extensible system
Modeling the large and complex system
S
Some
benefits
b fi
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System of flexible autonomous agents where these agents are loosely connected
and act in the environment to achieve their goals
Increase computation speed because of parallel computation and asynchronous
operations
Graceful degradation
g
of system
y
when one or more agents
g
fail
Scalability and flexibility of adding and removing agents
Reusability of agents
Critical challenges
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Unstable
U
bl bbehavior
h i iin changing
h i environment
i
Converge to sub-optimal solution due to limited visibility
Action or decision taken by an agent may not be suitable for another agent
p
is when to
which can be reduced byy sharingg information. But the problem
communicate and to which agent
Difficult in debugging and testing parallel and distributed system
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Day Ahead Thermal Generation Scheduling
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In restructured power system
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Generator companies (GENCOs) are independent and
autonomous
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GENCO performs a day ahead scheduling task based on the
forecast data
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These companies compete with each other for selling the power and
reserve in the power market to earn profit
Aim: To maximize their profit by generating desired amount of power
and reserve by optimally scheduling the thermal generators
I is important problem
It
bl
ffor GENCO while
h l bidding
b dd in power market
k
We assume that the forecast data is given
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Contd.
Scheduling involves two decision making processes
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ON/OFF status of every generator (Unit Commitment)
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2000
1500
1000
500
0
0
4
8
12
16
20
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Hours -->
Desired amount of power delivery (Economic Power Dispatch)
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In peak load hours, more number of units
should be committed that can earn profit
I off-peak
In
ff
k lload
d hhours, appropriate
i t units
it
should be committed that can earn profit
Because of the physical constraints, any
generator
t can nott start
t t or shut-down,
h td
immediately.
Thus, optimal scheduling is required
Load Demand (MW)
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Distribute the power generation among the committed generators
optimally in order to maximize the profit
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Profit Maximization for a GENCO
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Objective:
Maximize Profit = Revenue –
O
Operation
C
Cost
 Revenue: By selling power and
reserve to market
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Power is sold at forecast spot price
GENCO can receive reserve price
per generator of reserve for every
hour that the reserve is allocated
but not used.
used
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If used, then it is sold at spot price
Operation cost: Fuel cost of
committed generators and startup cost off these generators
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Fuel Cost:
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Start-up cost: If generator was OFF
previously and now committed
Power Spot price
On/Off
status
Probability of
reserve calling
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Reserve
R
price
Reserve
Contd.
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Constraints
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System Constraints
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Load demand at time t :
Reserve requirement at time t :
Unit Constraints
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Power Generation Limits
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Minimum Up/Down Time
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Generator
G
t mustt bbe ON/OFF for
f
minimum number of hours
before shut-down or start-up
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Characteristics of thermal generation scheduling
•High-dimensional
•Mixed-variable
•Non-linear
•Combinatorial
Combinatorial
•Constrained optimization problem
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Existing Problem Solving Techniques
Priority List
1)
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Give priority to generators and commit or de-commit them accordingly
Computationally
p
y efficient but based on heuristics that can lead to sub-optimal
p
solution
Dynamic Programming
2)
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Solving complex problem by dividing it to sub-problems
Can find near optimal solution but mathematically complex and consumes more
computation time
Mathematical Techniques like Lagrange Relaxation (LR), Branch-and-Bound
method etc
3)
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Efficient in solving large scale problem and also consumes less CPU time
Sensitive to parameters and susceptible to converge at sub-optimal solution
Stochastic Algorithms like Genetic Algorithm (GA), Particle Swarm Optimization
(PSO), Evolutionary Programming (EP) etc
4)
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Can avoid premature convergence but computationally expensive
Hybrid Techniques like LR-EP, LR-GA, EP-Tabu Search etc
5)
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Can obtain near optimal solution for large scale in reasonable computation time
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Multi-Agent Modeling for Profit
Maximization
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Multi-Agent system
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Coordinating agent (CA)
Generator agents (GenAgents)
Architecture of Agents
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Optimization
p
pproblem is decomposed
p
and functionalities are assigned
g
CA (Summation over time is decomposed)
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Takes decision for committing GenAgents based on profit
Communicate and store data for GenAgents
Responsible to satisfy load demand and reserve constraints and also to keep track of
remaining demand and reserve
Asks GenAgents to check their minimum up and down time constraints
GenAgents (Summation over N is broken down by creating N agents)
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Decide the desired amount of power and reserve to be sold and evaluates profit
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Simplified constraints on load demand and reserve:
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Checks minimum up and down time constraints and take action, if not satisfied
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Communication and
Negotiation
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Interaction: Steps 1-3
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Competing Scenarios: Steps 4-7
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Power sharing for committing other GenAgents which
increase the profit of system for remaining demand
Up and down time constraint satisfaction: Steps 13-15
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CA commits maximum profit generating GenAgents
Cooperative scenario: Step 8-12
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Share data with GenAgents and these agents evaluate their
po t
profit
GenAgents check these constraints when asked by CA
CA. If any
constraint is not satisfied, GenAgent assigned “must commit”
condition so that the profit of the system can further
increase
Termination: Steps 16-18
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Current profit is same as last iteration profit from
committed GenAgents
Also, there is no GenAgent with “must commit” condition
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Data
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Forecast data
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Generator data
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Simulation Results and Discussion
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Ten Generator System
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Approach is referred as: TGMAM
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Simulation Results for Large Systems
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Compare with LR, GA and LRGA
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Contd.
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Working Behavior
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Conclusions
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Execution Time
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Comparison
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LR and TGMAM
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With other MAS approaches
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Problem decomposition
Rules vs iterations
Deterministic rules vs stochastic
approach
pp
New and efficient rules for
scheduling
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Developed TGMAM for a
GENCO in deregulated power
market
Best profit solution for small to
large systems
Less computation time against
benchmark techniques
Efficient rules for exploring
many scenarios of profit
maximization
Parameter-less as opposed to
LR
C i t t against
Consistent
i t hheuristic
i ti or
stochastic algorithm like GA,
LRGA etc.
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Concluding Remarks
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Computational intelligence techniques were developed
for solving complex real world problems
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Genetic Algorithm
g
was customized
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Generated improved topologies of mechanism
Provided better decision making via multiple solutions
Multi-agent model was developed for a generator
company in
i restructured
d power system
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Obtained best profit solutions
Substantially smaller computation time
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Thank you for your kind attention!
Happy to answer queries 