Computational Intelligence For Optimization

Deepak SharmaDeepak SharmaResearch Fellow

Department of Electrical and Computer EngineeringNational University of Singapore

Email: eledeepa@nus.edu.sg

Overview of TalkOverview of Talk Genetic Algorithm for Designing Introduction and Procedure of GA Introduction and Procedure of GA Application in designing mechanism Approach Results and Discussion Conclusions

M l i A M d li f h d li Multi-Agent Modeling for scheduling Introduction of MAS and Thermal generation scheduling Problem formulation Problem formulation Approach Results and Discussion Conclusions

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Borrowed from the lecture notes of Dr Dipti Srinivasan @ NUS

Genetic Algorithm for DesigningGenetic Algorithm for Designing Introduction Computerized search and optimization technique 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's Can avoid premature convergence to local optima s Suitable for complex problems

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 Initialize Procedure Initialize Population

Fitness evaluation of individuals

Population Based Meta-Heuristic Algorithm Initial random population of candidate

solutions

Ranking

Termination

Parent Population

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 Termination criterion

met?

SelectionElimination

No

Yes

ppopulation based on fitness values Selection: Survival of fittest by choosing good

solutions based on ranking Crossover: Create new individuals from the

selected parentsTerminate

selected parents Mutation: Perturb the newly created individuals Fitness evaluation of new population Ranking of new population Report

resultsCrossoverRanking Elimination to propagate good individuals

Termination criterion Report results

results

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MutationFitness evaluation

Child Population

Application in DesigningApplication in Designing Goal: To design a mechanism Path generating compliant mechanismg g p

One piece flexible elastic mechanism that has to generate user defined path

Identify the locations where ymaterial has to be filled optimally

Advantage over traditional mechanism Joint-less and monolithic structureJ Less friction wear and noise Light weight Easy to manufacture without assemblyasy to a u actu e w t out asse b y

Applications Micro-actuators Micro switches

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Micro-switches

Designing criterion in literature Minimizing the gap between actual and user

defined paths (single or multi objective)defined paths (single or multi-objective) Limitation: Without limiting the gap, actual

and prescribed paths can be apart from each other

Motivation 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 d A h Proposed Approach Objective:

Minimum weight Constraints:

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Constraints:

Characteristics of given designing problemg g g p•Discrete search space

•Mixed-variables•Non-linear

•C t i d ti i ti bl•Constrained optimization problem

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Multi-ObjectivizationMulti Objectivization Definition: Provide solution to single objective optimization by adding helper g j p y g p

objective(s) and deal with the problem as multi-objective optimization

AdvantagesG id h h f l i l i h id l l i Guide the search for evolutionary algorithms to avoid local optima

Maintain the diversity in the population

Further Benefit Multiple optimal solutions

Bi-Objectives: Minimize weight of structure (Primary objective) Minimize supplied input energy to structure (Secondary Objective)

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Customized Genetic AlgorithmCustomized Genetic Algorithm Structure

representationrepresentation

Domain specific initial population

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Contd.Contd. Chromosome

Shape C diti

Connectivity and repairing techniques To connect topology Conditions To connect topology Single point connectivity Floating element

2D crossover operator

Finite element analysis S d d fl i l i Stress and deflection analysis

Parallel Computing Master-Slave architecture F d i th t ti

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For reducing the computation time

Contd.Contd. Local search: Post processing Mutation and hill-climbing Mutation and hill climbing Weighted sum method to reduce the bi-objective problem into

single objective

Weights Weights

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Results and DiscussionResults and Discussion Comparison Customized Initialization of structure shapes 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.Contd. Performance test R-indicator: Closeness to R indicator: Closeness to

the reference Pareto-OptimalfrontH l i di S d Hypervolume-indicator: Spreadand closeness

Path traced by solutions

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Contd.Contd. Shapes of structures

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Contd.Contd. Optimum conditions Main Findings

Formulation that can guarantee feasible designs

Multiple solutions for decision making

Computation time

ec s o a g Optimum set of conditions Better performance of

customized GA against customized GA against random initialization based GA

Customized schemes able Customized schemes able to generate practically feasible designs

P ll l t i d GA

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Parallel customized GA

Multi-Agent Modeling for SchedulingMulti Agent Modeling for Scheduling Multi-Agent System (MAS)

System of flexible autonomous agents where these agents are loosely connected and act in the environment to achieve their goals

Broadly classified approaches for exploiting MAS Building flexible-robust-extensible system Modeling the large and complex systemS b fi Some benefits Increase computation speed because of parallel computation and asynchronous

operations Graceful degradation of system when one or more agents failg y g Scalability and flexibility of adding and removing agents Reusability of agents

Critical challengesU bl b h i i h i i Unstable behavior in changing environment

Converge to sub-optimal solution due to limited visibility Action or decision taken by an agent may not be suitable for another agent

which can be reduced by sharing information. But the problem is when to

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y g pcommunicate and to which agent

Difficult in debugging and testing parallel and distributed system

Day Ahead Thermal Generation SchedulingDay Ahead Thermal Generation Scheduling In restructured power system Generator companies (GENCOs) are independent and Generator companies (GENCOs) are independent and

autonomous These companies compete with each other for selling the power and

reserve in the power market to earn profitreserve 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 bl f GENCO h l b dd k It is important problem for GENCO while bidding in power market

GENCO performs a day ahead scheduling task based on the forecast data We assume that the forecast data is given

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Contd.Contd. Scheduling involves two decision making processes ON/OFF status of every generator (Unit Commitment) ON/OFF status of every generator (Unit Commitment)

In peak load hours, more number of units should be committed that can earn profit

I ff k l d h i t it 1500

2000

(M

W)

In off-peak load hours, appropriate units should be committed that can earn profit

Because of the physical constraints, anyt t t t h t d

0

500

1000

0 4 8 12 16 20 24Load

Dem

and

generator can not start or shut-down,immediately.

Thus, optimal scheduling is required

Hours -->

Desired amount of power delivery (Economic Power Dispatch) Distribute the power generation among the committed generators

optimally in order to maximize the profit

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Profit Maximization for a GENCOProfit Maximization for a GENCO Objective:

Maximize Profit = Revenue –O COperation Cost

Revenue: By selling power and reserve to market Power is sold at forecast spot price

Power Spot priceOn/Off status

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 Probability of Rbut not used. If used, then it is sold at spot price

Operation cost: Fuel cost of committed generators and start-

f

Probability of reserve calling

Reserveprice

Reserve

up cost of these generators Fuel Cost:

Start-up cost: If generator was OFF

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Start-up cost: If generator was OFF previously and now committed

Contd.Contd. Constraints System Constraints System Constraints

Load demand at time t : Reserve requirement at time t :

Unit Constraints Power Generation Limits Power Generation Limits

Minimum Up/Down TimeG t t b ON/OFF f Generator must be ON/OFF for 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•CombinatorialCombinatorial

•Constrained optimization problem

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Existing Problem Solving TechniquesExisting Problem Solving Techniques1) Priority List

Give priority to generators and commit or de-commit them accordingly Computationally efficient but based on heuristics that can lead to sub-optimal solutionp y p

2) Dynamic Programming Solving complex problem by dividing it to sub-problems Can find near optimal solution but mathematically complex and consumes more Can find near optimal solution but mathematically complex and consumes more

computation time

3) Mathematical Techniques like Lagrange Relaxation (LR), Branch-and-Bound method etcmethod etc

Efficient in solving large scale problem and also consumes less CPU time Sensitive to parameters and susceptible to converge at sub-optimal solution

4) Stochastic Algorithms like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Evolutionary Programming (EP) etc

Can avoid premature convergence but computationally expensive

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5) Hybrid Techniques like LR-EP, LR-GA, EP-Tabu Search etc Can obtain near optimal solution for large scale in reasonable computation time

Multi-Agent Modeling for Profit MaximizationMaximization Multi-Agent system

Coordinating agent (CA) Generator agents (GenAgents) Generator agents (GenAgents)

Architecture of Agents Optimization problem is decomposed and functionalities are assignedp p p g CA (Summation over time is decomposed)

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 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) Decide the desired amount of power and reserve to be sold and evaluates profit Decide the desired amount of power and reserve to be sold and evaluates profit

Simplified constraints on load demand and reserve:

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Checks minimum up and down time constraints and take action, if not satisfied

Communication and NegotiationNegotiation Interaction: Steps 1-3

Share data with GenAgents and these agents evaluate their profitp o t

Competing Scenarios: Steps 4-7 CA commits maximum profit generating GenAgents

Cooperative scenario: Step 8-12 Power sharing for committing other GenAgents which

increase the profit of system for remaining demand Up and down time constraint satisfaction: Steps 13-15

GenAgents check these constraints when asked by CA If any GenAgents check these constraints when asked by 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 Termination: Steps 16-18 Current profit is same as last iteration profit from

committed GenAgents Also, there is no GenAgent with “must commit” condition

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DataData Forecast data Generator data

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Simulation Results and DiscussionSimulation Results and Discussion Ten Generator System Approach is referred as: TGMAM Approach is referred as: TGMAM

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Simulation Results for Large SystemsSimulation Results for Large Systems Compare with LR, GA and LRGA

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Contd.Contd. Working Behavior Conclusions

Developed TGMAM for a GENCO in deregulated power

Execution Time

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

Comparison LR and TGMAM

Problem decomposition

many scenarios of profit maximization

Parameter-less as opposed to LR

C i t t i t h i ti Rules vs iterations With other MAS approaches

Deterministic rules vs stochastic approach

Consistent against heuristic or stochastic algorithm like GA, LRGA etc.

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pp New and efficient rules for

scheduling

Concluding RemarksConcluding Remarks Computational intelligence techniques were developed

for solving complex real world problemsfor solving complex real world problems

Genetic Algorithm was customized g Generated improved topologies of mechanism Provided better decision making via multiple solutions

Multi-agent model was developed for a generator i d company in restructured power system

Obtained best profit solutions Substantially smaller computation time

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Substantially smaller computation time

Thank you for your kind attention!

Happy to answer queries