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The Traveling Salesman
• NP Complete• It is likely that the worst case
running time for any algorithm for the TSP increases exponentially with the number of cities.
304/15/23 DD - North Dakota State University
Classes of Search Methods
Search Method
Calculus Based Method
Guided Random Search Method
Enumerative Method
BFSDFS Dynamic Programming
Tabu Search
Hill Climbing
Simulated Anealing
Evolutionary Algorithms
Genetic Algorithms
Fibonacci Sort
Swarm Intelligence
Particle Swarm
Ant Colony
Differential Evolution
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Evolutionary Algorithms
• Emulate evolutionary processes.• Operate on population of individuals.
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List of Parts for Real Parameter Optimization with EA
• A function to optimize
• A domain in which to optimize
• An Evolutionary Algorithm
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The Function and The Domain
Function:We want to find the minimum value on the landscape.
8
Global Minimum
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The Algorithm-Differential Evolution
• Real Parameter Optimizer• Utilizes a pre-specified number of random solutions • Continuously improves them through a series of mutations and re-
combinations• Usually, the number of pre-specified solutions i.e. the population size
does not change during the lifetime of the algorithm
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Important Nomenclature
• D = Dimensionality of the problem• NP = No. of solution vectors in a
population • G = No. of generations the population has to go
through• F = Scaling Factor• Cr = Crossover rate
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Mutation
• Mutation is a change in the gene characteristics of a chromosome.• Applied to evolutionary computation it means a change in the
parameters of the vector through a perturbation with a random element.
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Mutation
• A parent vector from the current generation is called target vector• The mutant vector obtained through differential perturbation is
called donor vector • The offspring obtained through recombination of target and donor is
called trial vector
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Create Trial Vector
• Suppose: rand =0.945, Cr =0.9
• If rand < Cr, pick the parameter from the donor
• Else from the parent
• Do this for all 10 parameters
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Selection- Choose between Parent and Child/Trial Vector
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Control Parameters
• NP, F and Cr are collectively termed as control parameters of DE• The performance of DE is very sensitive to the values of control
parameters• Every problem/function may respond differently to different sets of
control parameters.
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Benchmark Functions- IEEE CEC 2013 Test Suite
• State of the art benchmark functions used in CEC Real Parameter Optimization Competitions and Conferences
• Emulate the properties of real world large scale optimization problems
• IEEE CEC Test suites have constantly evolved over time with the advances in the field of Large Scale Global Optimization
• All the problems listed in the Test Suite are minimization problems
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Scaling Factor
Scales the difference of solutions and controls the step size
Many Authors have reported that its effective values lie between [0.4, 1]
though it may ultimately also depend upon the problem landscape
Contradicting results have been reported for what should be good values
for the scaling factor
So what do we do?
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Altering the Scaling Vector
Deterministic - the parameters are altered based on some user defined rules
Adaptive - the parameters are allowed to adapt based on some feedback from
the algorithm
Evolutionary - the parameters are encoded into the solution itself and they
evolve as a part of the general population
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In Our First Paper
• We primarily focus our attention towards deterministic parameter control methods and the control parameter, scale factor (F), in particular.
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DETVSF - DE with Time Varying Scale Factor
Linear Reduction
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DEDASF - DE with Dither and Annealed Scale Factor
Non Linear Reduction
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Result 2 - Hocheberg’s Post Hoc Procedure: significance level 0.1
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Second Paper - Objective
• To detect, classify and count the type of moving vehicles
34Source: http://www.123rf.com/stock-photo/highway.html04/15/23 DD - North Dakota State University
How to Identify Axles?
• Axles are circular
• Shape recognition algorithm must be employed
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Hough Transform
• Is a feature extraction technique used in image analysis• Can be used to detect lines, circles, and ellipses or any shape
represented by a set of parameters• We focus on circle detection
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Recognition Example (1)
• dp (accumulator resolution)=1.25
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Stages In Object Tracking
• Object Initialization• Appearance model Initialization• Search – Object Localization• Appearance model Updation
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Modeling The Target
• Represent the target as• Vector• Matrix• Histogram• Wavelets
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Modeling – A Difficult Task
• Scene changes• Illumination • Background• Occlusion• Deformation• Noise
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