Evolutionary computation and_applications

Evolutionary Computation And

ApplicationsDeepak Dawar

04/15/23 DD - North Dakota State University 1

Problems Galore!

204/15/23 DD - North Dakota State University

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.


Evolutionary Algorithms


Classes of Search Methods

Search Method

Calculus Based Method

Guided Random Search Method

Enumerative Method

BFSDFS Dynamic Programming

Tabu Search

Hill Climbing

Simulated Anealing


Genetic Algorithms

Fibonacci Sort

Swarm Intelligence

Particle Swarm

Ant Colony

Differential Evolution



• Emulate evolutionary processes.• Operate on population of individuals.


List of Parts for Real Parameter Optimization with EA

• A function to optimize

• A domain in which to optimize

• An Evolutionary Algorithm


The Function and The Domain

Function:We want to find the minimum value on the landscape.

8

Global Minimum


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


Differential Evolution


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


Initialization


Initial Population


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.


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


Mutation


Crossover


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


Selection- Choose between Parent and Child/Trial Vector


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.


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


Rotated Ackley’s Function


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?


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


In Our First Paper

• We primarily focus our attention towards deterministic parameter control methods and the control parameter, scale factor (F), in particular.


Dither


DETVSF - DE with Time Varying Scale Factor

Linear Reduction


DEDASF - DE with Dither and Annealed Scale Factor

Non Linear Reduction


Birds Eye View


What do we achieve?


Result 1 - FriedMan’s Test - Ranks


Result 2 - Hocheberg’s Post Hoc Procedure: significance level 0.1


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

Vehicle Recognition Steps


How to Identify Axles?

• Axles are circular

• Shape recognition algorithm must be employed


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


Recognition Example (1)

• Original Image



• dp (accumulator resolution)=1.25



DEMO

Paper 3 - Object Tracking


Stages In Object Tracking

• Object Initialization• Appearance model Initialization• Search – Object Localization• Appearance model Updation


Modeling The Target

• Represent the target as• Vector• Matrix• Histogram• Wavelets


Modeling – A Difficult Task

• Scene changes• Illumination • Background• Occlusion• Deformation• Noise


Univariate Gaussian


Multivariate Gaussian


Gaussian Mixture


Segmentation using GMM


Demo



Thank You

Evolutionary computation and_applications

Education

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