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GENETIC ALGORITHMSSEMINAR REPORT Submitted by

PRAVEEN R S Roll No: 27322To The University of Kerala In partial fulfillment of the requirements for the award of the degree Of Bachelor of Technology in Mechanical Stream Industrial Engineering

Department Of Mechanical EngineeringCollege of Engineering, Thiruvananthapuram 16 November, 2010

DEPARTMENT OF MECHANICAL ENGINEERING COLLEGE OF ENGINEERING THIRUVANANTHAPURAM 16

CERTIFICATE This is to certify that the report entitled GENETIC ALGORITHMS, submitted by Praveen R S, S7 Industrial, Roll No. 27322 to the University of Kerala in partial fulfillment of the requirements for the award of the Degree of Bachelor of Technology in Mechanical stream-Industrial Engineering is a bonafide record of the seminar presented by him.

Sri. V S Unnikrishnan (Asst. Professor)

Dr. Regikumar V (Lecturer)

Sri. M S Subramony (Senior Lecturer)

Prof. Z A Samitha (Senior Staff Advisor)

Prof. E Abdul Rasheed (Head of the Department)

Acknowledgement

I express my gratitude to my guides, Sri. V S Unnikrishnan (Asst. Professor, Department of Mechanical Engineering), Sri. M S Subramony (Lecturer, Department of Mechanical Engineering) and Sri. Rejikumar V (Lecturer, Department of Mechanical Engineering) from College of Engineering, Trivandrum for their expert guidance and advice in presenting the seminar.

I express my sincere thanks to Sri. K Sunilkumar (Lecturer & Staff Advisor, Department of Mechanical Engineering), Prof. Z A Samitha (Professor & Senior Staff Advisor, Department of Mechanical Engineering), Prof. E Abdul Rasheed (Head of Department, Department of Mechanical Engineering), Dr. J Letha (Principal, College of Engineering, Trivandrum) for giving me this opportunity and for their kind cooperation during the course of this work.

I would also wish to record my gratefulness to all my friends and classmates for their help and support in carrying out this work successfully. I also thank the Lord Almighty for the grace, strength and hope to make my endeavour a success.

Praveen R S

AbstractGenetic Algorithm is one among the different Bio-inspired computing algorithms. It applies the Principle of survival of the fittest to find better and better solutions. The feasible solutions from the solution space are evaluated using a fitness function and they are selected for reproduction on the basis of their fitness value. Reproduction involves cross over and mutation. The successive generations would have better average fitness value, compared to the previous generation. The iteration process is continued till the required convergence is attained. Genetic Algorithm usually exhibits a reduced chance of converging to local optimum. It has got a wide variety of applications is Operations Research related problems like Transportation problems, Travelling salesman problem, Scheduling, Spanning tree problem, etc. Keywords: Fitness function, Selection, Cross over, Mutation

Table of contentsSection 1: Section 2: Introduction 1.1 Evolutionary Algorithms Genetic Algorithms 2.1 Genetic Algorithms Overview 2.2 Structure of a Single Population Genetic Algorithm 2.3 Genetic Algorithm Operators 2.3.(i) Selection 2.3.(ii) Recombination or Crossover 2.3.(iii) Mutation Encoding 3.1 Encoding Techniques 3.2 Genotypes and Phenotypes 3.3 Random Keys Selection 4.1 Fitness Function 4.2 Selection Techniques 4.2.(i) Fitness Proportional Selection 4.2.(ii) Ranked Selection 4.2.(iii) Stochastic Universal Sampling 4.2.(iv) Roulette Wheel Selection 4.2.(v) Truncation Selection 4.2.(vi) Tournament Selection Recombination or Crossover 5.1 Recombination Techniques 5.1.(i) One point Crossover 5.1.(ii) Two point Crossover 5.1.(iii) Uniform Crossover 5.1.(iv) Shuffle Crossover 5.1.(v) Partially Matched Crossover 5.1.(vi) Order Crossover 5.1.(vii) Cycle Crossover 5.2 Crossover Probability (pc) Mutation 6.1 Mutation Techniques 6.1.(i) Flip bit Mutation 6.1.(ii) Boundary Mutation 6.1.(iii) Uniform Mutation 6.2 Mutation Probability(pm) Convergence 7.1 Premature Convergence 7.2 Slow Finishing Solution of a Transportation problem using GA 8.1 Problem Statement 8.2 Encoding 8.3 Prfer Number 8.4 GA Operators Conclusion References 1 2 3 3 5 6 6 7 7 8 8 9 9 10 10 10 11 11 11 12 13 13 14 14 14 14 15 15 16 16 17 18 19 20 20 20 20 21 22 22 23 24 24 24 25 25 26 29

Section 3:

Section 4:

Section 5:

Section 6:

Section 7:

Section 8:

Section 9: Section 10:

List of Figures1. The Placement of Genetic Algorithms in the hierarchy of Knowledge Based Information Systems . 1 2. Structure of a simple Genetic Algorithm ............................................................................................ 6 3. Stochastic Universal Sampling ......................................................................................................... 12 4. Chromosome Fitness on a Roulette Wheel ....................................................................................... 12 5. One point Crossover ......................................................................................................................... 14 6. Two point Crossover ......................................................................................................................... 14 7. Uniform Crossover............................................................................................................................ 15 8. Flip Bit Mutation............................................................................................................................... 20 9. Boundary Mutation ........................................................................................................................... 20 10. A Feasible Solution for the Transportation Problem ...................................................................... 24 11. Spanning Tree Representation ........................................................................................................ 24 12. Prfer Number ................................................................................................................................ 25

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1. IntroductionKnowledge-based information systems or Evolutionary computing algorithms are designed to mimic the performance of biological systems. Evolutionary computing algorithms are used for search and optimization applications and also include fuzzy logic, which provides an approximate reasoning basis for representing uncertain and imprecise knowledge. The no free lunch theorem states that no search algorithm is better on all problems. All search methods show on average the same performance over all possible problem instances. The present trend is to combine these fields into a hybrid in order that the drawbacks of one may be offset by the merits of another. Neural networks, fuzzy logic and evolutionary computing have shown capability on many problems, but have not yet been able to solve the really complex problems that their biological counterparts can.

Knowledge Based Information Systems Approximate Reasoning Approaches Search/ Optimisation Approaches

Probabilistic Models

Multivalued & Fuzzy logic

Neural Networks

Evolutionary Algorithms

Evolutionary Strategies

Evolutionary Programming

Genetic Algorithms

Genetic Programming

Figure 1: The Placement of Genetic Algorithms in the hierarchy of Knowledge Based Information Systems

Page |2 1.1.Evolutionary Algorithms Evolutionary algorithms can be used successfully in many applications requiring the optimization of a certain multi-dimensional function. The population of possible solutions evolves from one generation to the next, ultimately arriving at a satisfactory solution to the problem. These algorithms differ in the way a new population is generated from the present one, and in the way the members are represented within the algorithm. They are part of the derivative-free optimization and search methods that comprise, Genetic Algorithms Simulated annealing (SA) which is a stochastic hill-climbing algorithm based on the analogy with the physical process of annealing. Hill climbing, in essence, finds an optimum by following the local gradient of the function (thus, they are also known as gradient methods). Random Search Algorithms - Random searches simply perform random walks of the problem space, recording the best optimum values found. They do not use any knowledge gained from previous results and are inefficient. Randomized Search Techniques - These algorithms use random choice to travel through the search space using the knowledge gained from previous results in the search. Downhill simplex search Tabu search which is usually applied to combinatorial optimization problems

Evolutionary algorithms exhibit an adaptive behavior that allows them to handle nonlinear, high dimensional problems without requiring differentiability or explicit knowledge of the problem structure. They also are very robust to time-varying behavior, even though they may exhibit low speed of convergence.

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2. Genetic Algorithms2.1. Genetic Algorithms Overview Genetic Algorithms (GAs) were invented by John Holland in the 1960s and were developed with his students and colleagues at the University of Michigan in the 1970s. Holland's original goal was to investigate the mechanisms of adaptation in nature and to develop methods in which these mechanisms could be imported into computer systems. Genetic algorithms are search methods that employ processes found in natural biological evolution. These algorithms search or operate on a given population of potential solutions to find those that approach some specification or criteria. To do this, the algorithm applies the principl