Genetic Algorithms: A Tutorial “Genetic Algorithms are good at

Genetic Algorithms: A Tutorial “Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of things, solutions you might not otherwise find in a lifetime.” - Salvatore Mangano Computer Design, May 1995 Wendy Williams Metaheuristic Algorithms 1 Genetic Algorithms: A Tutorial

The Genetic Algorithm Directed search algorithms based on the mechanics of biological evolution Developed by John Holland, University of Michigan (1970’s) To understand the adaptive processes of natural systems To design artificial systems software that retains the robustness of natural systems Wendy Williams Metaheuristic Algorithms 2 Genetic Algorithms: A Tutorial

The Genetic Algorithm (cont.) Provide efficient, effective techniques for optimization and machine learning applications Widely-used today in business, scientific and engineering circles Wendy Williams Metaheuristic Algorithms 3 Genetic Algorithms: A Tutorial

Classes of Search Techniques S e a rc h te c h n iq u e s C a lc u lu s - b a s e d t e c h n iq u e s D ir e c t m e t h o d s F in o n a c c i G u id e d ra n d o m s e a rc h te c h n iq u e s I n d ir e c t m e t h o d s N e w to n E v o lu tio n a ry a lg o rith m s E v o lu t io n a r y s t r a t e g ie s Wendy Williams Metaheuristic Algorithms D y n a m ic p r o g r a m m in g G e n e tic a lg o rith m s P a ra lle l C e n tra liz e d S im u la t e d a n n e a lin g E n u m e r a t iv e t e c h n iq u e s S e q u e n tia l D is trib u te d 4 S te a d y -s ta te G e n e ra tio n a l Genetic Algorithms: A Tutorial

Components of a GA A problem to solve, and . Encoding technique (gene, chromosome) Initialization procedure (creation) Evaluation function (environment) Selection of parents (reproduction) Genetic operators (mutation, recombination) Parameter settings (practice and art) Wendy Williams Metaheuristic Algorithms 5 Genetic Algorithms: A Tutorial

Simple Genetic Algorithm { initialize population; evaluate population; while TerminationCriteriaNotSatisfied { select parents for reproduction; perform recombination and mutation; evaluate population; } } Wendy Williams Metaheuristic Algorithms 6 Genetic Algorithms: A Tutorial

The GA Cycle of Reproduction reproduction children modification modified children parents population evaluated children evaluation deleted members discard Wendy Williams Metaheuristic Algorithms 7 Genetic Algorithms: A Tutorial

Population population Chromosomes could be: Bit strings Real numbers Permutations of element Lists of rules Program elements . any data structure . Wendy Williams Metaheuristic Algorithms (0101 . 1100) (43.2 -33.1 . 0.0 89.2) (E11 E3 E7 . E1 E15) (R1 R2 R3 . R22 R23) (genetic programming) 8 Genetic Algorithms: A Tutorial

Reproduction children reproduction parents population Parents are selected at random with selection chances biased in relation to chromosome evaluations. Wendy Williams Metaheuristic Algorithms 9 Genetic Algorithms: A Tutorial

Chromosome Modification children modification modified children Modifications are stochastically triggered Operator types are: Mutation Crossover (recombination) Wendy Williams Metaheuristic Algorithms 10 Genetic Algorithms: A Tutorial

Mutation: Local Modification Before: (1 0 1 1 0 1 1 0) After: (0 1 1 0 0 1 1 0) Before: (1.38 -69.4 326.44 0.1) After: (1.38 -67.5 326.44 0.1) Causes movement in the search space (local or global) Restores lost information to the population Wendy Williams Metaheuristic Algorithms 11 Genetic Algorithms: A Tutorial

Crossover: Recombination P1 P2 * (0 1 1 0 1 0 0 0) (1 1 0 1 1 0 1 0) (0 1 0 0 1 0 0 0) (1 1 1 1 1 0 1 0) C1 C2 Crossover is a critical feature of genetic algorithms: It greatly accelerates search early in evolution of a population It leads to effective combination of schemata (subsolutions on different chromosomes) Wendy Williams Metaheuristic Algorithms 12 Genetic Algorithms: A Tutorial

Evaluation evaluated children modified children evaluation The evaluator decodes a chromosome and assigns it a fitness measure The evaluator is the only link between a classical GA and the problem it is solving Wendy Williams Metaheuristic Algorithms 13 Genetic Algorithms: A Tutorial

Deletion population discarded members discard Generational GA: entire populations replaced with each iteration Steady-state GA: a few members replaced each generation Wendy Williams Metaheuristic Algorithms 14 Genetic Algorithms: A Tutorial

An Abstract Example Distribution of Individuals in Generation 0 Distribution of Individuals in Generation N Wendy Williams Metaheuristic Algorithms 15 Genetic Algorithms: A Tutorial

A Simple Example “The Gene is by far the most sophisticated program around.” - Bill Gates, Business Week, June 27, 1994 Wendy Williams Metaheuristic Algorithms 16 Genetic Algorithms: A Tutorial

A Simple Example The Traveling Salesman Problem: Find a tour of a given set of cities so that each city is visited only once the total distance traveled is minimized Wendy Williams Metaheuristic Algorithms 17 Genetic Algorithms: A Tutorial

Representation Representation is an ordered list of city numbers known as an order-based GA. 1) London 2) Venice 3) Dunedin 4) Singapore CityList1 (3 5 7 2 1 6 4 8) CityList2 (2 5 7 6 8 1 3 4) Wendy Williams Metaheuristic Algorithms 5) Beijing 7) Tokyo 6) Phoenix 8) Victoria 18 Genetic Algorithms: A Tutorial

Crossover Crossover combines inversion and recombination: * * Parent1 (3 5 7 2 1 6 4 8) Parent2 (2 5 7 6 8 1 3 4) Child (2 5 7 2 1 6 3 4) This operator is called the Order1 crossover. Wendy Williams Metaheuristic Algorithms 19 Genetic Algorithms: A Tutorial

Mutation Mutation involves reordering of the list: Before: * * (5 8 7 2 1 6 3 4) After: (5 8 6 2 1 7 3 4) Wendy Williams Metaheuristic Algorithms 20 Genetic Algorithms: A Tutorial

TSP Example: 30 Cities 100 90 80 70 y 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 x Wendy Williams Metaheuristic Algorithms 21 Genetic Algorithms: A Tutorial

Solution i (Distance 941) TSP30 (Performance 941) 100 90 80 70 y 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 x Wendy Williams Metaheuristic Algorithms 22 Genetic Algorithms: A Tutorial

Solution j(Distance 800) TSP30 (Performance 800) 100 90 80 70 y 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 x Wendy Williams Metaheuristic Algorithms 23 Genetic Algorithms: A Tutorial

Solution k(Distance 652) TSP30 (Performance 652) 100 90 80 70 y 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 x Wendy Williams Metaheuristic Algorithms 24 Genetic Algorithms: A Tutorial

Best Solution (Distance 420) TSP30 Solution (Performance 420) 100 90 80 70 y 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 x Wendy Williams Metaheuristic Algorithms 25 Genetic Algorithms: A Tutorial

Overview of Performance TSP30 - Overview of Performance 1600 1400 D is tan c e 1200 1000 800 600 400 200 0 1 3 5 7 9 11 13 15 17 19 Generations (1000) Wendy Williams Metaheuristic Algorithms 26 21 23 25 27 29 31 Best Worst Average Genetic Algorithms: A Tutorial

Considering the GA Technology “Almost eight years ago . people at Microsoft wrote a program [that] uses some genetic things for finding short code sequences. Windows 2.0 and 3.2, NT, and almost all Microsoft applications products have shipped with pieces of code created by that system.” - Nathan Myhrvold, Microsoft Advanced Technology Group, Wired, September 1995 Wendy Williams Metaheuristic Algorithms 27 Genetic Algorithms: A Tutorial

Issues for GA Practitioners Choosing basic implementation issues: representation population size, mutation rate, . selection, deletion policies crossover, mutation operators Termination Criteria Performance, scalability Solution is only as good as the evaluation function (often hardest part) Wendy Williams Metaheuristic Algorithms 28 Genetic Algorithms: A Tutorial

Benefits of Genetic Algorithms Concept is easy to understand Modular, separate from application Supports multi-objective optimization Good for “noisy” environments Always an answer; answer gets better with time Inherently parallel; easily distributed Wendy Williams Metaheuristic Algorithms 29 Genetic Algorithms: A Tutorial

Benefits of Genetic Algorithms (cont.) Many ways to speed up and improve a GA-based application as knowledge about problem domain is gained Easy to exploit previous or alternate solutions Flexible building blocks for hybrid applications Substantial history and range of use Wendy Williams Metaheuristic Algorithms 30 Genetic Algorithms: A Tutorial

When to Use a GA Alternate solutions are too slow or overly complicated Need an exploratory tool to examine new approaches Problem is similar to one that has already been successfully solved by using a GA Want to hybridize with an existing solution Benefits of the GA technology meet key problem requirements Wendy Williams Metaheuristic Algorithms 31 Genetic Algorithms: A Tutorial

Some GA Application Types Domain Application Types Control gas pipeline, pole balancing, missile evasion, pursuit Design Scheduling semiconductor layout, aircraft design, keyboard configuration, communication networks manufacturing, facility scheduling, resource allocation Robotics trajectory planning Machine Learning Signal Processing designing neural networks, improving classification algorithms, classifier systems filter design Game Playing poker, checkers, prisoner’s dilemma Combinatorial Optimization set covering, travelling salesman, routing, bin packing, graph colouring and partitioning Wendy Williams Metaheuristic Algorithms 32 Genetic Algorithms: A Tutorial

Conclusions Question: ‘If GAs are so smart, why ain’t they rich?’ Answer: ‘Genetic algorithms are rich - rich in application across a large and growing number of disciplines.’ - David E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning Wendy Williams Metaheuristic Algorithms 33 Genetic Algorithms: A Tutorial