Introduction to Genetic Algorithms Son Kuswadi Robotics and Automation Based on Biologically-Inspired Technology (RABBIT) Research Groups Electronic Engineering Polytechnic Institute of Surabaya (EEPIS) Institut Teknologi Sepuluh Nopember (ITS)

Road Map Basic Idea Quick Review Classes of Search Techniques Simple GA State of The Art

Road Map Basic Idea Quick Review Classes of Search Techniques Simple GA State of The Art

Basic Idea Suppose you have a problem You don’t know how to solve it What can you do? Can you use a computer to somehow find a solution for you? This would be nice! Can it be done?

Basic Idea A dumb solution A “blind generate and test” algorithm: Repeat Generate a random possible solution Test the solution and see how good it is Until solution is good enough

Basic Idea Can we used this dumb idea? Sometimes - yes: if there are only a few possible solutions and you have enough time then such a method could be used For most problems - no: many possible solutions with no time to try them all so this method can not be used

Basic Idea Dumb Idea… but it was works…. M l h

Basic Idea A “less-dumb” idea (GA) Generate a set of random solutions Repeat Test each solution in the set (rank them) Remove some bad solutions from set Duplicate some good solutions make small changes to some of them Until best solution is good enough

How do you encode a solution? Basic Idea How do you encode a solution? Obviously this depends on the problem! GA’s often encode solutions as fixed length “bitstrings” (e.g. 101110, 111111, 000101) Each bit represents some aspect of the proposed solution to the problem For GA’s to work, we need to be able to “test” any string and get a “score” indicating how “good” that solution is

Silly Example - Drilling for Oil Basic Idea Silly Example - Drilling for Oil Imagine you had to drill for oil somewhere along a single 1km desert road Problem: choose the best place on the road that produces the most oil per day We could represent each solution as a position on the road Say, a whole number between [0..1000]

Basic Idea Where to drill for oil? 500 1000 Road Solution2 = 900 500 1000 Road Solution2 = 900 Solution1 = 300

Basic Idea Digging for Oil The set of all possible solutions [0..1000] is called the search space or state space In this case it’s just one number but it could be many numbers or symbols Often GA’s code numbers in binary producing a bitstring representing a solution In our example we choose 10 bits which is enough to represent 0..1000

Convert to binary string Basic Idea Convert to binary string 512 256 128 64 32 16 8 4 2 1 900 300 1023 In GA’s these encoded strings are sometimes called “genotypes” or “chromosomes” and the individual bits are sometimes called “genes”

Basic Idea Drilling for Oil Solution1 = 300 (0100101100) Road 1000 O I L 30 5 Location

Basic Idea We have seen how to: represent possible solutions as a number encoded a number into a binary string generate a score for each number given a function of “how good” each solution is - this is often called a fitness function

Back to the (GA) Algorithm Basic Idea Back to the (GA) Algorithm Generate a set of random solutions Repeat Test each solution in the set (rank them) Remove some bad solutions from set Duplicate some good solutions make small changes to some of them Until best solution is good enough

Replication and Mutation Basic Idea Replication and Mutation Various method inspired by Darwinian evolution are used to update the set or population of solutions (or chromosomes) Two high scoring “parent” bit strings or chromosomes are selected and combined Producing two new offspring (bit strings) Each offspring may then be changed randomly (mutation)

Basic Idea Selecting Parents Many schemes are possible so long as better scoring chromosomes more likely selected Score is often termed the fitness “Roulette Wheel” selection can be used: Add up the fitness's of all chromosomes Generate a random number R in that range Select the first chromosome in the population that - when all previous fitness’s are added - gives you at least the value R

Road Map Basic Idea Quick Review Classes of Search Techniques Simple GA State of The Art

Quick Review A class of probabilistic optimization algorithms Inspired by the biological evolution process Uses concepts of “Natural Selection” and “Genetic Inheritance” (Darwin 1859) Originally developed by John Holland (1975) Particularly well suited for hard problems where little is known about the underlying search space Widely-used in business, science and engineering

Quick Review Typically applied to: Attributed features: discrete optimization Attributed features: not too fast good heuristic for combinatorial problems Special Features: Traditionally emphasizes combining information from good parents (crossover) many variants, e.g., reproduction models, operators

Quick Review Holland’s original GA is now known as the simple genetic algorithm (SGA) Other GAs use different: Representations Mutations Crossovers Selection mechanisms

Road Map Basic Idea Quick Review Classes of Search Techniques Simple GA State of The Art

Classes of Search Techniques Search Techniqes Calculus Base Techniqes Enumerative Techniqes Guided random search techniqes Sort Dynamic Programming Fibonacci DFS BFS Evolutionary Algorithms Tabu Search Hill Climbing Simulated Anealing Genetic Programming Genetic Algorithms

References C. Darwin. On the Origin of Species by Means of Natural Selection; or, the Preservation of flavored Races in the Struggle for Life. John Murray, London, 1859. W. D. Hillis. Co-Evolving Parasites Improve Simulated Evolution as an Optimization Procedure. Artificial Life 2, vol 10, Addison-Wesley, 1991. J. H. Holland. Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor, Michigan, 1975. Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin, third edition, 1996. M. Sipper. Machine Nature: The Coming Age of Bio-Inspired Computing. McGraw-Hill, New-York, first edition, 2002. D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley, 1989

Road Map Basic Idea Quick Review Classes of Search Techniques Simple GA State of The Art

Simple GA produce an initial population of individuals evaluate the fitness of all individuals while termination condition not met do select fitter individuals for reproduction recombine between individuals mutate individuals evaluate the fitness of the modified individuals generate a new population End while

The Evolutionary Cycle parents selection modification modified offspring initiate & population evaluation evaluate evaluated offspring deleted members discard

Simple Example (Goldberg98) Simple problem: max x2 over {0,1,…,31} GA approach: Representation: binary code, e.g. 01101  13 Population size: 4 1-point xover, bitwise mutation Roulette wheel selection Random initialization We show one generational cycle done by hand

Selection

Crossover

Mutation

Simple GA Has been subject of many (early) studies still often used as benchmark for novel GAs Shows many shortcomings, e.g. Representation is too restrictive Mutation & crossovers only applicable for bit-string & integer representations Selection mechanism sensitive for converging populations with close fitness values

Road Map Basic Idea Quick Review Classes of Search Techniques Simple GA State of The Art

State of The Art Crossover: Alternative Operators Crossover vs Mutation Other Representation: Gray coding, integer, floating point Binary Representation: Required Precision Set

Crossover – Alternative Operators Performance with 1 Point Crossover depends on the order that variables occur in the representation more likely to keep together genes that are near each other Can never keep together genes from opposite ends of string This is known as Positional Bias Can be exploited if we know about the structure of our problem, but this is not usually the case

Crossover – Alternative Operators N-point crossover Choose n random crossover points Split along those points Glue parts, alternating between parents Generalisation of 1 point (still some positional bias)

Crossover – Alternative Operators Uniform crossover Assign 'heads' to one parent, 'tails' to the other Flip a coin for each gene of the first child Make an inverse copy of the gene for the second child Inheritance is independent of position

Crossover vs Mutation Decade long debate: which one is better / necessary / main-background Answer (at least, rather wide agreement): it depends on the problem, but in general, it is good to have both both have another role mutation-only-EA is possible, xover-only-EA would not work

Crossover vs Mutation Exploration: Discovering promising areas in the search space, i.e. gaining information on the problem Exploitation: Optimising within a promising area, i.e. using information There is co-operation AND competition between them Crossover is explorative, it makes a big jump to an area somewhere “in between” two (parent) areas Mutation is exploitative, it creates random small diversions, thereby staying near (in the area of ) the parent

Crossover vs Mutation Only crossover can combine information from two parents Only mutation can introduce new information (alleles) To hit the optimum you often need a ‘lucky’ mutation

Other Representation Gray coding of integers (still binary chromosomes) Gray coding is a mapping that means that small changes in the genotype cause small changes in the phenotype (unlike binary coding). “Smoother” genotype-phenotype mapping makes life easier for the GA Nowadays it is generally accepted that it is better to encode numerical variables directly as: Integers Floating point variables

Integer Representation Some problems naturally have integer variables, e.g. image processing parameters Others take categorical values from a fixed set e.g. {blue, green, yellow, pink} N-point / uniform crossover operators work Extend bit-flipping mutation to make “creep” i.e. more likely to move to similar value Random choice (esp. categorical variables) For ordinal problems, it is hard to know correct range for creep, so often use two mutation operators in tandem

Floating Point Representation Many problems occur as real valued problems, e.g. continuous parameter optimisation f :  n   Illustration: Ackley’s function (often used in EC)

Binary Representation For example, search space x [-1..2], with six places after decimal point Therefore 3x1000000 equal size ranges This means that 22 bit are required since: 2097152=221 <3000000<222=4194304

Binary Representation Mapping from binary string <b21b20…b0> into a real number x from range [-1..2]: convert the binary string <b21b20…b0> from the base 2 to base 10: find a corresponding real number x: