Lecture 10 Evolutionary Computation: Evolution strategies and genetic programming

Transcription

1 Lecture 10 Evolutionry Computtion: Evolution strtegies nd genetic progrmming Evolution strtegies Genetic progrmming Summry Negnevitsky, Person Eduction,

2 Evolution Strtegies Another pproch to simulting nturl evolution ws proposed in Germny in the erly 1960s. Unlike genetic lgorithms, this pproch clled n evolution strtegy ws designed to solve technicl optimistion prolems. Negnevitsky, Person Eduction,

3 In 1963 two students of the Technicl University of Berlin, Ingo Rechenerg nd Hns-Pul Schwefel,, were working on the serch for the optiml shpes of odies in flow. They decided to try rndom chnges in the prmeters defining the shpe following the exmple of nturl muttion. As result, the evolution strtegy ws orn. Evolution strtegies were developed s n lterntive to the engineer s s intuition. Unlike GAs,, evolution strtegies use only muttion opertor. Negnevitsky, Person Eduction,

4 Bsic evolution strtegies In its simplest form, termed s (1+1) 1)-evolution strtegy, one prent genertes one offspring per genertion y pplying normlly distriuted muttion. The (1+1) 1)-evolution strtegy cn e implemented s follows: Step 1: 1 Choose the numer of prmeters N to represent the prolem, nd then determine fesile rnge for ech prmeter: {, x }, {, x },..., { x, x } x1 min 1mx x2 min 2mx Nmin Nmx Define stndrd devition for ech prmeter nd the function to e optimised. Negnevitsky, Person Eduction,

5 Step 2: 2 Rndomly select n initil vlue for ech prmeter from the respective fesile rnge. The set of these prmeters will constitute the initil popultion of prent prmeters: x 1, x 2,..., x N Step 3: 3 Clculte the solution ssocited with the prent prmeters: X = f (x 1, x 2,..., x N ) Negnevitsky, Person Eduction,

6 Step 4: 4 Crete new (offspring) prmeter y dding normlly distriuted rndom vrile with men zero nd pre-selected devition δ to ech prent prmeter: x ( ) i = xi + 0, δ i = 1, 2,..., N Normlly distriuted muttions with men zero reflect the nturl process of evolution (smller chnges occur more frequently thn lrger ones). Step 5: 5 Clculte the solution ssocited with the offspring prmeters: ( x x ) X = f 1, 2,..., Negnevitsky, Person Eduction, x N

7 Step 6: 6 Compre the solution ssocited with the offspring prmeters with the one ssocited with the prent prmeters. If the solution for the offspring is etter thn tht for the prents, replce the prent popultion with the offspring popultion. Otherwise, keep the prent prmeters. Step 7: 7 Go to Step 4, nd repet the process until stisfctory solution is reched, or specified numer of genertions is considered. Negnevitsky, Person Eduction,

8 An evolution strtegy reflects the nture of chromosome. A single gene my simultneously ffect severl chrcteristics of the living orgnism. On the other hnd, single chrcteristic of n individul my e determined y the simultneous interctions of severl genes. The nturl selection cts on collection of genes, not on single gene in isoltion. Negnevitsky, Person Eduction,

9 Genetic progrmming One of the centrl prolems in computer science is how to mke computers solve prolems without eing explicitly progrmmed to do so. Genetic progrmming offers solution through the evolution of computer progrms y methods of nturl selection. In fct, genetic progrmming is n extension of the conventionl genetic lgorithm, ut the gol of genetic progrmming is not just to evolve it- string representtion of some prolem ut the computer code tht solves the prolem. Negnevitsky, Person Eduction,

10 Genetic progrmming is recent development in the re of evolutionry computtion. It ws gretly stimulted in the 1990s y John Koz. According to Koz, genetic progrmming serches the spce of possile computer progrms for progrm tht is highly fit for solving the prolem t hnd. Any computer progrm is sequence of opertions (functions) pplied to vlues (rguments), ut different progrmming lnguges my include different types of sttements nd opertions, nd hve different syntctic restrictions. Negnevitsky, Person Eduction,

11 Since genetic progrmming mnipultes progrms y pplying genetic opertors, progrmming lnguge should permit computer progrm to e mnipulted s dt nd the newly creted dt to e executed s progrm. For these resons, LISP ws chosen s the min lnguge for genetic progrmming. Negnevitsky, Person Eduction,

12 LISP structure LISP hs highly symol-oriented oriented structure. Its sic dt structures re toms nd lists.. An tom is the smllest indivisile element of the LISP syntx. The numer 21,, the symol X nd the string This is string re exmples of LISP toms. A list is n oject composed of toms nd/or other lists. LISP lists re written s n ordered collection of items inside pir of prentheses. Negnevitsky, Person Eduction,

13 For exmple, the list ( ( * A B) C) clls for the ppliction of the sutrction function ( )) to two rguments, nmely the list (*A B) nd the tom C. First, LISP pplies the multipliction function (*) to the toms A nd B. Once the list (*A B) is evluted, LISP pplies the sutrction function ( )( ) to the two rguments, nd thus evlutes the entire list ( ( * A B) C). LISP structure Negnevitsky, Person Eduction,

14 Grphicl representtion of LISP S-expressionsS Both toms nd lists re clled symolic expressions or S-expressions.. In LISP, ll dt nd ll progrms re S-expressions. S This gives LISP the ility to operte on progrms s if they were dt. In other words, LISP progrms cn modify themselves or even write other LISP progrms. This remrkle property of LISP mkes it very ttrctive for genetic progrmming. Any LISP S-expression S cn e depicted s rooted point-lelled tree with ordered rnches. Negnevitsky, Person Eduction,

15 LISP S-expression S ( ( (*A B) C) * C A B Negnevitsky, Person Eduction,

16 How do we pply genetic progrmming to prolem? Before pplying genetic progrmming to prolem, we must ccomplish five preprtory steps: 1. Determine the set of terminls. 2. Select the set of primitive functions. 3. Define the fitness function. 4. Decide on the prmeters for controlling the run. 5. Choose the method for designting result of the run. Negnevitsky, Person Eduction,

17 The Pythgoren Theorem helps us to illustrte these preprtory steps nd demonstrte the potentil of genetic progrmming. The theorem sys tht the hypotenuse, c,, of right tringle with short sides nd is given y 2 c = + 2 The im of genetic progrmming is to discover progrm tht mtches this function. Negnevitsky, Person Eduction,

18 To mesure the performnce of the s-yet yet- undiscovered computer progrm, we will use numer of different fitness cses.. The fitness cses for the Pythgoren Theorem re represented y the smples of right tringles in Tle. These fitness cses re chosen t rndom over rnge of vlues of vriles nd. Side Side Hypotenuse c Side Side Hypotenuse c Negnevitsky, Person Eduction,

19 Step 1: 1 Determine the set of terminls. The terminls correspond to the inputs of the computer progrm to e discovered. Our progrm tkes two inputs, nd. Step 2: 2 Select the set of primitive functions. The functions cn e presented y stndrd rithmetic opertions, stndrd progrmming opertions, stndrd mthemticl functions, logicl functions or domin-specific functions. Our progrm will use four stndrd rithmetic opertions +,,, * nd/,, nd one mthemticl function sqrt. Negnevitsky, Person Eduction,

20 Step 3: 3 Define the fitness function. A fitness function evlutes how well prticulr computer progrm cn solve the prolem. For our prolem, the fitness of the computer progrm cn e mesured y the error etween the ctul result produced y the progrm nd the correct result given y the fitness cse. Typiclly, the error is not mesured over just one fitness cse, ut insted clculted s sum of the solute errors over numer of fitness cses. The closer this sum is to zero, the etter the computer progrm. Negnevitsky, Person Eduction,

21 Step 4: 4 Decide on the prmeters for controlling the run. For controlling run, genetic progrmming uses the sme primry prmeters s those used for GAs. They include the popultion size nd the mximum numer of genertions to e run. Step 5: 5 Choose the method for designting result of the run. It is common prctice in genetic progrmming to designte the est-so so-fr generted progrm s the result of run. Negnevitsky, Person Eduction,

22 Once these five steps re complete, run cn e mde. The run of genetic progrmming strts with rndom genertion of n initil popultion of computer progrms. Ech progrm is composed of functions +,, *,/ nd sqrt,, nd terminls nd. In the initil popultion, ll computer progrms usully hve poor fitness, ut some individuls re more fit thn others. Just s fitter chromosome is more likely to e selected for reproduction, so fitter computer progrm is more likely to survive y copying itself into the next genertion. Negnevitsky, Person Eduction,

23 Crossover in genetic progrmming: Two prentl S-expressionsS / + * sqrt sqrt sqrt / + * * (/ ( (sqrt (+ (* ) ( ))) ) (* )) (+ ( (sqrt ( (* ) )) ) (sqrt (/ ))) Negnevitsky, Person Eduction,

24 Crossover in genetic progrmming: Two offspring S-expressionsS / + sqrt sqrt sqrt * / + * * (/ ( (sqrt (+ (* ) ( ))) ) (sqrt ( (* ) ))) (+ ( (* ) ) (sqrt (/ ))) Negnevitsky, Person Eduction,

25 Muttion in genetic progrmming A muttion opertor cn rndomly chnge ny function or ny terminl in the LISP S-expression. S Under muttion, function cn only e replced y function nd terminl cn only e replced y terminl. Negnevitsky, Person Eduction,

26 Muttion in genetic progrmming: Originl S-expressionsS / + * sqrt sqrt sqrt / + * * (/ ( (sqrt (+ (* ) ( ))) ) (* )) (+ ( (sqrt ( (* ) )) ) (sqrt (/ ))) Negnevitsky, Person Eduction,

27 Muttion in genetic progrmming: Mutted S-expressionsS / + + * sqrt sqrt sqrt / + * * (/ (+ (sqrt (+ (* ) ( ))) ) (* )) (+ ( (sqrt ( (* ) )) ) (sqrt (/ ))) Negnevitsky, Person Eduction,

28 In summry, genetic progrmming cretes computer progrms y executing the following steps: Step 1: 1 Assign the mximum numer of genertions to e run nd proilities for cloning, crossover nd muttion. Note tht the sum of the proility of cloning, the proility of crossover nd the proility of muttion must e equl to one. Step 2: Generte n initil popultion of computer progrms of size N y comining rndomly selected functions nd terminls. Negnevitsky, Person Eduction,

29 Step 3: 3 Execute ech computer progrm in the popultion nd clculte its fitness with n pproprite fitness function. Designte the est- so-fr individul s the result of the run. Step 4: 4 With the ssigned proilities, select genetic opertor to perform cloning, crossover or muttion. Negnevitsky, Person Eduction,

30 Step 5: 5 If the cloning opertor is chosen, select one computer progrm from the current popultion of progrms nd copy it into new popultion. If the crossover opertor is chosen, select pir of computer progrms from the current popultion, crete pir of offspring progrms nd plce them into the new popultion. If the muttion opertor is chosen, select one computer progrm from the current popultion, perform muttion nd plce the mutnt into the new popultion. Negnevitsky, Person Eduction,

31 Step 6: 6 Repet Step 4 until the size of the new popultion of computer progrms ecomes equl to the size of the initil popultion, N. Step 7: 7 Replce the current (prent) popultion with the new (offspring) popultion. Step 8: 8 Go to Step 3 nd repet the process until the termintion criterion is stisfied. Negnevitsky, Person Eduction,

32 Fitness history of the est S-expressionS sqrt F i t n e s s, % * + * G e n e r t i o n s B e s t o f g e n e r t i o n Negnevitsky, Person Eduction,

33 Wht re the min dvntges of genetic progrmming compred to genetic lgorithms? Genetic progrmming pplies the sme evolutionry pproch. However, genetic progrmming is no longer reeding it strings tht represent coded solutions ut complete computer progrms tht solve prticulr prolem. The fundmentl difficulty of GAs lies in the prolem representtion, tht is, in the fixed-length coding. A poor representtion limits the power of GA, nd even worse, my led to flse solution. Negnevitsky, Person Eduction,

34 A fixed-length coding is rther rtificil. As it cnnot provide dynmic vriility in length, such coding often cuses considerle redundncy nd reduces the efficiency of genetic serch. In contrst, genetic progrmming uses high-level uilding locks of vrile length. Their size nd complexity cn chnge during reeding. Genetic progrmming works well in lrge numer of different cses nd hs mny potentil pplictions. Negnevitsky, Person Eduction,