Document Sample

GENETIC ALGORITHMS AND GENETIC PROGRAMMING John R. Koza Consulting Professor (Medical Informatics) Department of Medicine School of Medicine Consulting Professor Department of Electrical Engineering School of Engineering Stanford University Stanford, California 94305 koza@stanford.edu http://www.smi.stanford.edu/people/koza/ DEFINITION OF THE GENETIC ALGORITHM (GA) The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation. GENETIC ALGORITHM (GA) Generation 0 Generation 1 Individuals Fitness Offspring 011 $3 111 001 $1 010 110 $6 110 010 $2 010 HAMBURGER RESTAURANT PROBLEM • Price 1 = $ 0.50 price 0 = $10.00 price • Drink 1 = Coca Cola 0 = Wine • Ambiance 1 = Fast snappy service 0 = Leisurely service with tuxedoed waiter CHROMOSOME (GENOME) OF THE GLOBAL OPTIMUM McDONALD's 1 1 1 THE SEARCH SPACE 1 000 2 001 3 010 4 011 5 100 6 101 7 110 8 111 • Alphabet size K=2, Length L=3 • Size of search space: KL=2L=23=8 IMPRACTICALITY OF RANDOM OR ENUMERATIVE SEARCH • 81-bit problems are very small for GA • However, even if L is as small as 81, 281 ~ 1027 = number of nanoseconds since the beginning of the universe 15 billion years ago GA FLOWCHART GENERATION 0 Generation 0 1 011 3 2 001 1 3 110 6 4 010 2 Total Worst Average Best DEFINITION OF THE GENETIC ALGORITHM (GA) The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation. PROBABILISTIC SELECTION BASED ON FITNESS • Better individuals are preferred • Best is not always picked • Worst is not necessarily excluded • Nothing is guaranteed • Mixture of greedy exploitation and adventurous exploration • Similarities to simulated annealing (SA) PROBABILISTIC SELECTION BASED ON FITNESS 0.17 0.25 0.08 0.5 DARWINIAN FITNESS PROPORTIONATE SELECTION Generation 0 Mating pool 1 011 3 .25 011 3 2 001 1 .08 110 6 3 110 6 .50 110 6 4 010 2 .17 010 2 Total 12 17 Worst 1 2 Average 3.00 4.5 Best 6 6 DEFINITION OF THE GENETIC ALGORITHM (GA) The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation. MUTATION OPERATION • Parent chosen probabilistically based on fitness Parent 010 • Mutation point chosen at random Parent --0 • One offspring Offspring 011 AFTER MUTATION OPERATION Generation 0 Mating pool Generation 1 1 011 3 .25 011 3 2 001 1 .08 110 6 3 110 6 .50 110 6 4 010 2 .17 010 2 --- 011 3 Total 12 17 Worst 1 2 Average 3.00 4.5 Best 6 6 CROSSOVER OPERATION • 2 parents chosen probabilistically based on fitness Parent 1 Parent 2 011 110 CROSSOVER (CONTINUED) • Interstitial point picked at random Fragment 1 Fragment 2 01- 11- • 2 remainders Remainder 1 Remainder 2 --1 --0 • 2 offspring produced by crossover Offspring 1 Offspring 2 111 010 AFTER CROSSOVER OPERATION Generation 0 Mating pool Generation 1 1 011 3 .25 011 3 2 111 7 2 001 1 .08 110 6 2 010 2 3 110 6 .50 110 6 4 010 2 .17 010 2 Total 12 17 Worst 1 2 Average 3.00 4.5 Best 6 6 AFTER REPRODUCTION OPERATION Generation 0 Mating pool Generation 1 1 011 3 .25 2 001 1 .08 3 110 6 .50 110 6 --- 110 6 4 010 2 .17 Total 12 17 Worst 1 2 Average 3.00 4.5 Best 6 6 DEFINITION OF THE GENETIC ALGORITHM (GA) The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation. GENERATION 1 Generation 0 Mating pool Generation 1 1 011 3 .25 011 3 2 111 7 2 001 1 .08 110 6 2 010 2 3 110 6 .50 110 6 --- 110 6 4 010 2 .17 010 2 --- 011 3 Total 12 17 18 Worst 1 2 2 Average 3.00 4.5 4.5 Best 6 6 7 DEFINITION OF THE GENETIC ALGORITHM (GA) The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation. DEFINITION OF THE GENETIC ALGORITHM (GA) The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation. PROBABILISTIC STEPS • The initial population is typically random • Probabilistic selection based on fitness - Best is not always picked - Worst is not necessarily excluded • Random picking of mutation and crossover points • Often, there is probabilistic scenario as part of the fitness measure ANTENNA DESIGN ANTENNA DESIGN • The problem (Altshuler and Linden 1998) is to determine the x-y-z coordinates of the 3- dimensional position of the ends (X1, Y1, Z1, X2, Y2, Z2,… , X7, Y7, Z7) of 7 straight wires so that the resulting 7-wire antenna satisfies certain performance requirements • The first wire starts at feed point (0, 0, 0) in the middle of the ground plane • The antenna must fit inside the 0.5 cube ANTENNA GENOME X1 Y1 Z1 X2 Y2 Z2 … +0010 -1110 +0001 +0011 -1011 +0011 … • 105-bit chromosome (genome) • Each x-y-z coordinate is represented by 5 bits (4-bit granularity for data plus a sign bit) • Total chromosome is 3 7 5 = 105 bits ANTENNA FITNESS • Antenna is for ground-to-satellite communications for cars and handsets • We desire near-uniform gain pattern 10 above the horizon • Fitness is measured based on the antenna's radiation pattern. The radiation pattern is simulated by National Electromagnetics Code (NEC) ANTENNA FITNESS • Fitness is sum of the squares of the difference between the average gain and the antenna's gain • Sum is taken for angles between -90 and +90 and all azimuth angles from 0 to 180 • The smaller the value of fitness, the better GRAPH OF ANTENNA FITNESS U. S. PATENT 5,719,794 10-MEMBER TRUSS 10-MEMBER TRUSS • Prespecified topological arrangement of the 10 members, the load, and the wall (Goldberg and Samtani 1986) • Truss has 10 members (6 are length of 30 feet and 4 are length 30√2 = 41 feet) • The problem is to determine the cross-sectional areas (A1, … , A10) of each of the 10 members so as to minimize weight of the material for a truss that supports the 2 loads • The weight is based on volume (i.e., cross- sectional area length) TRUSS GENOME A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 0010 1110 0001 0011 1011 0011 1111 0011 0011 1010 • 40-bit chromosome (genome) • 4-bit granularity for truss diameters • 0000 = smallest diameter • 1111 = largest diameter • Total chromosome is 4 10 = 40 bits TRUSS FITNESS • Two-part (multiobjective) fitness measure – First, fitness is computed by taking the sum, over the 10 members, of the cross-sectional area of each member times the length of each member (30 feet or 30√2 = 41 feet). – Second, a penalty (up to 10%) is imposed for violating the stress constraints. Stresses are computed using standard mechanical engineering techniques. • The smaller the total fitness, the better CELLULAR AUTOMATA STATE TRANSITION TABLE # WWW WW W X E EE EEE Rule 0 0 0 0 0 0 0 1 a0 1 0 0 0 0 0 1 0 a1 2 0 0 0 0 1 0 0 a2 3 0 0 0 0 1 1 0 a3 4 0 0 1 1 0 0 0 a4 … … … … … … … … … 127 1 1 1 1 1 1 1 a127 CELLULAR AUTOMATA A0 A1 A2 … A127 a0 a1 a2 … a127 • 128-bit chromosome (genome) PROBLEM-SPECIFIC GENOMES N M GENOME 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 GENETIC ALGORITHM USING VARIABLE-LENGTH STRINGS • 5-WIRE ANTENNA (5 15 = 75 bits) X1 Y1 Z1 … X5 Y5 Z5 +0010 -1110 +0001 … +0010 -1110 +0001 • 4-WIRE ANTENNA (4 15 = 60 bits) X1 Y1 Z1 … X4 Y4 Z4 +1010 -0110 +1101 … +1010 -0110 +1001 GENETIC PROGRAMMING THE CHALLENGE "How can computers learn to solve problems without being explicitly programmed? In other words, how can computers be made to do what is needed to be done, without being told exactly how to do it?" Attributed to Arthur Samuel (1959) CRITERION FOR SUCCESS "The aim [is] ... to get machines to exhibit behavior, which if done by humans, would be assumed to involve the use of intelligence.― Arthur Samuel (1983) REPRESENTATIONS • Decision trees • Binary decision diagrams • If-then production • Formal grammars rules • Coefficients for • Horn clauses polynomials • Neural nets • Reinforcement • Bayesian networks learning tables • Frames • Conceptual clusters • Propositional logic • Classifier systems A COMPUTER PROGRAM GENETIC PROGRAMMING (GP) • GP applies the approach of the genetic algorithm to the space of possible computer programs • Computer programs are the lingua franca for expressing the solutions to a wide variety of problems • A wide variety of seemingly different problems from many different fields can be reformulated as a search for a computer program to solve the problem. GP MAIN POINTS • Genetic programming now routinely delivers high-return human-competitive machine intelligence. • Genetic programming is an automated invention machine. • Genetic programming has delivered a progression of qualitatively more substantial results in synchrony with five approximately order-of-magnitude increases in the expenditure of computer time. DEFINITION OF “HIGH- RETURN” The AI ratio (the ―artificial-to-intelligence‖ ratio) of a problem-solving method as the ratio of that which is delivered by the automated operation of the artificial method to the amount of intelligence that is supplied by the human applying the method to a particular problem DEFINITION OF “ROUTINE” A problem solving method is routine if it is general and relatively little human effort is required to get the method to successfully handle new problems within a particular domain and to successfully handle new problems from a different domain. CRITERIA FOR ―HUMAN-COMPETITIVENESS‖ • Previously patented, an improvement over a patented invention, or patentable today • Publishable in its own right as a new scientific result independent of the fact that the result was mechanically created • Holds it own in regulated competition against humans (or programs) • 5 other similar criteria that are ―arms-length‖ from the fields of AI, ML, GP PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP • Toy problems • Human-competitive non-patent results • 20th-century patented inventions • 21st-century patented inventions • Patentable new inventions GP FLOWCHART A COMPUTER PROGRAM IN C int foo (int time) { int temp1, temp2; if (time > 10) temp1 = 3; else temp1 = 4; temp2 = temp1 + 1 + 2; return (temp2); } OUTPUT OF C PROGRAM Time Output 0 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 6 11 7 12 7 PROGRAM TREE (+ 1 2 (IF (> TIME 10) 3 4)) CREATING RANDOM PROGRAMS CREATING RANDOM PROGRAMS • Available functions F = {+, -, *, %, IFLTE} • Available terminals T = {X, Y, Random-Constants} • The random programs are: – Of different sizes and shapes – Syntactically valid – Executable GP GENETIC OPERATIONS • Reproduction • Mutation • Crossover (sexual recombination) • Architecture-altering operations MUTATION OPERATION MUTATION OPERATION • Select 1 parent probabilistically based on fitness • Pick point from 1 to NUMBER-OF-POINTS • Delete subtree at the picked point • Grow new subtree at the mutation point in same way as generated trees for initial random population (generation 0) • The result is a syntactically valid executable program • Put the offspring into the next generation of the population CROSSOVER OPERATION CROSSOVER OPERATION • Select 2 parents probabilistically based on fitness • Randomly pick a number from 1 to NUMBER-OF- POINTS for 1st parent • Independently randomly pick a number for 2nd parent • The result is a syntactically valid executable program • Put the offspring into the next generation of the population • Identify the subtrees rooted at the two picked points REPRODUCTION OPERATION • Select parent probabilistically based on fitness • Copy it (unchanged) into the next generation of the population FIVE MAJOR PREPARATORY STEPS FOR GP • Determining the set of terminals • Determining the set of functions • Determining the fitness measure • Determining the parameters for the run • Determining the method for designating a result and the criterion for terminating a run ILLUSTRATIVE GP RUN SYMBOLIC REGRESSION Independent Dependent variable X variable Y -1.00 1.00 -0.80 0.84 -0.60 0.76 -0.40 0.76 -0.20 0.84 0.00 1.00 0.20 1.24 0.40 1.56 0.60 1.96 0.80 2.44 1.00 3.00 PREPARATORY STEPS Objective: Find a computer program with one input (independent variable X) whose output equals the given data 1 Terminal set: T = {X, Random-Constants} 2 Function set: F = {+, -, *, %} 3 Fitness: The sum of the absolute value of the differences between the candidate program’s output and the given data (computed over numerous values of the independent variable x from –1.0 to +1.0) 4 Parameters: Population size M = 4 5 Termination: An individual emerges whose sum of absolute errors is less than 0.1 SYMBOLIC REGRESSION POPULATION OF 4 RANDOMLY CREATED INDIVIDUALS FOR GENERATION 0 SYMBOLIC REGRESSION x2 + x + 1 FITNESS OF THE 4 INDIVIDUALS IN GEN 0 x+1 x2 + 1 2 x 0.67 1.00 1.70 2.67 SYMBOLIC REGRESSION x2 + x + 1 GENERATION 1 Second offspring First offspring of of crossover of Mutant of (c) crossover of (a) (a) and (b) and (b) picking ―+‖ of Copy of (a) picking ―2‖ picking ―+‖ of parent (a) and as mutation parent (a) and point left-most ―x‖ of left-most ―x‖ of parent (b) as parent (b) as crossover points crossover points CLASSIFICATION GP TABLEAU – INTERTWINED SPIRALS Objective: Create a program to classify a given point in the x-y plane to the red or blue spiral 1 Terminal set: T = {X,Y,Random-Constants} 2 Function set: F = {+,-,*,%,IFLTE,SIN,COS} 3 Fitness: The number of correctly classified points (0 – 194) 4 Parameters: M = 10,000. G = 51 5 Termination: An individual program scores 194 WALL-FOLLOWER FITNESS BEST OF GENERATION 57 BOX MOVER – BEST OF GEN 0 BOX MOVER GEN 45 – FITNESS CASE 1 TRUCK BACKER UPPER TRUCK BACKER UPPER • 4-Dimensional control problem – horizontal position, x – vertical position, y – angle between trailer and horizontal, t – angle between trailer and cab, d • One control variable (steering wheel turn angle) • State transition equations map the 4 state variables into 1 output (the control variable) • Simulation run over many initial conditions and over hundreds of time steps GENETIC PROGRAMMING: ON THE PROGRAMMING OF COMPUTERS BY MEANS OF NATURAL SELECTION (Koza 1992) 2 MAIN POINTS FROM 1992 BOOK • Virtually all problems in artificial intelligence, machine learning, adaptive systems, and automated learning can be recast as a search for a computer program. • Genetic programming provides a way to successfully conduct the search for a computer program in the space of computer programs. SOME RESULTS FROM 1992 BOOK • Intertwined Spirals • Randomizer • Truck Backer Upper • Cellular Automata • Broom Balancer • Task Prioritization • Wall Follower • Image Compression • Box Mover • Econometric Equation • Artificial Ant • Optimization • Differential Games • Inverse Kinematics • Boolean Function Learning • Central Place Foraging • Co-Evolution of Game- • Block Stacking Playing Strategies PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP • Toy problems • Human-competitive non-patent results • 20th-century patented inventions • 21st-century patented inventions • Patentable new inventions COMPUTER PROGRAMS • Subroutines provide one way to REUSE code possibly with different instantiations of the dummy variables (formal parameters) • Loops (and iterations) provide a 2nd way to REUSE code • Recursion provide a 3rd way to REUSE code • Memory provides a 4th way to REUSE the results of executing code SYMBOLIC REGRESSION Fitness case L0 W0 H0 L1 W1 H1 Dependent variable D 1 3 4 7 2 5 3 54 2 7 10 9 10 3 1 600 3 10 9 4 8 1 6 312 4 3 9 5 1 6 4 111 5 4 3 2 7 6 1 -18 6 3 3 1 9 5 4 -171 7 5 9 9 1 7 6 363 8 1 2 9 3 9 2 -36 9 2 6 8 2 6 10 -24 10 8 1 10 7 5 1 45 EVOLVED SOLUTION (- (* (* W0 L0) H0) (* (* W1 L1) H1)) DIFFERENCE IN VOLUMES D = L0W0H0 – L1W1H1 AUTOMATICALLY DEFINED FUNCTION volume AUTOMATICALLY DEFINED FUNCTION volume (progn (defun volume (arg0 arg1 arg2) (values (* arg0 (* arg1 arg2)))) (values (- (volume L0 W0 H0) (volume L1 W1 H1)))) AUTOMATICALLY DEFINED FUNCTIONS • ADFs provide a way to REUSE code • Code is typically reused with different instantiations of the dummy variables (formal parameters) ADDITION OF V0 AND V1 Fitness case L0 W0 H0 L1 W1 H1 V0 V1 D 1 3 4 7 2 5 3 84 30 54 2 7 10 9 10 3 1 630 30 600 3 10 9 4 8 1 6 360 48 312 4 3 9 5 1 6 4 135 24 111 5 4 3 2 7 6 1 24 42 -18 6 3 3 1 9 5 4 9 180 -171 7 5 9 9 1 7 6 405 42 363 8 1 2 9 3 9 2 18 54 -36 9 2 6 8 2 6 10 96 120 -24 10 8 1 10 7 5 1 80 35 45 DIVIDE AND CONQUER DIVIDE AND CONQUER • Decompose a problem into sub-problems • Solve the sub-problems • Assemble the solutions of the sub- problems into a solution for the overall problem CHANGE OF REPRESENTATION CHANGE OF REPRESENTATION • Identify regularities • Change the representation • Solve the overall problem ADF IMPLEMENTATION • Each overall program in population includes – a main result-producing branch (RPB) and – function-defining branch (i.e., automatically defined function, ADF) • In generation 0, create random programs with different ingredients for the RPB and the ADF – Terminal set for ADF typically contains dummy arguments (formal parameters), such as ARG0, ARG1, … – Function set of the RPB contains ADF0 – ADFs are private and associated with a particular individual program in the population ADF MUTATION • Select parent probabilistically on the basis of fitness • Pick a mutation point from either RPB or an ADF • Delete sub-tree rooted at the picked point • Grow a new sub-tree at the picked point composed of the allowable ingredients appropriate for the picked point • The offspring is a syntactically valid executable program ADF CROSSOVER • Select parent probabilistically on the basis of fitness • Pick a crossover point from either RPB or an ADF of the FIRST patent • The choice of crossover point in the SECOND parent is RESTRICTED to the picked RPB or to the picked ADF • The sub-trees are swapped • The offspring are syntactically valid executable programs GENETIC PROGRAMMING II: AUTOMATIC DISCOVERY OF REUSABLE PROGRAMS (Koza 1994) MAIN POINTS OF 1994 BOOK • Scalability is essential for solving non-trivial problems in artificial intelligence, machine learning, adaptive systems, and automated learning • Scalability can be achieved by reuse • Genetic programming provides a way to automatically discover and reuse subprograms in the course of automatically creating computer programs to solve problems COMPUTER PROGRAMS • Subroutines provide one way to REUSE code possibly with different instantiations of the dummy variables (formal parameters) • Loops (and iterations) provide a 2nd way to REUSE code • Recursion provide a 3rd way to REUSE code • Memory provides a 4th way to REUSE the results of executing code MEMORY Settable Indexed Matrix Relational memory (named) vector memory variables memory LANGDON'S DATA STRUCTURES • Stacks • Queues • Lists • Rings COMPUTER PROGRAMS • Subroutines provide one way to REUSE code possibly with different instantiations of the dummy variables (formal parameters) • Loops (and iterations) provide a 2nd way to REUSE code • Recursion provide a 3rd way to REUSE code • Memory provides a 4th way to REUSE the results of executing code AUTOMATICALLY DEFINED ITERATION (ADI) • The overall program includes an iteration- performing branch (IPB) in addition to a result-producing branch (RPB) and function- defining branches (ADF) • There are no infinite loops because the iteration is performed over a known, fixed set – protein or DNA sequence (of varying length) – time-series data – two-dimensional array of pixels • Memory is usually involved and is used to communicate between IPB, RPB, and ADF TRANSMEMBRANE SEGMENT IDENTIFICATION PROBLEM Goal is to classify a given protein segment as being a transmembrane domain or non-transmembrane area of the protein TRANSMEMBRANE SEGMENT IDENTIFICATION PROBLEM (progn (defun ADF0 () (ORN (ORN (ORN (I?) (H?)) (ORN (P?) (G?))) (ORN (ORN (ORN (Y?) (N?)) (ORN (T?) (Q?))) (ORN (A?) (H?)))))) (defun ADF1 () (values (ORN (ORN (ORN (A?) (I?)) (ORN (L?) (W?))) (ORN (ORN (T?) (L?)) (ORN (T?) (W?)))))) (defun ADF2 () (values (ORN (ORN (ORN (ORN (ORN (D?) (E?)) (ORN (ORN (ORN (D?) (E?)) (ORN (ORN (T?) (W?)) (ORN (Q?) (D?)))) (ORN (K?) (P?)))) (ORN (K?) (P?))) (ORN (T?) (W?))) (ORN (ORN (E?) (A?)) (ORN (N?) (R?)))))) (progn (loop-over-residues (SETM0 (+ (- (ADF1) (ADF2)) (SETM3 M0)))) (values (% (% M3 M0) (% (% (% (- L -0.53) (* M0 M0)) (+ (% (% M3 M0) (% (+ M0 M3) (% M1 M2))) M2)) (% M3 M0)))))) TRANSMEMBRANE SEGMENT IDENTIFICATION PROBLEM • in-sample correlation of 0.976 • out-of-sample correlation of 0.968 • out-of-sample error rate 1.6% AUTOMATICALLY DEFINED LOOP (ADL) • loop initialization branch, LIB • loop condition branch, LCB • loop body branch, LBB • loop update branch, LUB ADL COMPUTER PROGRAMS • Subroutines provide one way to REUSE code possibly with different instantiations of the dummy variables (formal parameters) • Loops (and iterations) provide a 2nd way to REUSE code • Recursion provide a 3rd way to REUSE code • Memory provides a 4th way to REUSE the results of executing code AUTOMATICALLY DEFINED RECURSION (ADR) • recursion condition branch, RCB • recursion body branch, RBB • recursion update branch, RUB • recursion ground branch, RGB ADR HUMAN-COMPETITIVE RESULTS (NOT RELATED TO PATENTS) Transmembrane segment identification problem for proteins Motifs for D–E–A–D box family and manganese superoxide dismutase family of proteins Cellular automata rule for Gacs-Kurdyumov-Levin (GKL) problem Quantum algorithm for the Deutsch-Jozsa “early promise” problem Quantum algorithm for Grover’s database search problem Quantum algorithm for the depth-two AND/OR query problem Quantum algorithm for the depth-one OR query problem Protocol for communicating information through a quantum gate Quantum dense coding Soccer-playing program that won its first two games in the 1997 Robo Cup competition Soccer-playing program that ranked in the middle of field in 1998 Robo Cup competition Antenna designed by NASA for use on spacecraft Sallen-Key filter PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP • Toy problems • Human-competitive non-patent results • 20th-century patented inventions • 21st-century patented inventions • Patentable new inventions GENETIC PROGRAMMING III: DARWINIAN INVENTION AND PROBLEM SOLVING (Koza, Bennett, Andre, Keane 1999) SUBROUTINE DUPLICATION SUBROUTINE CREATION SUBROUTINE DELETION ARGUMENT DUPLICATION ARGUMENT DELETION 16 ATTRIBUTES OF A SYSTEM FOR AUTOMATICALLY CREATING COMPUTER PROGRAMS • Starts with "What needs • Self-organization of to be done" hierarchies • Tells us "How to do it" • Automatic determination of • Produces a computer program architecture program • Wide range of • Automatic determination programming constructs of program size • Well-defined • Code reuse • Problem-independent • Parameterized reuse • Wide applicability • Internal storage • Scalable • Iterations, loops, and • Competitive with human- recursions produced results GENETIC PROGRAMMING PROBLEM SOLVER (GPPS) AUTOMATIC SYNTHESIS OF BOTH THE TOPOLOGY AND SIZING OF ANALOG ELECTRICAL CIRCUITS BY MEANS OF DEVELOPMENTAL GENETIC PROGRAMMING AUTOMATED CIRCUIT SYNTHESIS • The topology of a circuit includes specifying the gross number of components in the circuit, the type of each component (e.g., a capacitor), and a netlist specifying where each lead of each component is to be connected. • Sizing involves specifying the values (typically numerical) of each of the circuit's components. COMPONENT-CREATING FUNCTIONS • Resistor R function • Capacitor C function • Inductor L function • Diode D function • Transistor Q function (3-leaded) COMPONENT-CREATING FUNCTIONS TOPOLOGY-MODIFYING FUNCTIONS • SERIES division • PARALLEL division • VIA • FLIP TOPOLOGY-MODIFYING FUNCTIONS DEVELOPMENT-CONTROLLING FUNCTIONS • END function • NOP (No Operation) function • SAFE_CUT function THE INITIAL CIRCUIT DEVELOPMENTAL GP (LIST (C (– 0.963 (– (– -0.875 -0.113) 0.880)) (series (flip end) (series (flip end) (L -0.277 end) end) (L (– - 0.640 0.749) (L -0.123 end)))) (flip (nop (L -0.657 end))))) CAPACITOR-CREATING FUNCTION (LIST (C (– 0.963 (– (– -0.875 -0.113) 0.880)) (series (flip end) (series (flip end) (L – 0.277 end) end) (L (– -0.640 0.749) (L -0.123 end)))) (flip (nop (L -0.657 end))))) CAPACITOR-CREATING FUNCTION SERIES DIVISION FUNCTION (LIST (C (– 0.963 (– (– -0.875 -0.113) 0.880)) (series (flip end) (series (flip end) (L – 0.277 end) end) (L (– -0.640 0.749) (L -0.123 end)))) (flip (nop (L -0.657 end))))) SERIES DIVISION DEVELOPMENTAL GP EVALUATION OF FITNESS z0 IN OUT + Embryonic Circuit Program Tree Fully Designed Circuit (NetGraph) Circuit Netlist (ascii) Circuit Simulator (SPICE) Circuit Behavior (Output) Fitness DESIRED BEHAVIOR OF A LOWPASS FILTER EVOLVED CAMPBELL FILTER U. S. patent 1,227,113 George Campbell American Telephone and Telegraph 1917 EVOLVED ZOBEL FILTER U. S. patent 1,538,964 Otto Zobel American Telephone and Telegraph Company 1925 EVOLVED SALLEN-KEY FILTER EVOLVED DARLINGTON EMITTER- FOLLOWER SECTION U. S. patent 2,663,806 Sidney Darlington Bell Telephone Laboratories 1953 NEGATIVE FEEDBACK HAROLD BLACK’S RIDE ON THE LACKAWANNA FERRY Courtesy of Lucent Technologies 20th-CENTURY PATENTS Campbell ladder topology for filters Zobel “M-derived half section” and “constant K” filter sections Crossover filter Negative feedback Cauer (elliptic) topology for filters PID and PID-D2 controllers Darlington emitter-follower section and voltage gain stage Sorting network for seven items using only 16 steps 60 and 96 decibel amplifiers Analog computational circuits Real-time analog circuit for time-optimal robot control Electronic thermometer Voltage reference circuit Philbrick circuit NAND circuit Simultaneous synthesis of topology, sizing, placement, and routing PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP • Toy problems • Human-competitive non-patent results • 20th-century patented inventions • 21st-century patented inventions • Patentable new inventions SIX POST-2000 PATENTED INVENTIONS EVOLVED HIGH CURRENT LOAD CIRCUIT REGISTER-CONTROLLED CAPACITOR CIRCUIT LOW-VOLTAGE CUBIC CIRCUIT VOLTAGE-CURRENT-CONVERSION CIRCUIT LOW-VOLTAGE BALUN CIRCUIT TUNABLE INTEGRATED ACTIVE FILTER 21st-CENTURY PATENTED INVENTIONS Low-voltage balun circuit Mixed analog-digital variable capacitor circuit High-current load circuit Voltage-current conversion circuit Cubic function generator Tunable integrated active filter PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP • Toy problems • Human-competitive non-patent results • 20th-century patented inventions • 21st-century patented inventions • Patentable new inventions NOVELTY-DRIVEN EVOLUTION • Two factors in fitness measure – Circuit’s behavior in the frequency domain – Largest number of nodes and edges (circuit components) of a subgraph of the given circuit that is isomorphic to a subgraph of a template representing the prior art. Graph isomorphism algorithm with the cost function being based on the number of shared nodes and edges (instead of just the number of nodes). NOVELTY-DRIVEN EVOLUTION • For circuits not scoring the maximum number of hits (101), the fitness of a circuit is the product of the two factors. • For circuits scoring 101 hits (100%- compliant individuals), fitness is the number of shared nodes and edges divided by 10,000. PRIOR ART TEMPLATE NON-INFRINGING SOLUTION NO. 1 NON-INFRINGING SOLUTION NO. 5 GP AS AN INVENTION MACHINE CIRCUIT-CONSTRUCTING PROGRAM TREE WITH ADFs LOWPASS FILTER WITH ADFs ADF0 AUTOMATIC SYNTHESIS OF CIRCUIT LAYOUT INCLUDING THE PLACEMENT OF COMPONENTS AND ROUTING OF WIRES ALONG WITH THE TOPOLOGY AND SIZING CIRCUIT LAYOUT • Circuit placement involves the assignment of each of the circuit's components to a particular physical location on a printed circuit board or silicon wafer. • Routing involves the assignment of a particular physical location to the wires between the leads of the circuit's components. LAYOUT LAYOUT — GENERATION 0 100%-COMPLIANT LOWPASS FILTER GENERATION 25 WITH 5 CAPACITORS AND 11 INDUCTORS AREA OF 1775.2 100%-COMPLIANT LOWPASS FILTER GENERATION 30 WITH 10 INDUCTORS AND 5 CAPACITORS AREA OF 950.3 100%-COMPLIANT LOWPASS FILTER BEST-OF-RUN CIRCUIT OF GENERATION 138 WITH 4 INDUCTORS AND 4 CAPACITORS AREA OF 359.4 LAYOUT 60 DB AMPLIFIER AUTOMATIC SYNTHESIS OF BOTH THE TOPOLOGY AND TUNING OF CONTROLLERS PROGRAM TREE FOR A CONTROLLER CONTROLLER BLOCKS • gain • lead • integrator • lag • differentiator • two-parameter lag • adder • absolute value • subtractor • limiter • multiplier • divider • differential input • delay integrators • conditional operators • inverter (switches) FUNCTION SET FOR CONTROLLER SYNTHESIS F = {GAIN,INVERTER,LEAD,LAG,LAG2, DIFFERENTIAL_INPUT_INTEGRATOR, DIFFERENTIATOR, ADD_SIGNAL, SUB_SIGNAL,ADD_3_SIGNAL,ADF0, ADF1,ADF2,ADF3,ADF4} TERMINAL SET FOR CONTROLLER SYNTHESIS T = { REFERENCE_SIGNAL, CONTROLLER_OUTPUT, PLANT_OUTPUT} CONSTRAINED SYNTACTIC STRUCTURE • A grammar that specifies what functions and terminals are allowed as arguments to particular functions • For example, the first argument of the GAIN function must be a value-setting subtree whereas the second can be from the general pool of functions • Also known as strong typing TWO-LAG PLANT 8 FITNESS CASES • 8 elements of the fitness measure represent 2 2 2 choices: – 2 different values of the plant's internal gain, K (1.0 and 2.0), – 2 different values of the plant's time constant (0.5 and 1.0), – 2 different values for the height of the reference signal (rising from 0 to 1 volts or from 0 to 1 microvolts at t = 100 milliseconds FITNESS MEASURE • For each of these 8 fitness cases, a transient analysis (time domain) is performed using the SPICE simulator. • The contribution to fitness for the 8 elements is – Integral of time-weighted absolute error (ITAE) – e(t) is difference between plant output and reference signal. – Multiplication by B (106 or 1) makes both reference signals equally influential. – Additional weighting function, A, heavily penalizes non-compliant amounts of overshoot. A weights all variations up to 2% above the reference signal by 1.0, but bigger variations by 10.0. EVOLVED CONTROLLER FOR TWO-LAG PLANT LESS ITAE AND OVERSHOOT BETTER DISTURBANCE REJECTION REVERSE ENGINEERING OF METABOLIC PATHWAYS EVOLVED PATHWAY ANTENNA SYNTHESIS USING GP (PROGN3 (TURN-RIGHT 0.125) (LANDMARK (REPEAT 2 (PROGN2 (DRAW 1.0 HALF-MM-WIRE) (DRAW 0.5 NO-WIRE))) (TRANSLATE-RIGHT 0.125 0.75)) USING A TURTLE TO DRAW TWO- DIMENSIONAL ANTENNA BEST-OF-RUN ANTENNA FROM GENERATION 90 3-DIMENSIONAL ANTENNA NASA EVOLVED ANTENNA To be on satellite to be launched in 2004 OTHER STRUCTURES GENETIC NETWORK FOR lac operon EVOLVED NETWORK (IF (< LACTOSE_LEVEL 9.139 ) (IF (< REPRESSOR_LEVEL 6.270 ) (IF (> GLUCOSE_LEVEL 5.491 ) 2.02 (IF (< CAP_LEVEL 0.639 ) 2.033 (IF (< CAP_LEVEL 4.858 ) (IF (> LACTOSE_LEVEL 2.511 ) (IF (> CAP_LEVEL 7.807 ) 5.586 (IF (> LACTOSE_LEVEL 2.114 ) 1.978 2.137 ) ) 0.0 ) (IF (> REPRESSOR_LEVEL 4.015 ) 0.036 (IF (< GLUCOSE_LEVEL 5.128 ) 10.0 (IF (< REPRESSOR_LEVEL 4.268 ) 2.022 9.122 ) ) ) ) ) ) (IF (> CAP_LEVEL 0.842 ) 0.0 5.97 ) ) (IF (< CAP_LEVEL 1.769 ) 2.022 (IF (< GLUCOSE_LEVEL 2.382 ) (IF (> LACTOSE_LEVEL 1.256 ) (IF (> LACTOSE_LEVEL 1.933 ) (IF (> GLUCOSE_LEVEL 2.022 ) (IF (< GLUCOSE_LEVEL 5.183 ) 6.323 (IF (> CAP_LEVEL 1.208 ) 9.713 0.842 ) ) 10.0 ) (IF (> GLUCOSE_LEVEL 6.270 ) 2.109 ) 1.965 ) ) 0.665 ) 1.982 ) ) ) IN C-STYLE PSEUDO CODE if(LACTOSE_LEVEL < 9.139) else { { if(CAP_LEVEL < 1.769) if(REPRESSOR_LEVEL < { 6.270) LAC_mRNA_LEVEL = { 2.022; LAC_mRNA_LEVEL = } 2.022; else } { else if(GLUCOSE_LEVEL < { 2.382) { LAC_mRNA_LEVEL = LAC_mRNA_LEVEL 0.0; = 10.0; } } } else { LAC_mRNA_LEVEL = 1.982; } } } PARAMETERIZED TOPOLOGIES • One of the most important characteristics of computer programs is that they ordinarily contain inputs (free variables) and conditional operations PARAMETERIZED TOPOLOGY FOR LOWPASS FILTER PARAMETERIZED TOPOLOGY FOR HIGHPASS FILTER PARAMETERIZED TOPOLOGY FOR GENERAL-PURPOSE CONTROLLER EVOLVED EQUATIONS FOR GENERAL- PURPOSE CONTROLLER EVOLVED EQUATIONS FOR GENERAL- PURPOSE CONTROLLER PATENTABLE NEW INVENTIONS PID tuning rules that outperform the Ziegler-Nichols and Åström-Hägglund tuning rules General-purpose controllers outperforming Ziegler-Nichols and Åström-Hägglund rules PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP • Toy problems • Human-competitive non-patent results • 20th-century patented inventions • 21st-century patented inventions • Patentable new inventions PARALLELIZATION WITH SEMI-ISOLATED SUBPOPULATIONS GP PARALLELIZATION • Like Hormel, Get Everything Out of the Pig, Including the Oink • Keep on Trucking • It Takes a Licking and Keeps on Ticking • The Whole is Greater than the Sum of the Parts PETA-OPS • Human brain operates at 1012 neurons operating at 103 per second = 1015 ops per second • 1015 ops = 1 peta-op = 1 bs (brain second) EVOLVABLE HARDWARE CORNER OF XILINX XC6216 FUNCTION UNIT FOR CELL OF XILINIX XC6216 SORTING NETWORK A B C D H G F E EVOLVED SORTING NETWORK GP 1987–2002 System Dates Speed-up Human- Problem Category over first competitive system results Serial LISP 1987–1994 1 (base) 0 toy problems 64 transputers 1994–1997 9 2 human-competitive results not related to patented inventions 64 PowerPC’s 1995–2000 204 12 20th-century patented inventions 70 Alpha’s 1999–2001 1,481 2 20th-century patented inventions 1,000 Pentium II’s 2000–2002 13,900 12 21st-century patented inventions 4-week runs on 2002-2003 130,000 2 patentable new 1,000 Pentium II’s inventions PROMISING GP APPLICATION AREAS • Problem areas involving many variables that are interrelated in highly non-linear ways • Inter-relationship of variables is not well understood • Discovery of the size and shape of the solution is a major part of the problem • "Black art" problems PROMISING GP APPLICATION AREAS (CONTINUED) • Areas where you simply have no idea how to program a solution, but where you know what you want PROMISING GP APPLICATION AREAS (CONTINUED) • Problem areas where a good approximate solution is satisfactory design control bioinformatics classification data mining system identification forecasting PROMISING GP APPLICATION AREAS (CONTINUED) Areas where large computerized databases are accumulating and computerized techniques are needed to analyze the data genome, protein, microarray data satellite image data astronomical data petroleum databases financial databases medical records marketing databases PROMISING GP APPLICATION AREAS (CONTINUED) Areas for which humans find it very difficult to write good programs parallel computers cellular automata multi-agent strategies field-programmable game arrays digital signal processors swarm intelligence CHARACTERISTICS SUGGESTING USE OF GP (1) discovering the size and shape of the solution, (2) reusing substructures, (3) discovering the number of substructures, (4) discovering the nature of the hierarchical references among substructures, (5) passing parameters to a substructure, (6) discovering the type of substructures (e.g., subroutines, iterations, loops, recursions, or storage), (7) discovering the number of arguments possessed by a substructure, (8) maintaining syntactic validity and locality by means of a developmental process, or (9) discovering a general solution in the form of a parameterized topology containing free variables DESIGNING A GIRAFFE • Long neck • Long tongue • Vegetable-digesting enzymes in stomach • 4 legs • Long legs • Brown coloration THE DESIGN OF A GOOD GIRAFE Neck Tongue Carnivorous? Number Leg Coloration length length of legs length 15.11 14 inches No 4 9.96 feet Brown feet Floating Floating Boolean Integer Floating Categorical point point point NON-LINEARITY — GIRAFE • Taken one-by-one, some gene values found in a giraffe, such as the long neck contribute (alone) negatively to fitness – requires considerable material to construct – requires considerable energy to maintain – prone to injury (thereby hurting rate of survival and reproduction) • Thus, maximizing any one variable will not lead to the global optimum solution NON-LINEARITY (CONTINUED) • When the variables are taken in pairs (there are 15 possible pairs), many combinations of pairs (e.g., Long neck and long tongue) are doubly detrimental NON-LINEARITY (CONTINUED) • But, certain combinations of traits, when taken together, are "co-adapted sets of alleles" that yield a very fit animal for eating high acacia leaves in the jungle environment, having good camouflage, having high escape velocity when faced with predators, and exploiting a niche (and avoiding competition) with other animals feeding on low-hanging vegetation SEARCH METHODS IN GENERAL • Initial structure(s) • Fitness measure • Operations for creating new structures • Parameters • Termination criterion and method of designating the result SPACE WITH MANY LOCAL OPTIMA SEARCH METHODS • Blind random search does not use acquired information in deciding on the future direction of the search • Hill combing and gradient descent use acquired information; however, they are prone to becoming trapped on local optima • The previous point is especially true for non- trivial search spaces 7 DIFFERENCES BETWEEN GP AND ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING APPROACHES REPRESENTATION Genetic programming overtly conducts it search for a solution to the given problem in program space ROLE OF POINT-TO-POINT TRANSFORMATIONS IN THE SEARCH Genetic programming does not conduct its search by transforming a single point in the search space into another single point, but instead transforms a set of points into another set of points ROLE OF HILL CLIMBING IN THE SEARCH Genetic programming does not rely exclusively on greedy hill climbing to conduct its search, but instead allocates a certain number of trials, in a principled way, to choices that are known to be inferior DETERMINISM IN THE SEARCH Genetic programming conducts its search probabilistically ROLE OF AN EXPLICIT KNOWLEDGE BASE Genetic programming does NOT make use of a knowledge base ROLE OF FORMAL LOGIC IN THE SEARCH Genetic programming does not utilize formal logic in it’s search strategy. Contradictory alternatives are created and actively maintained. UNDERPINNINGS OF THE TECHNIQUE Biologically inspired TURING (1948) Turing made the connection between searches and the challenge of getting a computer to solve a problem without explicitly programming it in his 1948 essay ―Intelligent Machines‖ "Further research into intelligence of machinery will probably be very greatly concerned with 'searches' ... ― TURING’S 3 APPROACHES TO MACHINE INTELLIGENCE (1948) LOGIC-BASED SEARCH One approach that Turing identified is a search through the space of integers representing candidate computer programs. TURING’S 3 APPROACHES (CONTINUED) CULTURAL SEARCH A second approach is the "cultural search― which relies on knowledge and expertise acquired over a period of years from others (akin to present-day knowledge- based systems). TURING’S 3 APPROACHES (CONTINUED) GENETICAL OR EVOLUTIONARY SEARCH "There is the genetical or evolutionary search by which a combination of genes is looked for, the criterion being the survival value.― TURING (1950) From Turing’s 1950 paper "Computing Machinery and Intelligence" … ―We cannot expect to find a good child- machine at the first attempt. One must experiment with teaching one such machine and see how well it learns. One can then try another and see if it is better or worse. There is an obvious connection between this process and evolution, by the identifications‖ TURING (1950) (CONTINUED) ―Structure of the child machine = Hereditary material ―Changes of the child machine = Mutations ―Natural selection = Judgment of the experimenter‖

DOCUMENT INFO

Shared By:

Categories:

Tags:
genetic programming, genetic algorithms, evolutionary algorithms, evolutionary computation, genetic algorithm, artificial intelligence, fitness function, stanford university, computer programs, neural networks, evolution strategies, genetic operators, crossover operator, practical applications, modern concepts

Stats:

views: | 18 |

posted: | 6/13/2010 |

language: | English |

pages: | 242 |

OTHER DOCS BY ygq15756

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.