Flowchart (Executional Steps) of Genetic Programming

Genetic programming is problem-independent in the sense that the flowchart specifying the basic sequence of executional steps is not modified for each new run or each new problem.

There is usually no discretionary human intervention or interaction during a run of genetic programming (although a human user may exercise judgment as to whether to terminate a run).

The figure below is a flowchart showing the executional steps of a run of genetic programming. The flowchart shows the genetic operations of crossover, reproduction, and mutation as well as the architecture-altering operations. This flowchart shows a two-offspring version of the crossover operation.

Overview of Flowchart

Genetic programming starts with an initial population of computer programs composed of functions and terminals appropriate to the problem. The individual programs in the initial population are typically generated by recursively generating a rooted point-labeled program tree composed of random choices of the primitive functions and terminals (provided by the human user as part of the first and second preparatory steps of a run of genetic programming). The initial individuals are usually generated subject to a pre-established maximum size (specified by the user as a minor parameter as part of the fourth preparatory step). In general, the programs in the population are of different size (number of functions and terminals) and of different shape (the particular graphical arrangement of functions and terminals in the program tree).

Each individual program in the population is executed. Then, each individual program in the population is either measured or compared in terms of how well it performs the task at hand (using the fitness measure provided in the third preparatory step). For many problems (including all problems in this book), this measurement yields a single explicit numerical value, called fitness. The fitness of a program may be measured in many different ways, including, for example, in terms of the amount of error between its output and the desired output, the amount of time (fuel, money, etc.) required to bring a system to a desired target state, the accuracy of the program in recognizing patterns or classifying objects into classes, the payoff that a game-playing program produces, or the compliance of a complex structure (such as an antenna, circuit, or controller) with user-specified design criteria. The execution of the program sometimes returns one or more explicit values. Alternatively, the execution of a program may consist only of side effects on the state of a world (e.g., a robot’s actions). Alternatively, the execution of a program may produce both return values and side effects.

The fitness measure is, for many practical problems, multiobjective in the sense that it combines two or more different elements. The different elements of the fitness measure are often in competition with one another to some degree.

For many problems, each program in the population is executed over a representative sample of different fitness cases. These fitness cases may represent different values of the program’s input(s), different initial conditions of a system, or different environments. Sometimes the fitness cases are constructed probabilistically.

The creation of the initial random population is, in effect, a blind random search of the search space of the problem. It provides a baseline for judging future search efforts. Typically, the individual programs in generation 0 all have exceedingly poor fitness. Nonetheless, some individuals in the population are (usually) more fit than others. The differences in fitness are then exploited by genetic programming. Genetic programming applies Darwinian selection and the genetic operations to create a new population of offspring programs from the current population.

The genetic operations include crossover (sexual recombination), mutation, reproduction, and the architecture-altering operations. These genetic operations are applied to individual(s) that are probabilistically selected from the population based on fitness. In this probabilistic selection process, better individuals are favored over inferior individuals. However, the best individual in the population is not necessarily selected and the worst individual in the population is not necessarily passed over.

After the genetic operations are performed on the current population, the population of offspring (i.e., the new generation) replaces the current population (i.e., the now-old generation). This iterative process of measuring fitness and performing the genetic operations is repeated over many generations.

The run of genetic programming terminates when the termination criterion (as provided by the fifth preparatory step) is satisfied. The outcome of the run is specified by the method of result designation. The best individual ever encountered during the run (i.e., the best-so-far individual) is typically designated as the result of the run.

All programs in the initial random population (generation 0) of a run of genetic programming are syntactically valid, executable programs. The genetic operations that are performed during the run (i.e., crossover, mutation, reproduction, and the architecture-altering operations) are designed to produce offspring that are syntactically valid, executable programs. Thus, every individual created during a run of genetic programming (including, in particular, the best-of-run individual) is a syntactically valid, executable program.

There are numerous alternative implementations of genetic programming that vary from the foregoing brief description.

Creation of Initial Population of Computer Programs

Genetic programming starts with a primordial ooze of thousands of randomly-generated computer programs. The set of functions that may appear at the internal points of a program tree may include ordinary arithmetic functions and conditional operators. The set of terminals appearing at the external points typically include the program's external inputs (such as the independent variables X and Y) and random constants (such as 3.2 and 0.4). The randomly created programs typically have different sizes and shapes. Click here for animated example of random creation of two illustrative computer programs.

Main Generational Loop of Genetic Programming

The main generational loop of a run of genetic programming consists of the fitness evaluation, Darwinian selection, and the genetic operations. Each individual program in the population is evaluated to determine how fit it is at solving the problem at hand. Programs are then probabilistically selected from the population based on their fitness to participate in the various genetic operations, with reselection allowed. While a more fit program has a better chance of being selected, even individuals known to be unfit are allocated some trials in a mathematically principled way. That is, genetic programming is not a purely greedy hill-climbing algorithm.

The individuals in the initial random population and the offspring produced by each genetic operation are all syntactically valid executable programs.

After many generations, a program may emerge that solves, or approximately solves, the problem at hand.

Mutation Operation

In the mutation operation, a single parental program is probabilistically selected from the population based on fitness. A mutation point is randomly chosen, the subtree rooted at that point is deleted, and a new subtree is grown there using the same random growth process that was used to generate the initial population. This asexual mutation operation is typically performed sparingly (with a low probability of, say, 1% during each generation of the run). Click here for animated example of mutation operation.

Crossover (Sexual Recombination) Operation

In the crossover, or sexual recombination operation, two parental programs are probabilistically selected from the population based on fitness. The two parents participating in crossover are usually of different sizes and shapes. A crossover point is randomly chosen in the first parent and a crossover point is randomly chosen in the second parent. Then the subtree rooted at the crossover point of the first, or receiving, parent is deleted and replaced by the subtree from the second, or contributing, parent. Crossover is the predominant operation in genetic programming (and genetic algorithm) work and is performed with a high probability (say, 85% to 90%). Click here for animated example of crossover operation.

Reproduction Operation

The reproduction operation copies a single individual, probabilistically selected based on fitness, into the next generation of the population.

Architecture-Altering Operations

Simple computer programs consist of one main program (called a result-producing branch). However, more complicated programs contain subroutines (also called automatically defined functions, ADFs, or function-defining branches), iterations (automatically defined iterations or ADIs), loops (automatically defined loops or ADLs), recursions (automatically defined recursions or ADRs), and memory of various dimensionality and size (automatically defined stores or ADSs). If a human user is trying to solve an engineering problem, he or she might choose to simply prespecify a reasonable fixed architectural arrangement for all programs in the population (i.e., the number and types of branches and number of arguments that each branch possesses). Genetic programming can then be used to evolve the exact sequence of primitive work-performing steps in each branch.

However, sometimes the size and shape of the solution is the problem (or at least a major part of it). Genetic programming is capable of making all architectural decisions dynamically during the run of genetic programming. Genetic programming uses architecture-altering operations to automatically determine program architecture in a manner that parallels gene duplication in nature and the related operation of gene deletion in nature. Architecture-altering operations provide a way, dynamically during the run of genetic programming, to add and delete subroutines and other types of branches to individual programs to add and delete arguments possessed by the subroutines and other types of branches. These architecture-altering operation quickly create an architecturally diverse population containing programs with different numbers of subroutines, arguments, iterations, loops, recursions, and memory and, also, different hierarchical arrangements of these elements. Programs with architectures that are well-suited to the problem at hand will tend to grow and prosper in the competitive evolutionary process, while programs with inadequate architectures will tend to wither away under the relentless selective pressure of the problem's fitness measure. Thus, the architecture-altering operations relieve the human user of the task of prespecifying program architecture.

There are several different architecture-altering operations (described below). They are each applied sparingly during the run (say, with a probability of 1/2% of 1% on each generation).

The subroutine duplication operation duplicates a preexisting subroutine in an individual program gives a new name to the copy and randomly divides the preexisting calls to the old subroutine between the two. This operation changes the program architecture by broadening the hierarchy of subroutines in the overall program. As with gene duplication in nature, this operation preserves semantics when it first occurs. The two subroutines typically diverge later, sometimes yielding specialization. Click here for animated example of the subroutine duplication operation.

The argument duplication operation duplicates one argument of a subroutine, randomly divides internal references to it, and preserves overall program semantics by adjusting all calls to the subroutine. This operation enlarges the dimensionality of the subspace on which the subroutine operates. Click here for animated example of the argument duplication operation.

The subroutine creation operation can create a new subroutine from part of a main result-producing branch thereby deepening the hierarchy of references in the overall program, by creating a hierarchical reference between the main program and the new subroutine. The subroutine creation operation can also create a new subroutine from part of an existing subroutine further deepening the hierarchy of references, by creating a hierarchical reference between a preexisting subroutine and a new subroutine and a deeper and more complex overall hierarchy. Click here for animated example of the subroutine creation operation.

The architecture-altering operation of subroutine deletion deletes a subroutine from a program thereby making the hierarchy of subroutines either narrower or shallower. Click here for animated example of the subroutine deletion operation.

The argument deletion operation deletes an argument from a subroutine thereby reducing the amount of information available to the subroutine, a process that can be viewed as generalization. Click here for animated example of the argument deletion operation.

Other architecture-altering operations add and delete automatically defined iterations, automatically defined loops, automatically defined recursions, and automatically defined stores (memory).

Click here for an example of an illustrative run of genetic programming for a problem of symbolic regression of a quadratic polynomial.

· The home page of Genetic Programming Inc. at www.genetic-programming.com.

· For information about the field of genetic programming in general, visit www.genetic-programming.org

· The home page of John R. Koza at Genetic Programming Inc. (including online versions of most papers) and the home page of John R. Koza at Stanford University

· Information about the 1992 book Genetic Programming: On the Programming of Computers by Means of Natural Selection, the 1994 book Genetic Programming II: Automatic Discovery of Reusable Programs, the 1999 book Genetic Programming III: Darwinian Invention and Problem Solving, and the 2003 book Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Click here to read chapter 1 of Genetic Programming IV book in PDF format.

· For information on 3,198 papers (many on-line) on genetic programming (as of June 27, 2003) by over 900 authors, see William Langdon’s bibliography on genetic programming.

· For information on the Genetic Programming and Evolvable Machines journal published by Kluwer Academic Publishers

· For information on the Genetic Programming book series from Kluwer Academic Publishers, see the Call For Book Proposals

· For information about the annual Genetic and Evolutionary Computation (GECCO) conference (which includes the annual GP conference) to be held on June 26–30, 2004 (Saturday – Wednesday) in Seattle and its sponsoring organization, the International Society for Genetic and Evolutionary Computation (ISGEC). For information about the annual NASA/DoD Conference on Evolvable Hardware Conference (EH) to be held on June 24-26 (Thursday-Saturday), 2004 in Seattle. For information about the annual Euro-Genetic-Programming Conference to be held on April 5-7, 2004 (Monday – Wednesday) at the University of Coimbra in Coimbra Portugal.

Last updated on August 27, 2003