Introduction Genetic programming is a domain-independent problem-solving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover (sexual recombination) and mutation. John Holland's pioneering Adaptation in Natural and Artificial Systems (1975) described how an analog of the evolutionary process can be applied to solving mathematical problems and engineering optimization problems using what is now called the genetic algorithm (GA). The genetic algorithm attempts to find a good (or best) solution to the problem by genetically breeding a population of individuals over a series of generations. In the genetic algorithm, each individual in the population represents a candidate solut

Introduction The rapid growth of programs produced by genetic programming (GP) is a well documented phenomenon [Koza, 1992; Blickle and Thiele, 1994; Nordin and Banzhaf, 1995; McPhee and Miller, 1995; Soule et al., 1996; Greeff and Aldrich, 1997; Soule, 1998] . This growth, often referred to as "code bloat", need not be correlated with increases in the fitness of the evolving programs and consists primarily of code which does not change the semantics of the evolving program. The rate of growth appears to vary depending upon the particular genetic programming paradigm being used, but exponential rates of growth have been documented [Nordin and Banzhaf, 1995] . Code bloat occurs in both tree based and linear genomes [Nordin, 1997; Nordin and Banzhaf, 1995; Nordin et al., 1997] and with automatically defined functions [Langdon, 1995] . Recent research suggests that code bloat will occur in most fitness based search techniques which allow variable length solutions [Langdon, 1998b; Langdo

Size fair and homologous crossover genetic operators for tree based genetic programming are described and tested. Both produce considerably reduced increases in program size and no detrimental e ect on GP performance. GP search spaces are partitioned by the ridge in the number of program v. their size and depth. A ramped uniform random initialisation is described which straddles the ridge. With subtree crossover trees increase about one level per generation leading to sub-quadratic bloat in length. 1

The problem of evolving an artificial ant to follow the Santa Fe trail is used to study the well known genetic programming feature of growth in solution length. Known variously as "bloat", "fluff" and increasing "structural complexity", this is often described in terms of increasing "redundancy" in the code caused by "introns". Comparison between runs with and without fitness selection pressure, backed by Price's Theorem, shows the tendency for solutions to grow in size is caused by fitness based selection. We argue that such growth is inherent in using a fixed evaluation function with a discrete but variable length representation. With simple static evaluation search converges to mainly finding trial solutions with the same fitness as existing trial solutions. In general variable length allows many more long representations of a given solution than short ones. Thus in search (without a length bias) we expect longer representations to occur more often and so representation length to te...

s: Jan. 1992 -- Dec. 1994 ffl CTI: Current Technology Index Jan./Feb. 1993 -- Jan./Feb. 1994 ffl DAI: Dissertation Abstracts International: Vol. 53 No. 1 -- Vol. 55 No. 4 (1994) ffl EEA: Electrical & Electronics Abstracts: Jan. 1991 -- Dec. 1994 ffl P: Index to Scientific & Technical Proceedings: Jan. 1986 -- Feb. 1995 (except Nov. 1994) ffl EI A: The Engineering Index Annual: 1987 -- 1992 ffl EI M: The Engineering Index Monthly: Jan. 1993 -- Dec. 1994 The following GA researchers have already kindly supplied their complete autobibliographies and/or proofread references to their papers: Dan Adler, Patrick Argos, Jarmo T. Alander, James E. Baker, Wolfgang Banzhaf, Ralf Bruns, I. L. Bukatova, Thomas Back, Yuval Davidor, Dipankar Dasgupta, Marco Dorigo, Bogdan Filipic, Terence C. Fogarty, David B. Fogel, Toshio Fukuda, Hugo de Garis, Robert C. Glen, David E. Goldberg, Martina Gorges-Schleuter, Jeffrey Horn, Aristides T. Hatjimihail, Mark J. Jakiela, Richard S. Judson, Akihiko Konaga...

Two important problems in genetic programming (GP) are its tendency to find unnecessarily large trees (bloat), and the general evolutionary algorithms problem that diversity in the population can be lost prematurely. The prevention of these problems is frequently an implicit goal of basic GP. We explore the potential of techniques from multi-objective optimization to aid GP by adding explicit objectives to avoid bloat and promote diversity. The even 3, 4, and 5-parity problems were solved efficiently compared to basic GP results from the literature. Even though only non-dominated individuals were selected and populations thus remained extremely small, appropriate diversity was maintained. The size of individuals visited during search consistently remained small, and solutions of what we believe to be the minimum size were found for the 3, 4, and 5-parity problems.

Abstract. The problem of evolving, using mutation, an artificial ant to follow the Santa Fe trail is used to study the well known genetic programming feature of growth in solution length. Known variously as “bloat”, “fluff ” and increasing “structural complexity”, this is often described in terms of increasing “redundancy ” in the code caused by “introns”. Comparison between runs with and without fitness selection pressure, backed by Price’s Theorem, shows the tendency for solutions to grow in size is caused by fitness based selection. We argue that such growth is inherent in using a fixed evaluation function with a discrete but variable length representation. With simple static evaluation search converges to mainly finding trial solutions with the same fitness as existing trial solutions. In general variable length allows many more long representations of a given solution than short ones. Thus in search (without a length bias) we expect longer representations to occur more often and so representation length to tend to increase. I.e. fitness based selection leads to bloat.

Parsimony pressure, the explicit penalization of larger programs, has been increasingly used as a means of controlling code growth in genetic programming. However, in many cases parsimony pressure degrades the performance of the genetic program. In this paper we show that poor average results with parsimony pressure are a result of "failed" populations that overshadow the results of populations that incorporate parsimony pressure successfully. Additionally, we show that the effect of parsimony pressure can be measured by calculating the relationship between program size and performance within the population. This measure can be used as a partial indicator of success or failure for individual populations. Keywords Code growth, code bloat, parsimony, genetic programming, introns. 1. Introduction The use of parsimony pressure as a means of controlling the size of programs generated with genetic programming (GP) has grown considerably in recent years. In many cases parsimony pr...

Abstract- In many cases programs length’s increase (known as “bloat”, ‘‘fluff ” and increasing “structural complexity”) during artificial evolution. We show bloat is not specific to genetic programming and suggest it is inherent in search techniques with discrete variable length representations using simple static evaluation functions. We investigate the bloating characteristics of three non-population and one population based search techniques using a novel mutation operator. An artificial ant following the Santa Fe trail problem is solved by simulated annealing, hill climbing, strict hill climbing and population based search using two variants of the the new subtree based mutation operator. As predicted bloat is observed when using unbiased mutation and is absent in simulated annealing and both hill climbers when using the length neutral mutation however bloat occurs with both mutations when using a population. We conclude that there are two causes of bloat 1) search operators with no length bias tend to sample bigger trees and 2) competition within populations favours longer programs as they can usually reproduce more accurately. I.

In earlier work we predicted program size would grow in the limit at a quadratic rate and up to fifty generations we measured bloat O(generations 1:2\Gamma1:5 ). On two simple benchmarks we test the prediction of bloat O(generations 2:0 ) up to generation 600. In continuous problems the limit of quadratic growth is reached but convergence in the discrete case limits growth in size. Measurements indicate subtree crossover ceases to be disruptive with large programs (1,000,000) and the population effectively converges (even though variety is near unity). Depending upon implementation, we predict run time O(no. generations 2:0\Gamma3:0 ) and memory O(no. generations 1:0\Gamma2:0 ). 1 INTRODUCTION It has been known for some time that programs within GP populations tend to rapidly increase in size as the population evolves [ Koza, 1992, Altenberg, 1994, Tackett, 1994, Blickle and Thiele, 1994, Nordin and Banzhaf, 1995, Nordin, 1997, McPhee and Miller, 1995, Langdon,...