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On the Utility of Redundant Encodings in Mutationbased Evolutionary Search
 In
, 2002
"... A number of recent works in the evolutionary computation eld have suggested that introducing large amounts of genetic redundancy may increase the evolvability of a population in an evolutionary algorithm. These works have variously claimed that the reliability of the search, the nal tness achi ..."
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A number of recent works in the evolutionary computation eld have suggested that introducing large amounts of genetic redundancy may increase the evolvability of a population in an evolutionary algorithm. These works have variously claimed that the reliability of the search, the nal tness achieved, the ability to cope with changing environments, and the robustness to high mutation rates, may all be improved by employing this strategy. In this paper we dispute some of these claims, arguing that adding random redundancy cannot be generally useful for optimization purposes. By way of example we report on experiments where a proposed neutral encoding scheme (based on random Boolean networks) is compared to a direct encoding in two mutationonly EAs, at various mutation rates. Our ndings show that with the appropriate choice of perbit mutation rate, the evolvability of populations using the direct encoding is no less than with the redundant one.
What bloat? Cartesian Genetic Programming on Boolean problems
 2001 GENETIC AND EVOLUTIONARY COMPUTATION CONFERENCE LATE BREAKING PAPERS
, 2001
"... This paper presents an empirical study of the variation of program size over time, for a form of Genetic Programming called Cartesian Genetic Programming. Two main types of Cartesian genetic programming are examined: one uses a fully connected graph, with no redundant nodes, while the other al ..."
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This paper presents an empirical study of the variation of program size over time, for a form of Genetic Programming called Cartesian Genetic Programming. Two main types of Cartesian genetic programming are examined: one uses a fully connected graph, with no redundant nodes, while the other allows partial connectedness and has redundant nodes. Studies are reported here for fitness based search and for a flat fitness landscape.
An Empirical Investigation of How and Why Neutrality Affects Evolutionary Search
 Proceedings of the Genetic and Evolutionary Computation Conference GECCO 2006, ACM
, 2006
"... The effects of neutrality on evolutionary search have been considered in a number of studies, the results of which, however, have been contradictory. Some have found neutrality to be beneficial to aid evolution whereas others have argued that neutrality in the evolutionary process is useless. We be ..."
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The effects of neutrality on evolutionary search have been considered in a number of studies, the results of which, however, have been contradictory. Some have found neutrality to be beneficial to aid evolution whereas others have argued that neutrality in the evolutionary process is useless. We believe that this confusion is due to several reasons: many studies have based their conclusions on performance statistics rather than a more indepth analysis of population dynamics, studies often consider problems, representations and search algorithms that are relatively complex and so results represent the compositions of multiple effects, there is not a single definition of neutrality and different studies have added neutrality to problems in radically different ways. In this paper, we try to shed some light on neutrality by addressing these problems. That is, we use the simplest possible definition of neutrality (a neutral network of constant fitness, identically distributed in the whole search space), we consider one of the simplest possible algorithms (a mutation based, binary genetic algorithm) applied to two simple problems (a unimodal landscape and a deceptive landscape), and analyse both performance figures and, critically, population flows from and to the neutral network and the basins of attraction of the optima.
Local Optima Networks of NK Landscapes with Neutrality
"... In previous work, we have introduced a networkbased model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness lan ..."
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In previous work, we have introduced a networkbased model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness landscape, while the arcs are transition probabilities between local optima basins. Here, we extend this formalism to neutral fitness landscapes, which are common in difficult combinatorial search spaces. By using two known neutral variants of the NK family (i.e. NKp and NKq) in which the amount of neutrality can be tuned by a parameter, we show that our new definitions of the optima networks and the associated basins are consistent with the previous definitions for the nonneutral case. Moreover, our empirical study and statistical analysis show that the features of neutral landscapes interpolate smoothly between landscapes with maximum neutrality and nonneutral ones. We found some unknown structural differences between the two studied families of neutral landscapes. But overall, the network features studied confirmed that neutrality, in landscapes with percolating neutral networks, may enhance heuristic search. Our current methodology requires the exhaustive enumeration of the underlying search space. Therefore, sampling techniques should be developed before this analysis can have practical implications. We argue, however, that the proposed model offers a new perspective into the problem difficulty of combinatorial optimization problems and may inspire the design of more effective search heuristics.
Beyond the complexity ceiling: Evolution, emergence and regeneration
 In Proc. GECCO 2004 Workshop on Regeneration and Learning in Developmental Systems
, 2004
"... Abstract. We argue that there is an upper limit on the complexity of software that can be constructed using current methods. Furthermore, this limit is orders of magnitude smaller than the complexity of living systems. We argue that many of the advantages of autonomic computing will not be possible ..."
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Abstract. We argue that there is an upper limit on the complexity of software that can be constructed using current methods. Furthermore, this limit is orders of magnitude smaller than the complexity of living systems. We argue that many of the advantages of autonomic computing will not be possible unless fundamental aspects of living systems are incorporated into a new paradigm of software construction. Truly selfhealing and maintaining software will require methods of construction that mimic the biological development of multicellular organisms. We demonstrate a prototype system which is capable of autonomous repair and regeneration without using engineered methods. A method for evolving programs that construct multicellular structures (organisms) is described. 1
Developments in Cartesian Genetic Programming: selfmodifying CGP
, 2010
"... Selfmodifying Cartesian Genetic Programming (SMCGP) is a general purpose, graphbased, developmental form of Genetic Programming founded on Cartesian Genetic Programming. In addition to the usual computational functions, it includes functions that can modify the program encoded in the genotype. Th ..."
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Selfmodifying Cartesian Genetic Programming (SMCGP) is a general purpose, graphbased, developmental form of Genetic Programming founded on Cartesian Genetic Programming. In addition to the usual computational functions, it includes functions that can modify the program encoded in the genotype. This means that programs can be iterated to produce an infinite sequence of programs (phenotypes) from a single evolved genotype. It also allows programs to acquire more inputs and produce more outputs during this iteration. We discuss how SMCGP can be used and the results obtained in several different problem domains, including digital circuits, generation of patterns and sequences, and mathematical problems. We find that SMCGP can efficiently solve all the problems studied. In addition, we prove mathematically that evolved programs can provide general solutions to a number of problems: ninput evenparity, ninput adder, and sequence approximation to p.
Evolving Dynamics in an Artificial Regulatory Network Model
 Proc. of the Paralell Problem Solving from Nature Conference, volume LNCS 3242
, 2004
"... In this paper artificial regulatory networks (ARN) are evolved to match the dynamics of test functions. The ARNs are based on a genome representation generated by a duplication / divergence process. ..."
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In this paper artificial regulatory networks (ARN) are evolved to match the dynamics of test functions. The ARNs are based on a genome representation generated by a duplication / divergence process.
On The Effects of BitWise Neutrality on Fitness Distance Correlation, Phenotypic Mutation Rates and Problem Hardness
 Foundations of Genetic Algorithms IX, Lecture Notes in Computer Science
, 2007
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Predicting prime numbers using cartesian genetic programming
 in Proceedings of 10th European Conference on Genetic Programming
"... Abstract. Prime generating polynomial functions are known that can produce sequences of prime numbers (e.g. Euler polynomials). However, polynomials which produce consecutive prime numbers are much more difficult to obtain. In this paper, we propose approaches for both these problems. The first uses ..."
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Abstract. Prime generating polynomial functions are known that can produce sequences of prime numbers (e.g. Euler polynomials). However, polynomials which produce consecutive prime numbers are much more difficult to obtain. In this paper, we propose approaches for both these problems. The first uses Cartesian Genetic Programming (CGP) to directly evolve integer based primeprediction mathematical formulae. The second uses multichromosome CGP to evolve a digital circuit, which represents a polynomial. We evolved polynomials that can generate 43 primes in a row. We also found functions capable of producing the first 40 consecutive prime numbers, and a number of digital circuits capable of predicting up to 208 consecutive prime numbers, given consecutive input values. Many of the formulae have been previously unknown. 1
Some Steps Towards Understanding How Neutrality Affects Evolutionary Search
"... Abstract. The effects of neutrality on evolutionary search have been considered in a number of interesting studies, the results of which, however, have been contradictory. We believe that this confusion is due to several reasons. In this paper, we shed some light on neutrality by addressing these pr ..."
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Abstract. The effects of neutrality on evolutionary search have been considered in a number of interesting studies, the results of which, however, have been contradictory. We believe that this confusion is due to several reasons. In this paper, we shed some light on neutrality by addressing these problems. That is, we use the simplest possible definition of neutrality, we consider one of the simplest possible algorithms, we apply it to two problems (a unimodal landscape and a deceptive landscape), which we analyse using fitness distance correlation, performance statistics and, critically, tracking the full evolutionary path of individuals within their family tree. 1