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... concludes this paper and provides a summary of key conclusions. II. SCALABILITY PROBLEMS AND STALLING EFFECT IN THE FITNESS FUNCTION In this section, the problem of scalability [1], [49], [60], [85]–=-=[87]-=- and the stalling effect in the fitness function for an EHW system are outlined. The word scalable, or scalability, as written in [93], has been used to describe how the size of the problem will influ...

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...evelopmentsof CGP that allows the construction and evolution of modules that can be called fromsthe main CGP code and has been shown to perform better than standard CGP on a series of parity problems =-=[14]-=-. In this paper we apply ECGP to the multiplier problem.sWe also introduce a new approach called Product Reduction (PR), which is designedsto make evolving digital multipliers easier.sThe plan for the...

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...ing (CGP), incorporating ideas from a technique known as Module Acquisition [1]. This allows the automatic acquisition, evolution and re-use of partial solutions in the form of modules. Previous work =-=[15, 17, 16]-=- has Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercia...

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...volutionary techniques cell-based Optimization [19] and Social Programming [24]. In addition a more powerful form of CGP with the equivalent of Automatically Defined Functions is also being developed =-=[25]-=-. Figure 1 shows the general form of Cartesian Program for an n input moutput function. There are three user-defined parameters: number of rows (r), number of columns (c) and levels-back (which define...

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...netic Programming Model. po24 po25 ECGP extends CGP by configuring it as a single line of functional nodes (nr = 1, l = nc) and by adding the automatic definition and reuse of sub-functions (modules) =-=[27]-=-. Modules are defined as compositions of primitive nodes, see Figure 5. The size of a module is restricted, which also restricts the maximal chromosome size. The functional set contains all boolean fu...

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... , po13 ,. . .} f8 m11 { , ,. . .} { , ,. . .} ∑ ∑ Category Detection Module Maximum Detector Category Fig. 3. Embedded cartesian genetic programming architecture and reuse of sub-functions (modules) =-=[13]-=-. While primitive nodes correspond to basic gate functions, modules are defined as compositions of primitive nodes. The size of a module is restricted, which also restricts the maximal genome size. As...

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...g a given task or when indirect or generative genotype to phenotype mappings are applied. Multiple chromosomes are introduced to account for multiple outputs in cartesian genetic programming (CGP) in =-=[25]-=-. Other approaches are (automatically) defined functions in genetic programming and building blocks [12], [25], incremental evolution [22] and decomposition of the task [21]. Generative genotype to ph...

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.... The main contribution of this paper is the introduction of novel techniques for identifying and dealing with modules, leveraging a previously discussed approach for module creation in the CGP model =-=[28]-=-. We present and evaluate two module creation techniques, called age-based and conebased module creation. Further, we develop and evaluate a novel cone-based crossover operator to be used with a genet...

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...te spine or indeed cells in multicellular organisms). One common method for implementing this principle in artificial evolution is an automatically defined function (ADF) or similar scheme (see, e.g. =-=[5, 15, 11, 9, 1, 21]-=-). However, these schemes are not geared towards the reuse of single primitives; indeed, many of them explicitly prohibit automaticallydiscovered subroutines from consisting of a single primitive. 2.3...