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Formal Search Algorithms + Problem Characterisations = Executable Search Strategies

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Theory and Principled Methods for the Design of Metaheuristics

Part of the book series: Natural Computing Series ((NCS))

Abstract

Traditional evolutionary algorithms use a standard, predetermined representation space, often in conjunction with a similarly standard and predetermined set of genetic move operators, themselves defined in terms of the representation space. This approach, while simple, is awkward and—we contend—inappropriate for many classes of problem, especially those in which there are dependencies between problem variables (e.g., problems naturally defined over permutations). For these reasons, over time a much wider variety of representations have come into common use. This paper presents a method for specifying algorithms with respect to abstract or formal representations, making them independent of both problem domain and representation. It also defines a procedure for generating an appropriate problem representation from an explicit characterisation of a problem domain that captures beliefs about its structure. We are then able to apply a formal search algorithm to a given problem domain by providing a suitable characterization of it and using this to generate a formal representation of problems in the domain, resulting in a practical, executable search strategy specific to that domain. This process is illustrated by showing how identical formal algorithms can be applied to both the travelling sales-rep problem (TSP) and real parameter optimisation to yield familiar (but superficially very different) concrete search strategies.

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Notes

  1. 1.

    See also the glossary in Sect. 11.7.

  2. 2.

    Thus the title of this paper has been inspired by but differentiated carefully from that of Wirth’s [30] and Michalewicz’s [13].

  3. 3.

    A Dedekind cut is a partitioning of the rational numbers into two non-empty sets, such that all the members of one are less than all those of the other. For example, the irrationals are formally defined as Dedekind cuts on the rationals (e.g. \(\sqrt{2} \triangleq \langle \{ x\bigm |{x}^{2} > 2\},\{x\bigm |{x}^{2} < 2\}\rangle\)).

  4. 4.

    BLX-0 is perhaps now more commonly known as box crossover.

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Author information

Authors and Affiliations

  1. Hopper Inc, 275 Third Street, Cambridge, MA, 02142, USA

    Patrick D. Surry

  2. Stochastic Solutions Limited, 5 Atholl Crescent, Edinburgh, EH3 8EJ, UK

    Nicholas J. Radcliffe

  3. Department of Mathematics, University of Edinburgh, King’s Buildings, EH9 3JZ, Edinburgh, UK

    Nicholas J. Radcliffe

Authors
  1. Patrick D. Surry
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Correspondence to Patrick D. Surry .

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Editors and Affiliations

  1. VisualDNA, London, United Kingdom

    Yossi Borenstein

  2. University of Birmingham School of Computer Science, Birmingham, United Kingdom

    Alberto Moraglio

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Surry, P.D., Radcliffe, N.J. (2014). Formal Search Algorithms + Problem Characterisations = Executable Search Strategies. In: Borenstein, Y., Moraglio, A. (eds) Theory and Principled Methods for the Design of Metaheuristics. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33206-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-33206-7_11

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