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Evolutionary Computation and Constraint Satisfaction

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Springer Handbook of Computational Intelligence

Part of the book series: Springer Handbooks ((SHB))

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Abstract

In this chapter we will focus on the combination of evolutionary computation (GlossaryTerm

EC

) techniques and constraint satisfaction problems (GlossaryTerm

CSP

s). Constraint programming (GlossaryTerm

CP

) is another approach to deal with constraint satisfaction problems. In fact, it is an important prelude to the work covered here as it advocates itself as an alternative approach to programming [1]. The first step is to formulate a problem as a GlossaryTerm

CSP

such that techniques from GlossaryTerm

CP

, GlossaryTerm

EC

, combinations of the two, often referred to as hybrids [2, 3], or other approaches can be deployed to solve the problem. The formulation of a problem has an impact on its complexity in terms of effort required to either find a solution or that proof no solution exists. It is, therefore, vital to spend time on getting this right.

GlossaryTerm

CP

defines search as iterative steps over a search tree where nodes are partial solutions to the problem where not all variables are assigned values. The search then maintains a partial solution that satisfies all variables with assigned values. Instead, in GlossaryTerm

EC

algorithms sample a space of candidate solutions where for each sample point variables are all assigned values. None of these candidate solutions will satisfy all constraints in the problem until a solution is found. Such algorithms are often classified as Davis–Putnam–Logemann–Loveland (GlossaryTerm

DPLL

) algorithms, after the first backtracking algorithm for solving GlossaryTerm

CSP

 [4].

Another major difference is that many constraint solvers from GlossaryTerm

CP

are sound, whereas GlossaryTerm

EC

solvers are not. A solver is sound if it always finds a solution if it exists. Furthermore, most constraint solvers from GlossaryTerm

CP

can easily be made complete, although this is often not a desired property for a constraint solver. A constraint solver is complete if it can find every solution to a problem.

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Abbreviations

3-CNF-SAT:

three variables/clause-conjunctive normal form-satisfiability

BINCSP:

binary constraint satisfaction problem

CNF:

conjunctive normal form

CP:

constraint programming

CSP:

constraint satisfaction problem

DPLL:

Davis–Putnam–Logemann–Loveland

EC:

evolutionary computation

PDDL:

planning domain definition language

SAT:

satisfiability

SCH:

school

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  1. Optos, Queensferry House, Carnegie Business Park, KY11 8GR, Dunfermline, UK

    Jano I. van Hemert

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  1. Jano I. van Hemert
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  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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van Hemert, J.I. (2015). Evolutionary Computation and Constraint Satisfaction. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_65

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