Topological Interpretation of Crossover

2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)

2008

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Abstract-Geometric particle swarm optimization (GPSO) is a recently introduced formal generalization of traditional particle swarm optimization (PSO) that applies naturally to both continuous and combinatorial spaces. In this paper we apply GPSO to the space of genetic programs represented as expression trees, uniting the paradigms of genetic programming and particle swarm optimization. The result is a particle swarm flying through the space of genetic programs. We present initial experimental results for our new algorithm.

Section: A Geometric Crossovermentioning

confidence: 99%

“…For vectors of reals, various types of blend or line crossovers, box recombinations, and discrete recombinations are geometric crossovers [10]. For binary and multary strings, all homologous crossovers are geometric [10] [12].…”

Section: A Geometric Crossovermentioning

confidence: 99%

Geometric PSO + GP = Particle Swarm Programming

Togelius

Nardi

2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)

2008

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“…For example, it includes: various types of blend or line crossovers, box recombinations, and discrete recombinations [7]; homologous crossovers [7,9]; PMX, Cycle crossover and merge crossover [8]; homologous GP crossovers [11]; and several others [12,7,8,10].…”

Section: Two-parent and Multi-parent Geometric Crossover Definition 1mentioning

confidence: 99%

“…These are representation-independent operators that generalise many pre-existing search operators for the major representations, such as binary strings [7], real vectors [7], permutations [8], syntactic trees [8] and sequences [12].…”

Section: Introductionmentioning

confidence: 99%

Geometric Particle Swarm Optimisation

Lecture Notes in Computer Science

Chio

Poli

2007

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Abstract. Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimization (PSO) and evolutionary algorithms. This connection enables us to generalize PSO to virtually any solution representation in a natural and straightforward way. We demonstrate this for the cases of Euclidean, Manhattan and Hamming spaces.

“…Geometric crossover and geometric mutation are representation-independent search operators that generalize many pre-existing search operators for the major representations used in evolutionary algorithms, such as binary strings [4], real vectors [4], permutations [6], syntactic trees [5] and sequences [7]. They are defined in geometric terms using the notions of line segment and ball.…”

Section: Introductionmentioning

confidence: 99%

Product Geometric Crossover

Parallel Problem Solving From Nature - PPSN IX

Poli

2006

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Abstract. Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In this paper, we introduce the important notion of product geometric crossover that allows to build new geometric crossovers combining pre-existing geometric crossovers in a simple way.