Geometric PSO + GP = Particle Swarm Programming

2009 IEEE Congress on Evolutionary Computation

Togelius

2009

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Abstract-Geometric particle swarm optimization (GPSO) is a recently introduced formal generalization of a simplified form of traditional particle swarm optimization (PSO) without the inertia term that applies naturally to both continuous and combinatorial spaces. In this paper, we propose an extension of GPSO, the inertial GPSO (IGPSO), that generalizes the traditional PSO endowed with the full equation of motion of particles to generic search spaces. We then formally derive the specific IGPSO for the Hamming space associated with binary strings and present experimental results for this new algorithm.

Section: Introductionmentioning

confidence: 99%

Inertial geometric particle swarm optimization

2009 IEEE Congress on Evolutionary Computation

Togelius

2009

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“…GPSO can be applied to any search space endowed with a distance and associated with any solution representation to derive formally a specific GPSO for the target space. Recently, specific GPSOs were derived for different types of continuous spaces and for the Hamming space associated with binary strings [8], for spaces associated with permutations [9] and for spaces associated with Genetic Programming trees [14].…”

Section: Introductionmentioning

confidence: 99%

Geometric differential evolution

Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation

Togelius

2009

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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. Differential Evolution (DE) is similar to PSO but it uses different equations governing the motion of the particles. This paper generalizes the DE algorithm to combinatorial search spaces extending its geometric interpretation to these spaces, analogously as what was done for the traditional PSO algorithm. Using this formal algorithm, Geometric Differential Evolution (GDE), we formally derive the specific GDE for the Hamming space associated with binary strings and present experimental results on a standard benchmark of problems.

“…In particular, these formal algorithms can be applied to any search space endowed with a distance and associated with any solution representation to derive formally specific PSO, DE and NMA for the target space and for the target representation. Specific GPSOs were derived for different types of continuous spaces and for the Hamming space associated with binary strings [9], for spaces associated with permutations [14] and for spaces associated with genetic programs [21]. GDE was specialized to the space of binary strings [15] and, very recently, to the space of genetic programs [13].…”

Section: Introductionmentioning

confidence: 99%

Geometric nelder-mead algorithm on the space of genetic programs

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

Silva

2011

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The Nelder-Mead Algorithm (NMA) is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). In recent work, PSO, DE and NMA have been generalized using a formal geometric framework that treats solution representations in a uniform way. These formal algorithms can be used as templates to derive rigorously specific PSO, DE and NMA for both continuous and combinatorial spaces retaining the same geometric interpretation of the search dynamics of the original algorithms across representations. In previous work, a geometric NMA has been derived for the binary string representation and permutation representation. Furthermore, PSO and DE have already been derived for the space of genetic programs. In this paper, we continue this line of research and derive formally a specific NMA for the space of genetic programs. The result is a Nelder-Mead Algorithm searching the space of genetic programs by acting directly on their tree representation. We present initial experimental results for the new algorithm. The challenge tackled in the present work compared with earlier work is that the pair NMA and genetic programs is the most complex considered so far. This combination raises a number of issues and casts light on how algorithmic features can interact with representation features to give rise to a highly peculiar search behaviour.