Geometric Particle Swarm Optimization

Abstract

Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new geometric PSO (GPSO) applies naturally to both continuous and combinatorial spaces. We demonstrate this for the cases of Euclidean, Manhattan, and Hamming spaces and report extensive experimental results. We also demonstrate the applicability of GPSO to more challenging combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic ideas because it is entertaining and instructive as well as being a nontrivial constrained combinatorial problem. We apply GPSO to solve the Sudoku puzzle.

Positive Impression of Low-Ranking Microrn as in Human Cancer Classification

“…For feature selection, we used the correlation-based feature selector (CFS) with different search algorithms: re-ranking search algorithm [13], best first search algorithm, particle swarm optimization (PSO) search algorithm [14,15], and tabu search algorithm [16,17]. We also used the ranker search method with different attribute evaluators: Pearson's correlation, chi-squared distribution, information gain, and gain ratio.…”

Geometric Differential Evolution on the Space of Genetic Programs

“…The notion of convex combination in metric spaces was introduced in the GPSO framework [7]. The convex combination C = CX((A, W A ), (B, W B )) of two …”

“…In particular, GDE can be applied to any search space endowed with a distance and associated with any solution representation to derive formally a specific GDE for the target space and for the target representation. GDE is related to Geometric Particle Swarm Optimization (GPSO) [7], which is a formal generalization of the Particle Swarm Optimization algorithm [3]. 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 [11] and for spaces associated with genetic programs [17].…”

Geometric nelder-mead algorithm on the space of genetic programs

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