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Thursday 22 May 2014An Overview of Geometric Algebra and an Application in Optimization

Juan Pablo Serrano Rubio - enter for Research in Mathematics (CIMAT), Mexico

Harrison 170 15:00-16:00

In this talk, we give an overview of Geometric Algebra (GA) and Conformal Geometric Algebra (CGA), and an application in optimization problems. GA is a geometric framework in which lines, planes, etc. are assigned to algebraic objects that can be (easily) manipulated by means of the geometric product.

On the other hand, CGA builds upon GA and provides a concise way to perform rigid Euclidean transformations (rotations, translations, reflections) and inversions on hyper-spheres. As an application, we present the Spherical Evolutionary Algorithm (SEA) for global continuous optimization. Two new geometric search operators are included in the design of the SEA: Inversion Search Operator (ISO) and Reflection Search Operator (RSO). The nonlinear geometric nature of the ISO furnishes the search capability of the algorithm and the RSO redistributes the population. The reproduction operators are described in the framework of the CGA.

We present the results comparing our proposal with other leading algorithms. The experiments are carried out by using several benchmark problems available in the literature.

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