This paper presents a new surface reconstruction method based on complex form functions, genetic algorithms and neural networks. Surfaces can be reconstructed in an analytical representation format. This representation is optimal in the sense of least-square fitting by predefined subsets of data points. The surface representations are achieved by evolution via repetitive application of crossover and mutation operations together with a back-propagation algorithm until a termination condition is met. The expression is finally classified into specific combinations of basic functions. The proposed method can be used for CAD model reconstruction of 3D objects and free smooth shape modelling. We have implemented the system demonstration with Visual C++ and MatLab to enable real time surface visualisation in the process of design.

CLARANS is an efficient and effective clustering method especially in spatial data mining. It is applicable to locate objects with polygon shape. Inspired by its randomized searching nature, and based on the standard particle swarm optimization (PSO) algorithm together with the widely used dynamic niche technology, this paper presents a new variation of CLARANS combined with the dynamic niche sharing technique with PSO algorithm. We proposed a cooperative particle swarm optimization CLARANS with cooperative multi-population.

In this paper, evolution and visualization of the existence of saddle points of nonlinear functionals or multi-variable functions in finite dimensional spaces are presented. New algorithms are developed based on the mountain pass lemma and link thery in nonlinear analysis. Further more, a simple comparison of the steepest descent algorithm and the genetic algorithm is given. The process of the saddle point finding is visualised in an inteactive graphical interface.

Based on the standard particle swarm optimization (PSO) algorithm together with the widely used dynamic niche technology, this paper presents a new variation combined with the dynamic niche sharing technique on the basis of traditional PSO algorithm. We proposed a cooperative particle swarm optimization model with cooperative multi-population. Applications are given on creative conceptual architectural design.