Gravitation field algorithm and its application in gene cluster

This paper proposes a novel searching optimization algorithm called Gravitation Field Algorithm (GFA) which is derived from the famous astronomy theory Solar Nebular Disk Model (SNDM) of planetary formation. GFA simulates the Gravitation field and outperforms GA and SA in some multimodal functions optimization problem. And GFA also can be used in the forms of unimodal functions. GFA clusters the dataset well from the Gene Expression Omnibus.The mathematical proof demonstrates that GFA could be convergent in the global optimum by probability 1 in three conditions for one independent variable mass functions. In addition to these results, the fundamental optimization concept in this paper is used to analyze how SA and GA affect the global search and the inherent defects in SA and GA. Some results and source code (in Matlab) are publicly available at http://ccst.jlu.edu.cn/CSBG/GFA webcite.Two of the most challenging tasks of optimization algorithms are to search the global optimum and to find all local optima of the space of solutions in clustering genes from available experimental data [1], e.g. the gene expression profiles, or given functions. In view of recent technological developments for large-scale measurements of DNA expression level, these two problems can often be formulated and many methods have been proposed. In particular, the heuristic searches are more promising than other kinds of searching approaches. These approaches include GA (genetic algorithm) [2], SA (simulated annealing) [3], PSO (Particle Swarm Optimization) [4] etc. But some inherent drawbacks, especially the inability to the multi-modal functions optimization, can be found from the traditional heuristic search algorithms above. Each of these concepts allows for several modifications, which multiplies the number of possible models for data analysis we can change the algorithm themselves, to find all the valleys of given functions. But we still have a lot of parameters to consider, as known as