The Electrostatic Field Model Of Evolutionary Algorithm

It is a dream for human beings that making intelligent machine which can substitute human work to release the labor force. From Artificial Intelligence to Computational Intelligence, People always want to find a way to make the machine intelligent. Recently Intelligent Optimization Algorithms have been wildly studied. There has been a series of intelligent optimization algorithms, such as Particle Swarm Optimization, ant Colony Algorithms and Differential Evolutions.It seems to be a new effective way to make the machines and algorithms intelligent from the imitation of the nature rules or mechanism and biological group behavior. Recent years the heuristic algorithm which simulates nature rules or mechanism, phenomenon is called the Nature Inspired Computation. As the Nature Inspired Computation has been solved many complicated problems which are hard for the traditional computing method and has significant prospect in large-scale complicated optimization problem solving and intelligent decision, so it comes to be the hot-spot for the researchers.With analyzing the classic genetic algorithm, the schema theorem can be explaining the effectiveness of the evolutionary algorithm so that it is the most important theorem of the evolutionary algorithm. The schema theorem indicates that gene which has good schema in evolutionary will be survived in large quantities finally which enhance the population searching optimization ability. From a macro view, the schema theorem indicates the ordering procedure of the population. In the classical physics, the field is the carrier of the material ordering.lit can enlarge the Nature Inspired Computation for the integration of the evolutionary algorithm and the Field theory. For the electrical field theory which has been made several achievements, this paper set up a description of evolutionary algorithm model by field theory and then design a new kind of evolutionary algorithm with the electrical field theory.The main innovations of this dissertation as follows:(1) We find out the physical explanations of the evolutionary operator and the schema theorem by analyzing the basic structure of the evolutionary algorithm and the schema theorem. The evolutionary process is the population ordering procedure: the crossover operator Oc which is satisfied the conservation of the momentum is action at a distance; the effect of the mutation operator Om which is F∝f(xi) all above are the basement of the electrical field model evolutionary algorithm. (2) According to the similarity of the electrostatic field and evolutionary optimization process, from the explanations of the Physics, we design the evolutionary operator. Through a large number of numerical experiments, it indicates that the average population fitness and the best fitness value are better than multi-parent crossover algorithm and particle swarm optimization. In addition, the influence of the evolu-tionary operator parameters selection is also analyzed by numerical experiment.(3) We set up the multi-objective evolutionary algorithm application model. Taking the infinity as the sampling center in objective function space, then the object-space will be extended through the Stercographic projection mapped the objective function space onto the Riemann sphere in order to sampling the Pareto front in the Riemann sphere. Finally it gets the precise, well-distributed Pareto Front experiment results on ZDT test functions.(4) For the single objective electrostatic field model evolutionary algorithm, we prove the convergence of the individual series by the differential equations theory and an-alyze the influence of the individual evolutionary convergence between the different operators. Using finite state Markov chain theory proved single-objective evolu-tionary algorithm based on electrostatic field model converges to the global optimal solution with probability 1.(5) We analyze the time complexity, space complexity of the Stcreographic projection Riemann-Sphere Sampling and prove the continuity, circle conservation, conformal, completeness and high-dimension extension.According to the analyzing the base model of the evolutionary algorithm, we get the physical description of the evolutionary algorithm model. For theses similarity of the physical properties, we set up the electrostatic field model evolutionary algorithm and design the single objective problem, multi-objective problem and combinatorial optimization evolutionary algorithm. All about these are benefit to the extensions of the Nature Inspired Computation.