Study On Mutation Operators And Simulation Platform Of Evolution Strategies

Improvements of the mutation operator of the evolution strategies (ES) are studied in this paper. All-gene mutation is applied to current mutation operators, single-gene mutation is proposed in the paper. Based on systemic analysis and comparison of the two types of mutation operators in the success probability, local convergence velocity, global convergence performance, mutation step-size control, computation costs, multi-population technique, single-population ES and multi-population ES based on single-gene mutation with descending mutation step-size control strategy are proposed respectively, finally establishment of a platform for evolutionary computation (EC) simulation and the application of the platform are discussed.The study on the ES and its mutation operators is originated from the knowledge that mutation operators play a dominant role in EC. With the experimentation on an improvement of the simple genetic algorithm (SGA) and analysis on the mechanism of crossover operators, it is proven that the local and global searching functions of crossover operators can be replaced by the mutation operators and the later plays a dominant role in EC.Originating from evolutionary theories and gene mutation ideas, the mutation operators of the ES take a manner of all-gene mutation, i.e. all the genes of an individual (or a chromosome) are varied at a time, single-gene mutation in which only one randomly selected gene is varied at a time is proposed in the paper. It is proven through theoretical analysis and simulation that single-mutation has a larger success probability than all-gene mutation under large mutation step-size for high-dimensional optimization, that the all-gene mutation suffers a stagnation of evolution and costs more especially for high-dimensional optimization.It is proven theoretically that when the success probability is about 0.445, the Gaussian distribution single-gene mutation can get the best local searching velocity, and a descending mutation step-size controlstrategy is correspondingly proposed. In order to intuitively analyze and compare the performances of different evolutionary operators, a novel method named as transverse simulation is proposed and is applied to the comparative study on the local convergence velocity of the single-gene mutation and all-gene mutation. It is proven through simulation that all-gene mutation under an appropriate mutation step-size and a small varying range has a lager local convergence velocity than single-gene mutation, and that the single-gene mutation can get a promising convergence velocity under a large mutation step-size and in a large varying range, and that the single-gene mutation operator shares an excellent robustness for the mutation step-size. Two counter examples demonstrate that Gaussian-distribution based single-gene mutation operator with descending step-size control has no enough global searching capability, a uniform-distribution mutation operator is introduced and the both operators are combined in ES, so a novel ES named as (// + X + k) - ES is proposed. Simulations under a set of typical 100-dimensional benchmark demonstrate that (/i + X + k) - ES has promising local and global searching capability and costs less.In order to promote the global searching capability of the({i + X + K)-ES and to solve the multi-modal function optimization (MFO) with multiple optima, a novel multi-population ES mx(ju + X + ic)-ES based on the (// + X + k) - ES is proposed. Sharing-radius is a difficult-determining and key parameter in crowding and (/or) sharing multi-population EC, hill-valley searching method is proposed and determination of the sharing-radius is avoided. A criterion is established to determine the convergence of a sub-population under a given accuracy and confidence, which is an applicable quantitative criterion. Simulations on a set of MFOs demonstrate that mx(jj + x + K)-ES can properly find all the optima.A platform for simulation and application is an important tool for EC, the basic idea and fundamental architecture of the platform is described based on the object-oriented programming (OOP ) and Visual C++. A platform is established and two actual examples -parametersoptimization of an electromechanical system's speed-control subsystem and optimal control of soccer robots are given to demonstrate the application of the platform and the algorithms proposed in this paper. Finally the future studying topics are given.