Research On The Evolutionary Computation Methods Under Uncertain Environment

Today, the evolutionary computation has been greatly used in many domains such as combinatorial optimization, auto-adapted control, machine learning and so on. In theory, most researches mainly focused on Holland's Simple Genetic Algorithm, concerning some improvements on the computation accuracy, the convergence and the premature. What needs to pay much attention is that the results are all obtained only for problems with certainty. But in real problems, there always exists objective or anthropic uncertainty, such as fuzziness, randomnesss and roughness etc. When using genetic algorithm for the uncertain optimization problems, on the one hand, the fitness of an individual cannot be expressed as a real number, so it is difficult to compare accurately the fitness of individuals, and then the selection and reproduction process cannot be done only according to the conventional proportion way, on the other hand, when the constraints of optimization are with uncertainty, the feasibility of solution can't be determined by using total ordering relation of real number, so solving operation can't be established directly; which simultaneously restrict greatly the application of genetic algorithms to uncertainty optimization problems. In this paper, we consider the uncertain evolutionary algorithm, including the ordering of uncertain information, the design of genetic operators, the convergence of algorithm, the uncertainty metric of decision results.Firstly, for assignment problem with fuzzy effective matrix, we propose the concept of level effect function, and give the method for fuzzy assignment problem based on genetic algorithm by using I_L-metric and LU - uncertainty of fuzzy number, andanalyse its convergence; secondly, for assignment problem with random variables as effective matrix, we introduce the concept of risk critical value of random variables, give the method for objective risk critical value model of random assignment problem based on genetic algorithm, and analyze the reliability of results; thirdly, for general fuzzy optimization with fuzzy coeeficients, fuzzy variables and fuzzy constraints, we introduce the axiomatic system for fuzzy inequity degree for solving the judgement of fuzzy constraints, by distinguishing the principal index and secondary indices, and coupled with the compound quantification discription for fuzzy number and the unconditional penalty transform strategy for conditional constraints, we propose a kind of fuzzy genetic algorithm based on the principal operation and inequity degree; finally, for the system of fuzzy equations with fuzzy coeeficients, fuzzy variables, we propose fuzzy metric based on level effect, on the basis of essential characteristic of fuzzy decision, we establish solution model based on metric and uncertainty restriction for system of fuzzy equations, combining genetic algorithm and variance description strategy of principal index of fuzzy variable, we give solution method based on genetic algorithm for system of fuzzy equations, and consider its convergence using Markov chain theory and analyze its performance through simulation.