Uncertain Programming Based On Swarm Intelligence

With the development of modern technology, the existing deterministic methods have encountered troublesome difficulties in many research areas. Many important decision problems can not be solved effectively by traditional mathematical programming models. Uncertain programming, as the theory and methodology of optimization under uncertain environment, provides a unified theoretic foundation for optimization problems under all kinds of uncertainties such as random, fuzzy, rough, birandom and fuzzy random environment. Research on the theory of uncertain programming has become the hotspots and frontal problems due to its potential developments and applicabilities in many areas of science and technology, such as electronics, communication, automatic control, optics and biology.To satisfy the need of solving uncertain programming model of large scale, it is necessary to make further improvement and new attempt on algorithm designing in the light of its complication, such as designing effective and powerful new swarm intelligence algorithms. In swarm intelligence complex goups and intelligent behave can emerge through interaction and cooperation among individuals.Swarm intelligence has great significance, both theoretically and practically, which provide powerful computational tools to solve diverse complex uncertain programming problems in many decision systems. This thesis devotes to the improvement and enlargement of the theory of swarm intelligence with applications to uncertain programming. Several novel swarm intelligence algorithms are designed and applied to solve uncertain programming problems, especially to random fault tolerant trajectory planning of space manipulator. The main research work and contributions of the present thesis are as follows:(1) The theory of swarm intelligence such as unified framework, convergence, robustness and survival analysis are proved and analyzed. Three basic courses of the uniform framework of swarm intelligence algorithms, that is, cooperation, adaptation and competition, are mathematically described and explained. The convenience of swarm intelligence is proved based on Markov chain and gragh theory, respectively. The robustness and sensitivity of swarm intelligence algorithms are analyzed. The disturbance of parameters is considered as a special input to test its influence on the performance of algorithms. The statistics measurement is used to provide mean value and variance for comparing different strategies. Multivariate survival analysis is for the first time introduced into evolutionary algorithm. Parametric survival model with concomitant variables is built up for the convergence process of ant colony optimization algorithm. Kaplan-Meier survival analysis method is used to compute the estimated survival time and survival function curve. The regression model of COX proportional danger rate is solved. The data statistics and analysis softerware, SPSS is used to analyze the influence of parameter choice on premature convergence.(2) Several novel swarm intelligence algorithms are proposed. Inspired by the principle of human social activity, dynamic multi-level differential evolution algorithm based on group election is proposed. Based on the complex social behaviour model of western political leader election, differential evolution algorithm integrating multiple level and dynamic changeable topology strategy is made up of the following three stages: election within the group, representative election and group rebuilding. Based on virus evolution theory, virus evolutionary differential evolution algorithm with transverse orientation and longitudinal orientation two layer structure is proposed through dynamically integrating global evolution of the main population and local evolution of the virus population. With multivariate survival analysis for the first time introduced into evolutionary algorithm, an ant colony optimization algorithm is proposed. Population size and the survival time of invidiuals are adjusted by a fuzzy adaptive controller through intergrating survival analysis, fuzzy control and ant colont optimization algorithm.(3) Swarm intelligence computation based on hypothesis test for uncertain programming. For uncertain programming with non-deterministic parameters, through integrating hypothesis test into swarm intelligence, effective performance evaluation and comparison can be done from the aspect of statistics, so as to improve the whole quality of population and guaranty the dispersion of population. Dynamic multi-level differential evolution algorithm based on group election is proposed by nesting multilayer differential evolution. Typical benchmark function optimization problems with multiple minima under uncertain environment are taken as experimental examples to validate the robustness of the proposed algorithm and its good performance of searching under different noise strength factor, the dimension of independent variable and scale of the group.(4) Robust swarm intelligence algorithm for double uncertain programming. Fuzzy dependence chance programming model and random fuzzy chance constrained programming model are built. An ant colony optimization algorithm based on fuzzy simulation is designed. A proof of its convergence is given and its convergence speed is analyzed through evaluating the expected time needed for convergence. Virus evolutionary differential evolution algorithm based on random fuzzy simulation is developed and its convergence is analyzed. The robustness of the proposed algorithm for dealing with double uncertain programming is discussed from the following five aspects: uncertain environment, parameter sensitivity, initial value independence, confidence level and noise disturbance resistance.(5) Random fault tolerant trajectory planning of space manipulator. The uncertainty of 6 D.O.F. space robot and 2 D.O.F. space robot systems is analyzed. The influence of joint parameters on trajectory precision such as errors of link length and joint angle is discussed based on the differential transformation method. A stochastic mathematical model of fault tolerant trajectory planning of a 6 D.O.F. space manipulator with both kinematical and dynamical restrictions before and after joint failures taken into account is built with minimal weighted driven torque as the objective of performance optimization. The optimal trajectory of the manipulator all along the work time before and after its joint failure is computed by ant colony optimization with fuzzy adaptive surviva, to guarantee that the manipulator has high manipulability after joint failure to accomplish its successive operational task continually. ADAMS, that is, the mechanical system dynamics analysis software and virtual prototype analysis development tool, is used in the simulation experiments.Taken as a collection, the proposed theoretics and method of swarm intelligence algorithm for uncertain programming has scientific significance and validity. Not only does it deserve deep research in theory, but also does it have better application values for engineering.