Quantum Competitive Decision Algorithm And Its Application Research

The optimization techniques have been applied to a wide range of engineeringtechnology, scientific research,economic management and so on, which are used toobtain optimal solution or satisfactory solution of various problems. As the scale ofobject problem becomes larger and constraint conditions are increasing, discontinuity,non-differentiation, uncertainty and high nonlinearity are basic characteristics of thesecomplex systems, or these problems are NP-hard combinatorial optimization problems.The traditional optimization methods have great limitation to solve complex anddifficult optimization problems because of these features. So the require for highefficiency intelligent optimization techniques is becoming more and more necessary,and exploring algorithms with intelligent characteristics for complicated calculation isresearch focus and important research direction.This dissertation proposes a novel optimization algorithm-quantum competitivedecision algorithm, which is based on competitive decision algorithm, evolutionarygame theory and quantum evolutionary algorithm. The algorithm is analyzed from theexperiment and theory aspects. The main innovations and improvements lie below:1The performance of competitive decision algorithm is influenced because of lackof the capacity of learning and self-evolution for competitors in the optimizationprocess. The introduction of evolutionary game theory makes competitors possess theability of self-adjusting and self-optimizing.2The decision-making method and other methods solve the suboptimal solution inevolutionary game theory and the degenerate problem in quantum evolutionaryalgorithm, and these make the algorithm have stronger global optimization ability.3The combination of quantum bit, superposition state and other concepts inquantum evolutionary algorithm and competitors can reduce the number of competitorsand speed up the convergence of the algorithm.4Competitive decision algorithm has won initial success in solving discreteoptimization problems, but there is no discussion of its convergence. There is also lessresearch on the convergence of quantum evolutionary algorithm. This dissertation givesconvergence analysis by Markov chain in theory.5The algorithm is applied to solve nonlinear0-1programming, large-scale TSPand complex function optimization. This dissertation gives their mathematicaldescriptions and develops a series of strategies for solving these different optimization problems. A large number of experiments and comparisons with existing algorithms aredone. All show that the algorithm is robust and efficient.6Competitive decision algorithm at present is only used in discrete combinatorialoptimization problems. quantum competitive decision algorithm can be effectively usedin function and discrete optimization problems. Quantum evolutionary algorithm hasbeen applied successfully to linear0-1knapsack problem, small-scale TSP and so on,but it can not effectively solve the complex optimization problems. Experiments onsolving nonlinear0-1programming, large-scale TSP and complex function optimizationindicate that quantum competitive decision algorithm has the good performance.Evolutionary game theory is applied extensively in biological, economic, political andso on, but it is less used in optimization problems. quantum competitive decisionalgorithm widens its application range.In a word, this dissertation theoretically presents a new method for optimizationproblems and gives the convergence proof of the algorithm. Practically, the dissertationputs forward a novel and effective algorithm for solving difficult and complexoptimization problems.