Stagnation Analysis Of A Class Of Computational Intelligence Approaches

How to seek solutions of complicated optimization problems is a challenging research subject in recent years. In addition to traditional optimization methods, the computational intelligence approaches have been attractive in fundamental research and real applications. A class of computational intelligence approaches which is represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization is derived from the emulation of natural evolution or collective behavior of animals to seek solutions of complicated optimization problems by exploring and exploiting search spaces efficiently and effectively.Stagnation is a crucial problem which is suffered by computational intelligence approaches when dealing with complicated optimization problems in the theory and application. On the one hand, it is related to how to set the structure and parameters of the existing computational intelligence methods to efficiently produce high-quality solutions. On the other hand, it involves how to design an effective and efficient computational intelligence method for solving complicated optimization problems.This paper makes an investigation on the stagnation of a class of computational intelligence approaches, and the main contributions given in this dissertation are as follows.(1) The influences of the diversification and the intensification of search strategies on the stagnation of solution set evolution are investigated. Through the analysis on the search characteristics of a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization, the concept of solution set diversity is introduced in this paper. And then two categories of fundamental search strategies, i.e. the diversification search and the intensification search, are defined in this paper on the basis of solution set diversity. Based on which the influences of the diversification and the intensification of search strategies on the stagnation of solution set evolution are investigated. Three popular swarm intelligent algorithms, i.e. the Canonical Generic Algorithm, the Ant Colony System and the Discrete Particle Swarm Optimization, are tested with a benchmark problem, and the results support the theoretical conclusions.(2) The sufficient conditions are derived for the almost sure convergence of a universal model for a class of computational intelligence approaches. A universal model is built up in this paper for a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization in order to describe the common features of these algorithms. Two quantification indices, i.e., the variation rate and the progress rate, are defined respectively to estimate the variety and the optimality of the solution sets generated in the search process of the model. Four types of probabilistic convergence are given for the solution set updating sequences, and their relations are discussed. By introducing a martingale approach into the Markov chain analysis, the sufficient conditions are derived for the almost sure weak convergence and the almost sure strong convergence of the model.(3) An adaptive cloud drops optimization algorithm is proposed for stagnation elimination. The feature parameters of solution sets are created by a multidimensional backward cloud model, and then adaptively adjusted based on the change of the elite solution candidates. The result is then used by a forward cloud model to produce the solution set of next generation. No any search parameters are predefined in the proposed algorithm, and, no matter what the initial solution set is, the whole system can adaptively approach to the global optimal solution. Based on the theory of stochastic processes, the almost sure convergence of the proposed algorithm is proved under certain conditions by introducing a martingale approach into traditional Markov Chain analysis. Two benchmark problems are tested with the proposed algorithm and the other four existing algorithms as a comparison. The results show that the proposed algorithm has faster convergence speed, better self-adaptability, and stronger ability to deal with stagnation phenomena effectively.(4) The problem of unknown parameters identification for chaotic systems is addressed by the cloud drops optimization in this paper. Through establishing an appropriate evaluation function, the problem of unknown parameters identification in chaotic systems is formulated as a multi-dimensional optimization problem. And then, the cloud drops optimization algorithm, which is not sensitive to initial solution set and parameters less, is applied to obtain the original parameters of various chaotic systems. Numerical simulations on the typical Lorenz chaotic system and Chen chaotic system are conducted. Numerical simulation and comparisons with the other two existing algorithms demonstrate the effectiveness and feasibility of the proposed algorithm.