Optimizing complex functions by chaos search. (English) Zbl 1012.90068

Summary: During past decades, the role of optimization has steadily increased in many fields. It is a hot problem in research on control theory. In practice, optimization problems become more and more complex. Traditional algorithms cannot solve them satisfactorily. Either they are trapped to local minima or they need much more search time. Chaos often exists in nonlinear systems. It has many good properties such as ergodicity, stochastic properties, and “regularity.” A chaotic motion can go nonrepeatedly through every state in a certain domain. By use of these properties of chaos, an effective optimization method is proposed: the chaos optimization algorithm (COA). With chaos search, some complex optimization problems are solved very well. The test results illustrate that the efficiency of COA is much higher than that of some stochastic algorithms such as the simulated annealing algorithm and chemotaxis algorithm, which are often used to optimize complex problems. The chaos optimization method provides a new and efficient way to optimize kinds of complex problems with continuous variables.


90C39 Dynamic programming
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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