Shuffled complex evolution approach for effective and efficient global minimization.

*(English)*Zbl 0792.90065Summary: The degree of difficulty in solving a global optimization problem is in general dependent on the dimensionality of the problem and certain characteristics of the objective function. This paper discusses five of these characteristics and presents a strategy for function optimization called the shuffled complex evolution (SCE) method, which promises to be robust, effective, and efficient for a broad class of problems. The SCE method is based on a synthesis of four concepts that have proved successful for global optimization: (a) combination of probabilistic and deterministic approaches; (b) clustering; (c) systematic evolution of a complex of points spanning the space, in the direction of global improvement; and (d) competitive evolution. Two algorithms based on the SCE method are presented. These algorithms are tested by running 100 randomly initiated trials on eight test problems of differing difficulty. The performance of the two algorithms is compared to that of the controlled random search CRS2 method presented by W. L. Price [J. Optimization Theory Appl. 40, 333-348 (1983; Zbl 0513.90070); ibid. 55, 133-146 (1987; Zbl 0622.90073)] and to a multistart algorithm based on the simplex method presented by J. A. Nelder and R. Mead [Computer J. 7, 308-313 (1965; Zbl 0229.65053)].

##### MSC:

90C30 | Nonlinear programming |

##### Keywords:

numerical optimization; global search; efficiency; effectiveness; complex of points; random search; global optimization; shuffled complex evolution; clustering; competitive evolution
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\textit{Q. Y. Duan} et al., J. Optim. Theory Appl. 76, No. 3, 501--521 (1993; Zbl 0792.90065)

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##### References:

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