Algorithm for Locating All Local Minima of Multidimensional Function
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    Abstract:

    This paper focuses on locating all local minima of box-constrained, non-linear optimization problems. A new algorithm based on Multistart method is proposed. A quality measure called G-measure is constructed to measure the local minima of a multidimensional continuous and differentiable function distribution inside bounded domain. This paper measures the distribution of local minima in three facets: Gradient, convexity and concavity, and rate of decline. Feasible region is divided into several small regions, and each is assigned a set of initial points in proportion to its G-measures. More initial points can be allocated in the region which includes more local minima. A condition judging whether an initial point is effective is aimed to decrease the run times of local optimal technique. The approximate computing method is constructed to reduce computational complexity of G-measure. Several benchmarks with large quantities of local minima are chosen. The performance of this new method is compared with that of Multistart and Minfinder on benchmark problems. Experimental results show that the proposed method performs better in search efficiency.

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刘杰,王宇平.一类求多变量函数所有局部极小点的算法.软件学报,2013,24(10):2267-2274

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History
  • Received:June 26,2012
  • Revised:October 19,2012
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  • Online: October 12,2013
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