Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization

S. Mahato, A. Bhunia
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引用次数: 49

Abstract

Firstly, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented, and then pointing out the drawbacks of these definitions, a new approach is proposed in the context of decision maker’s (optimistic and pessimistic) point of view. Secondly, an interval technique is proposed to solve unconstrained multimodal optimization problems with continuous variables. In this proposed method, the search region is divided into two equal subregions successively and in each subregion, the lower and upper bounds of the objective function are computed with the help of interval arithmetic. Then, by comparing these two interval objective values and considering the subregion containing the better objective value, the global optimal value of the objective function or close to it is obtained. Finally, the proposed method is applied to solve several number of test problems of global optimization with lower as well as higher dimension and is compared with the existing methods with respect to the number of function evaluations.
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面向区间算法的全局优化区间计算技术
本文首先对实数线上任意两个区间数的比较和排序的现有研究进行了简要的综述,然后指出了这些定义的缺陷,并在决策者(乐观和悲观)观点的背景下提出了一种新的方法。其次,提出了求解连续变量无约束多模态优化问题的区间技术。该方法将搜索区域依次划分为两个相等的子区域,在每个子区域中利用区间算法计算目标函数的下界和上界。然后,通过比较这两个区间目标值,并考虑包含较优目标值的子区域,得到目标函数的全局最优值或与其相近的全局最优值。最后,应用该方法求解了若干高维和低维全局优化测试问题,并与现有方法在函数求值次数方面进行了比较。
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