多峰性多変数関数の最大・最小と図形会話型処理

概要

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This paper discusses a new algorithm to locate the global maximum of a function defined in a multi-dimensional rectangular domain. The number of dimensions is as large as, or even more than, 5 or10. There are two important elements in this algorithm. One is the transformation of the object function in such a way that its global maximum corresponds to infinity while other secondary maxima are reduced to zero. Actually there is some departure from the ideal transformation because of possible overflows on computer. This portion of the algorithm precedes the interactive (or conversational)use of a graphic display system. This interactive part makes the other element of the algorithm. A multi-dimensional point is represented as a curve on the display screen. By projecting numerous points in the multi-dimensional space to similarly numerous curves on the screen of the graphic display device, the human eye can make overall recognition much more efficiently than computers. This fact is exploited to reduce the problem to that of a set of uni-modal peaks. Once the supporting domain for each of these peaks is separated by visual aid, one may leave the computer to handle the rest of the problem for itself. A number of numerical experiments are done and discussed to evidence the feasibility of the proposed algorithm.
一般社団法人情報処理学会の論文
1976-09-15