A Heuristic Method of Searching an Optimum Point of a Two-Dimensional Multimodal Criterion Function
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概要
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The paper investigates a method of heuristically searching an optimum point on a multimodal hill in a two-dimensional space.An experiment was conducted in order to extract heuristics evolved by a human searcher. First a subject recognizes visually a whole figure of trial result (coordinates and heights of trial points) recorded on a searching paper, then he chooses a new trial point. An experimenter answers the height of a test hill corresponding to the point. After recording the height on a searching paper, the subject repeats the same procedure to select a new trial point till he can be convinced of having searched an optimum point.From the experimental result, heuristics used in such a searching problem were generalized: The searching process is divided into three searching modes (global search mode "G-mode", local search mode "L-mode", and convergent search mode "C-mode"). Basic arrangement of trial points by each mode, and general properties of each mode are made clear. Transitions between these search modes are considered by a newly proposed "mode transition diagram".Two kinds of so-called "heuristic jump" were extracted: One is a jump (transition) from a vicinity of a certain base point to a vicinity of another base point, which are selected to be plausible base points having been selected after previous G-mode trials. The other is a jump to a new, open unsearched domain with a comparable extent to that of the most plausible highest peak obtained previously.The result of the paper will be applicable to a problem of optimizing a large-scale complex system with a multimodal nonlinear criterion function.
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