Heilbronn's Problem of Eight Points in the Square  

作　　者：DEHBI Lydia ZENG Zhenbing 

机构地区：[1]School of Software Engineering,East China Normal University,Shanghai 200062,China [2]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Journal of Systems Science & Complexity》2022年第6期2452-2480,共29页系统科学与复杂性学报（英文版）

基　　金：the National Natural Science Foundation of China under Grant Nos.12171159 and 12071282;“Digital Silk Road”Shanghai International Joint Lab of Trustworthy Intelligent Software under Grant No.22510750100。

摘　　要：In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the(38)triangles formed by them is maximal.Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution.All computations are done using Maple.

关 键 词：Global search Heilbronn’s problem optimal configuration smallest triangle’s area symbolic computations 

分 类 号：O221.2[理学—运筹学与控制论]