分组测试与迫进控制标准  

GROUP TESTING WITH PROXIMATE DOMINATING CRITERIA

作　　者：綦明男[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学应用数学系

出　　处：《高等学校计算数学学报》2006年第3期272-282,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：陕西省自然科学基金项目(2001SL03).

摘　　要：1引言 在第二次世界大战期间，珍珠港事件发生后，美国为了反击德国法西斯挑起的侵略战争，多次进行大规模的征兵活动．在征兵活动中，需要对大量报名入伍者进行健康检查，看其身体是否符合入伍的条件．其中一项健康检查的内容是血液抗体检测，通过血液抗体检测，查出梅毒的携带者．当时，由于被检测者数量巨大，部队又急需补充兵员，检测时间紧、任务重，这就需要找到一种科学的检测方法，用尽可能少的测试次数检测出所有病毒携带者，这一问题后来称为搜索坏硬币的最优化问题．在这个问题中，被检测者抽象为硬币，血液不带病毒者抽象为标准硬币，血液带病毒者抽象为伪硬币，检测的设备称为装置．如何用特定性能的若干台装置，以尽可能少的测试次数从由硬币组成的集合中检测出全部伪硬币，是一个有很强实际背景的最优化问题，正因为如此，近一段时间组合搜索中的伪硬币问题一直受到人们的广泛关注．The group testing problems also fall under the general heading of dynamic programming [1], in that they involve the determination of proximate control criteria for making a sequence of decisions during a group testing procedure, with the motive of minimizing some function of a set of parameters by which the group testing procedure is specified. In this paper the authors firstly establish a proximate control criteria for making a sequence of decisions during a group testing procedure, then consider the problem of ascertaining the minimum number of tests which suffice to determine one defective coin in a set of n coins by applying the fuzzy dominating criteria. In particular, this paper is concerned with proximate control problem, in which an optimal procedure for culling out one subset of a given set is obtained. The desired procedure is optimal in the sense of minimizing the average number of steps in the process.

关 键 词：分组测试 标准 抗体检测 第二次世界大战 最优化问题 控制 健康检查 测试次数 

分 类 号：O157[理学—数学]