摘要
在求解本题时,先对题中提出了四个要求进行相应的数学处理,处理的方法是将四个定性要求转化为定量化约束条件或目标函数,建立了每个问题的数学模型,借鉴组合数学中的平衡不完全区组设计相关概念和方法对问题一和问题三第一问进行了求解,得到了固定学生人数时老师人数的下限公式,构造一种启发式搜索算法再对问题一和问题三进行求解,得到问题一和问题三的确切老师人数近似最小值,经过分析求解过程和结果,指出算法的优缺点,并利用启发式算法对问题二进行求解,提出一种矩阵编码的遗传算法也对问题二和问题三第二问进行求解,对上述两种算法求解结果进行了分析比较,给出了最后的结果,阐明了算法的有效性.
In order to solve the problem, the qualitative requests were transformed into relevant quantitative restricts or object functions. The mathematic models were established. The relative concepts and method of balanced incomplete block design were used for reference to solve the first question and the third question. The floor level formula of teachers was deduced with the method mentioned above. A heuristic search algorithm was established to solve the first and the third questions again and the approximate least numbers of teachers were got. The strongpoint and shortcomings of algorithm were pointed out after analyze the process and results, The second question was solved with the heuristic algorithm mentioned above and genetic algorithm based on matrix coding. The genetic algorithm based on matrix coding was also applied on the third question. The two methods this paper presented and their＇respective results were compared and analyzed. The conchlsion was given out and the methods were effective after the analysis.
出处
《数学的实践与认识》
CSCD
北大核心
2007年第14期138-144,共7页
Mathematics in Practice and Theory
关键词
区组设计
启发式搜索
遗传算法
block design
heuristic search
genetic algorithm
