Abstract: In this paper, a concept of locus factor is introduced to measure the fitness differences among/between the order-1 schemata at a certain locus. According to the relationship between locus factor and order-1 building block, the ability of the linear-weighted coding employed to a linear fitness function to generate order-1 building blocks is analyzed. An upper limit of the locus factor at a particular locus in terms of the weights is given. The results show that, in order to guarantee the calculation accuracy, there always exist loci at which locus factors are very close to 1, not matter what the weights are. As a result, the local search efficiency of the linear-weighted-encoded genetic algorithms employed to a linear function is unavoidably low.

摘要： 本文引入基因座系数作为基因座上一阶模式适应度差别的衡量指标；通过基因座系数和一阶积木块的对应关系，分析了线性加权编码用于线性函数编码时生成一阶积木块的能力。分析结果给出了基因座系数的一个上限与加权值的关系。分析结果同时表明，为保证计算精度，无论加权值如何变化，总有部分基因座上的基因座系数接近于1，因此在相当部分的搜索子空间中搜索随机性强，效率低。