1. An optimization control apparatus for reading an input and generating optimum codes for a plurality of array descriptions having different subscript expressions, comprising: means for determining a scope of executing an optimization for said array descriptions, and deriving relations between said different subscript expressions of array descriptions on the basis of an optimization level determined in advance, the dimension number of an array of said array descriptions, and the array number of each dimensions; means for outputting said optimum codes within the scope of executing the optimization judged by said means for determining the scope of executing the optimization; means for extracting information about an array descriptive form which is for extracting the information representing each form of said array descriptions within said scope of executing the optimization, wherein the extracted information is stored in a list form; and common expression recognition means for detecting a common expression for each of said array descriptions from said information stored in the list form, and recognizing said information common to each of said array descriptions.