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In this article, a discussion of optimization issues occurring in the area of genomics such as string comparison and selection problems are discussed. With this objective, an important part of the existing results in this area will be discussed. The problems that are of interest in this paper include the closest string problem (CSP), closest substring problem (CSSP), farthest string problem (FSP), farthest substring problem (FSSP), and far from most string (FFMSP) problem. The paper presents a detailed view of the most important problems occurring in the area of string comparison and selection, using the Hamming distance measure is given.