As an intelligent search optimization technique, genetic algorithm (GA) is an important approach for non-deterministic polynomial (NP-hard) and complex nature optimization problems. GA has some internal weakness such as premature convergence and low computation efficiency, etc. Improving the performance of GA is a vital topic for complex nature optimization problems. The selection operator is a crucial strategy in GA, because it has a vital role in exploring the new areas of the search space and converges the algorithm, as well. The fitness proportional selection scheme has essence exploitation and the linear rank selection is influenced by exploration. In this article, we proposed a new selection scheme which is the optimal combination of exploration and exploitation. This eliminates the fitness scaling issue and adjusts the selection pressure throughout the selection phase. The χ 2 documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$chi ^2$$end{document} goodness-of-fit test is used to measure the average accuracy, i.e., mean difference between the actual and expected number of offspring. A comparison of the performance of the proposed scheme along with some conventional selection procedures was made using TSPLIB instances. The application of this new operator gives much more effective results regarding the average and standard deviation values. In addition, a two-tailed t test is established and its values showed the significantly improved performance by the proposed scheme. Thus, the new operator is suitable and comparable to established selection for the problems related to traveling salesman problem using GA.
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