Ranking solutions of the population in an evolutionary algorithm that solves a many objective optimization problem is a challenging task which has been vastly studied in recent years. Loss in the hypervolume of the population when a solution is omitted could be a good measure for ranking solutions but calculating this value for high dimensional problems is not tractable. In the selection operator of evolutionary algorithms, the actual hypervolume values are not important, with only a relative knowledge of these values we can select best solutions. In this paper we have proposed a novel method for approximating the ranking induced by the hypervolume indicator. This method is compared to the similar methods and its efficiency and performance is proved via proper experiments. The method is tested using benchmark test problems from the Walking Fish Group problem family which are scalable both in number of variables and objectives.
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