Convex hull ranking algorithm for multi-objective evolutionary algorithms

Due to many applications of multi-objective evolutionary algorithms in real world optimization problems, several studies have been done to improve these algorithms in recent years. since most multi-objective evolutionary algorithms are based on the non-dominated principle, and their complexity depends on finding non-dominated fronts, this paper introduces a new method for ranking the solutions of an evolutionary algorithm's population. first, we investigate the relation between the convex hull and non-dominated solutions, and discuss the complexity time of the convex hull and non-dominated sorting problems. then, we use convex hull concepts to present a new ranking procedure for multi-objective evolutionary algorithms. the proposed algorithm is very suitable for convex multi-objective optimization problems. finally, we apply this method as an alternative ranking procedure to nsga-ii for non-dominated comparisons, and test it using some benchmark problems.