A Fast Algorithm for Finding the non Dominated Set in Multiobjective Optimization

Abstract

In this paper, we explain a new algorithm for finding non dominated set of a multi objective optimization problem. In literature many algorithms are used for this task like naïve and slow method [2], fast and efficient method [3] and Kung et al method [7]. Recently two new algorithms are proposed by Ding [4] and Jun Du[1].The worst case time complexity of all algorithm(including recently proposed algorithm) is (OM(N)2),Previously Kung’s algorithm was best in its average and best case time complexity but Jun du in 2007 proved that his algorithm is best in comparison of kung’s algorithm. While we were unable to reduce worst case time complexity, The best case time complexity of proposed algorithm is O(NLog(N))( for any number of objective functions )which is a improvement as compared to othere algorithms. Also it follows a simple approach, no hectic summation and production method. The paper is organized into four sections. Section 2 presents some background detail of Different Preexisting Algorithms and specifies the necessary definition related to non dominated set. Section 3 describes the proposed approach and stepwise algorithm also difference between Kung’s algorithm and proposed algorithm is presented; In Section 4, an experimental analysis and complexity of the proposed algorithm are presented. Finally, Section 5 concludes the paper.