A Fast Elitist Non-Dominated Sorting Genetic Algorithm

Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) a2a4a3a6a5a8a7a10a9a12a11 computational complexity (where a5 is the number of objectives and a7 is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically,

a fast non-dominated sorting approach with a2a4a3a6a5a8a7a14a13a15a11 computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) a7 solutions. Simulation results on five difficult test problems show that the proposed NSGA-II is able to find much better spread of solutions in all problems compared to PAES—another elitist multi-objective EA which pays special attention towards creating a diverse Pareto-optimal front. Because of NSGA-II’s low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come. 1 Introduction Over the past decade, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested [9, 3, 5, 13]. The primary reason for this is their ability to find multiple Pareto-optimal solutions in one single run. Since the principal reason why a problem has a multi-objective formulation is because it is not possible to have a single solution which simultaneously optimizes all objectives, an algorithm that gives a large number of alternative solutions lying on or near the Pareto-optimal front is of great practical value. The Non-dominated Sorting Genetic Algorithm (NSGA) proposed in Srinivas and Deb [9] was one of the first such evolutionary algorithms. Over the years, the main criticism of the NSGA approach have been as follows: High computational complexity of non-dominated sorting: The non-dominated sorting algorithm in use uptil now is a16a8a17a19a18a21a20a23a22a12a24 which in case of large population sizes 2 Deb, Agrawal, Pratap, and Meyarivan is very expensive, especially since the population needs to be sorted in every gen- eration. Lack of elitism: Recent results [12, 8] show clearly that elitism can speed up the performance of the GA significantly, also it helps to prevent the loss of good solutions once they have been found. Need for specifying the sharing parameter a25a27a26a29a28a31a30a15a32a34a33 : Traditional mechanisms of insuring diversity in a population so as to get a wide variety of equivalent solutions have relied heavily on the concept of sharing. The main problem with sharing is that it requires the specification of a sharing parameter (a25 a26a29a28a31a30a15a32a35a33 ). Though there has been some work on dynamic sizing of the sharing parameter [4], a parameterless diversity preservation mechanism is desirable. In this paper, we address all of these issues and propose a much improved version of NSGA which...

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