A Novel Non-dominated Sorting Algorithm.
ABSTRACT Many multi-objective evolutionary algorithms (MOEA) require non-dominated sorting of the population. The process of non-dominated sorting is one of the main time consuming parts of MOEA. The performance of MOEA can be improved by designing efficient non-dominated sorting algorithm. The paper proposes Novel Non-dominated Sorting algorithm (NNS). NNS algorithm uses special arrangement of solutions which in turn helps to reduce total number of comparisons among solutions. Experimental analysis and comparison study show that NNS algorithm improves the process of non-dominated sorting for large population size with increasing number of objectives.
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ABSTRACT: This paper addresses the problem of how to evaluate the quality of a model built from the data in a multi-objective optimization scenario, where two or more quality criteria must be simultaneously optimized. A typical example is a scenario where one wants to maximize both the accuracy and the simplicity of a classification model or a candidate attribute subset in attribute selection. One reviews three very different approaches to cope with this problem, namely: (a) transforming the original multi-objective problem into a single-objective problem by using a weighted formula; (b) the lexicographical approach, where the objectives are ranked in order of priority; and (c) the Pareto approach, which consists of finding as many non-dominated solutions as possible and returning the set of non-dominated solutions to the user. One also presents a critical review of the case for and against each of these approaches. The general conclusions are that the weighted formula approach -- which is by far the most used in the data mining literature -- is to a large extent an ad-hoc approach for multi-objective optimization, whereas the lexicographic and the Pareto approach are more principled approaches, and therefore deserve more attention from the data mining community.ACM SIGKDD Explorations Newsletter 12/2004; 6(2):77-86.
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ABSTRACT: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN<sup>3</sup>) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN<sup>2</sup>) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observedIEEE Transactions on Evolutionary Computation 05/2002; · 5.55 Impact Factor
- Journal of the ACM 01/1975; 22(4):469-476. · 2.94 Impact Factor