Multiobjective evolutionary algorithms (EAs) that use nondominated sorting and sharing have been criticized mainly for their: 1) (3) computational complexity (where is the number of objectives and is the population size); 2) nonelitism approach; and 3) the need for specifying a sharing parameter. In this paper, we suggest a nondominated sorting-based multiobjective EA (MOEA), called nondominated sorting genetic algorithm II (NSGA-II), which alleviates all the above three difficulties. Specifically, a fast nondominated sorting approach with (2) 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 (with respect to fitness and spread) solutions. Simulation results on difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to Pareto-archived evolution strategy and strength-Pareto EA-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 multiobjective 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 multiobjective optimizer and much better performance of NSGA-II is observed.

No abstract

No abstract

Abstract. In this paper, we apply an elitist multi-objective genetic algorithm for solving mechanical component design problems with multiple objectives. Although there exists a number of classical techniques, evolutionary algorithms (EAs) have an edge over the classical methods in that they can find multiple Pareto-optimal solutions in one single simulation run. Recently, we proposed a much improved version of the originally proposed non-dominated sorting GA (we call NSGA-II) in that it is computationally faster, uses an elitist strategy, and it does not require fixing any niching parameter. In this paper, we use NSGA-II to handle constraints by using two implementations. On four mechanical component design problems borrowed from the literature, we show that the NSGA-II can find a much wider spread of solutions than classical methods and the NSGA. The results are encouraging and suggests immediate application of the proposed method to other more complex engineering design problems.

The MDD is defined as the maximum loss incurred from peak to bottom during a specified period of time. Mathematically it is given by where X ( t ) represents the equity curve of the trading system or fund. The maximum drawdown MDD is the most widespread risk measure among money managers and hedge funds. It is often preferred over some of the other risk measures because of the tight relationship between large drawdowns and fund redemptions. Also, a large drawdown can even indicate the start of a deterioration of an otherwise successful trading system, for example due to a market regime switch.Despite the importance of such a problem, there has been a lack of theoretical results covering that problem. In this article, we develop new analytic formulas that relate a 0-7803-7654-4/03/$I7.00 02003 IEEE 243 CIFEr'03 HONG KONG