Srinivas, N., Deb, K.: Multiobjective optimisation using non-dominated sorting in genetics algorithms. In: Evolutionary Computation. Volume 2. (1994)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....les m etaheuristiques. Plusieurs adaptations de m etaheuristiques ont et e propos ees dans la litt erature pour la r esolution de PMO et la d etermination des solutions Pareto : le recuit simul e [89] la recherche tabou [31] et les algorithmes evolutionnaires (algorithmes g en etiques [79][23] strat egies evolutionistes [47] Les approches utilis ees pour la r esolution de PMO peuvent etre class ees en trois cat egories (fig.4) ffl Approches bas ees sur la transformation du probl eme en un probl eme uni objectif : Cette classe d approches comprend par exemple les m ethodes ....

....premi eres m ethodes utilis ee pour la g en eration de solutions Pareto optimales. Elle consiste a transformer le probl eme (PMO) en un probl eme (PMO ) qui revient a combiner les diff erentes fonctions cout f i du probl eme en une seule fonction objectif F g en eralement de facon lin eaire [42][79]: F (x) n X i=1 i f i (x) o u les poids i 2 [0: 1] et P n i=1 i = 1. Diff erents poids fournissent diff erentes solutions support ees. La meme solution peut etre g en er ee en utilisant des poids diff erents. La figure 5 illustre le fonctionnement de la m ethode d agr egation ....

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N. Srinivas and K. Deb. Multiobjective optimisation using non-dominated sorting in genetic algorithms. Evolutionary Computation, 2(8):221--248, 1995.

....of standard. With the introduction of non dominance Pareto ranking and sharing (in order to distribute the solutions over the entire Pareto front) the Pareto GAs are a very efficient way to find wide range of solutions to a given problem [Goldberg, 1989] This approach was further developed in [Srinivas and Deb, 1995], and lead to many applications [Poloni, 1995, Makinen et al. 1996, Bristeau et al. 1999] All of these approaches are cooperative and based on Pareto ranking and use either sharing or mating restrictions to ensure diversity; a good overview can be found in [Fonseca and Fleming, 1995] However, ....

....front. The GA used is a real coded GA with a population of 20. The maximum authorized number of evaluations is 2000. 3.2 Pareto We ran a Pareto based GA to see how well it would capture the global front. The Pareto GA we used is a realcoded algorithm based on NSGA, with ranking and sharing [Srinivas and Deb, 1995]. The population size is 50. Table 3.2 shows the percentage of times the algorithm manages to capture the global front, depending on the number of generations it is allowed to run. Generations 40 100 200 300 400 Finds global front 60 60 90 90 100 Table 1: Convergence towards the global ....

Srinivas, N. and Deb, K. (1995). Multiobjective optimisation using non-dominated sorting in genetic algorithms. In Evolutionary Computation 2 (3), pages 221--248.

....to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimisation tasks. 1 Introduction Multiobjective optimisation using genetic algorithms has been investigated by many authors in recent years [2, 6, 7, 10, 11, 17, 19, 20]. However, in some real world optimisation problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealing and tabu search, either when a single objective is sought or when multiple objectives have been combined by the use of a weighted sum, ....

....good solutions comparable to the MOEA, and in significantly less time. Six test functions are used to provide further comparison between PAES and two well known and respected MOGAs, the Niched Pareto Genetic Algorithm (NPGA) of Horn and Napfliotis [11, 10] and a non dominated sorting GA (NDSGA) [20]. Four of the test problems have been used by several researchers previously ( 2, 11, 10, 6, 19] and the fifth is a new problem devised by us as a further hard challenge to find diverse Pareto optima. The aim of this comparison is to explore and demonstrate the applicability of the PAES approach ....

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Srinivas, N., Deb, K. (1994) Multiobjective optimisation using non-dominated sorting in genetic algorithms. Evolutionary Compuation, 2(3), 221-248.

....process of sharing. This approach enables the algorithm to find several solutions instead of converging toward a single minima. All the individuals of a given rank are assigned the same fitness value, depending on the rank. This fitness value is then decreased for the solutions which are similar [9] according to the Hamming distance. 3.1.4 Application : NACA with Gamma45 o and 45 o radar illuminations We consider in this application that the reflector might be illuminated by either a Gamma45 o a 45 o incident waves. The optimization task consists in finding the best distribution ....

N. Srinivas and K. Deb. Multiobjective optimisation using non-dominated sorting in genetic algorithms. In Evolutionary Computation 2 (3), pages 221--248, 1995.

....The archive serves two distinct purposes: to return the best solutions found from the run and to act as a comparison set to aid in the evaluation of all new solutions generated. 3 The Test Problems The performance of PAES was compared with the Niched Pareto GA [4] and a nondominated sorting GA [9] on a suite of standard test functions. The first four of these are the same as used by Bentley [1] i.e. Schaffer s functions F1, F2, and F3, and Fonseca s f1, renamed F4 here. Functions F1 F4 contain, respectively, a single objective and one optima, a single range of optima, two ranges of ....

Srinivas, N., Deb, K. (1994) Multiobjective optimisation using non-dominated sorting in genetic algorithms. Evolutionary Compuation, 2(3), 221248.

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Srinivas, N., Deb, K.: Multiobjective optimisation using non-dominated sorting in genetics algorithms. In: Evolutionary Computation. Volume 2. (1994)

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