new trends b.galvan - ntuavelos0.ltt.mech.ntua.gr/.../resources/5_april/new_trends_b.pdf ·...

Computación Evolutiva y AplicacionesInstituto Universitario de Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería (IUSIANI)

Universidad de Las Palmas de Gran Canaria.

http://ceani.ulpgc.es

New Trends in MultiobjectiveEvolutionary Algorithms

Blas J. Galván

Ercoftac 20065 - 7 April 2006




Introduction• The actual State of the Art in Multiobjective Evolutionary

Algorithms (MOEA) is the so called “second generation” (SG-MOEA) .

• SG-MOEA were mainly designed and tested with computationally non-expensive objective functions.

• Many Industrial applications have computationally expensive evaluation procedures.

• The performance of SG-MOEA in such cases is not good

enough.




MOEA for large-scale industrial applications

Computationally Expensive Objective Functions

“Intelligent” Reduction of the objective function evaluation calls

Surrogate models metamodelshierarchical Structures Distributed MOEA

Giannakoglou et. Al. Ercoftac 06







Surrogate models metamodelshierarchical Structures Distributed MOEA

Giannakoglou et. Al. Ercoftac 06

Local directional information

Modeling the search landscape

Adapting the operators

Best choices of algorithmic comp.

Scatter Search

Using MCDM in the MOEA

Solution Injection











Scatter Search


Solution Injection

Brown and Smith [2005]

Knowles [2006]

Rudenko and Schoenauer [2005]

Paquete et al. [2006]

Nebro et al. [2006]

Mendez et al. [2006]

Greiner et al [2006]











Scatter Search


Solution Injection

Brown and Smith [5]local framework for MOEA by geometrically analyzing the multiobjective concepts of descent, diversity and convergence/optimality. The central issue was to show how to efficiently re-use the local directional information contained within a population











Scatter Search


Solution Injection

Knowles [3]Extension of the single-objective Efficient Global Optimization (EGO) algorithm to multiobjectiveproblems. The introduced algorithm called ParEGO uses a design-of-experiments inspired initialization procedure and learns a Gaussian processes model of the search landscape, which is updated after every function evaluation











Scatter Search


Solution Injection

Rudenko and Schoenauer [1]Introduce a new idea to adapt the general variations operators to the particular context of the quest for Pareto-optimal set. They introduce a particular mating restriction for MOEA: the partner of a non-dominated individual will be preferable chosen among the individuals of the population that it dominates











Scatter Search


Solution Injection

Paquete et al. [2][6]Have explored the application of experimental design techniques to analyze the best choices of algorithmic components of Stochastic Local Search Techniques applied to Multiobjective Combinatorial Optimization Problems that are solved in terms of Pareto optimality











Scatter Search


Solution Injection

Nebro et al. [7]Adapts the well-known Scatter Search template for single objective optimization to the multiobjective domain. The result is a Hybrid metaheuristicalgorithm called AbYSS, which follows the scatter search structure but using mutation and crossover operators coming from the field of evolutionary algorithms….. “the method clearly outperforms these two algorithms concerning the diversity of the solutions”.











Scatter Search


Solution Injection

Mendez et al. [9][10]Have introduced the use of concepts from MulticriteriaDecision Making into the MOEA algorithm in order to find, at least, zones of maximum interest in the Pareto front











Scatter Search


Solution Injection

Greiner et al [8][11][12]Have used with success a Solution Injection procedure in some challenging optimization problems. The technique consists in to include in the first MOEA population one (or more) single-objective known solutions stored in previously algorithmic runs.




Some results

Mendez et al. [9][10]

Have introduced the use of concepts from MulticriteriaDecision Making into the MOEA algorithm in order to find, at least, zones of maximum interest in the Pareto front. On the one hand,

If the Decision Maker is interested in guiding the search towards a particular region of the efficient frontier, the related solutions can be found using one algorithm which merges the NSGA-II with the multi-criteria decision making technique TOPSIS




Some results

Mendez et al. [9][10]A set of “precision solutions” can be computed using the distances to the Ideal and Nadir points in the solutions space




Unv

Unv

Some results




Open questionsIf preferences or the actual design point are used (TD point at the figure)?

• ¿It is necessary to evolve using the dominance criterion in the zones I, II and III?

• OR, is better to identify only the Pareto Front in the zone III?

III

III IV




Open questions

Would this option be more adequate?

• Less objective function evaluation will be needed

• Will the expectatives be fullfilled better?

II

IV




Conclusions• Despite the great advenace in the MOEA field, there is a

clear demand of MOEA algorithms for ExpensiveObjective Functions

• Probably a “new concept” of MOEA needs to be introduced.

• It is necessary to define a set of test cases withExpensive Objective Functions.

• Hybridization seems to be a promising research area.

• Some experimental results have been presented showingthat it is possible to introduce new algorithmic elements in the MOEA search in order to find zones in the ParetoFront




New Trends in MultiobjectiveEvolutionary Algorithms

Thanks very much

Blas J. Galván

Ercoftac 20065 - 7 April 2006




Introducción

• En la actualidad la optimización multiobjetivo ha alcanzado un elevado grado de desarrollo (¿madurez?)

• Los métodos multiobjetivo de segunda generación (NSGA-II, SPEA-II, etc.) son muy eficientes: Obtienen frentes de Pareto:– Amplios– Uniformemente distribuidos– ……

• Muchos investigadores consideran que están preparados para ser usados como soporte a la toma de decisiones en problemas reales




En este trabajo:• Comparar el NSGA-II frente al criterio del

Tomador de Decisiones:

– Considerando un criterio simple de toma de decisiones

– Aplicado a un problema bien conocido• De solución conocida• De tamaño manejable• Realista

• Reconsiderar la metodología en base a los resultados




El problema a resolver

• Sistema de Inyección Spray en la Contención de una CN

• MISIÓN: Inyectar agua boradasi se produce un accidente del tipo Pérdida de Refrigerante

• Obtener diseño óptimo teniendo en cuenta los componentes de la tabla 1

• Funciones Objetivo: Indisponibilidad y Coste

• Modelo del Sistema: Árbol de Fallos con alternativas de diseño (Indisponibilidad)




NSGA II

• 100 Generaciones

• 30 Individuos/generación

• Las soluciones que se obtienen son del frente de Pareto

Unv




Método DDTD

• Considera una preferencia (una solución deseada, TD) del Tomador de Decisiones ( “a priori”)

•Se utiliza un criterio de distancia a TD (métrica p2) para valorar las soluciones.

• Se finaliza clasificando en fronteras la última población

• Las soluciones que se obtienen son las más cercanas al TD pero no necesariamente son del frente de Pareto

Unv




Conclusiones

• Se ha mostrado que es posible incluir una preferencia conocida “a priori” por el Tomador de Decisiones con modificaciones que no alteran lo esencial del NSGA II.

• El método empleado parece aplicable a cualquier método multiobjectivo de segunda generación.

• La metodología “favorece” la toma de decisiones en el tipo de problema planteado

new trends b.galvan - ntuavelos0.ltt.mech.ntua.gr/.../resources/5_april/new_trends_b.pdf ·...

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