Artículos regulares

 

Building General Hyper-Heuristics for Multi-Objective Cutting Stock Problems

 

Construyendo híper-heurísticas generales para problemas de corte multi-objetivo

 

Juan Carlos Gómez¹ and Hugo Terashima-Marín²

 

¹Department of Computer Science, KU Leuven, Belgium, juancarlos.gomez@cs.kuleuven.be

²Center for Robotics and Intelligent Systems, Tecnológico de Monterrey, Campus Monterrey, México, terashima@itesm.mx

 

Article received on 09/02/2011;
accepted on 03/11/2011.

 

Abstract

In this article we build multi-objective hyper-heuristics (MOHHs) using the multi-objective evolutionary algorithm NSGA-II for solving irregular 2D cutting stock problems under a bi-objective minimization schema, having a trade-off between the number of sheets used to fit a finite number of pieces and the time required to perform the placement of these pieces. We solve this problem using a multi-objective variation of hyper-heuristics called MOHH, whose main idea consists of finding a set of simple heuristics which can be combined to find a general solution, where a single heuristic is applied depending on the current condition of the problem instead of applying a unique single heuristic during the whole placement process. MOHHs are built after going through a learning process using the NSGA-II, which evolves combinations of condition-action rules producing at the end a set of Pareto-optimal MOHHs. We test the approximated MOHHs on several sets of benchmark problems and present the results.

Keywords: Hyper-heuristics, multi-objective, optimization, evolutionary computation, cutting problems.

 

Resumen

En este artículo se construyen Híper-Heurísticas Multi-Objetivo (MOHH por las siglas en Inglés), utilizando el algoritmo evolutivo multi-objetivo NSGA-II, para solucionar problemas de corte irregular en 2D empleando un esquema bi-objetivo; teniendo un balance entre el número de hojas usadas para ajustar un número finito de piezas y el tiempo requerido para realizar el acomodo de las piezas. Este problema es resuelto usando las MOHHs, cuya idea principal consiste en encontrar un conjunto de heurísticas simples que puedan ser combinadas para encontrar una solución general; donde una heurística simple es utilizada dependiendo de la condición actual del problema, en vez de aplicar una única heurística simple durante todo el proceso de acomodo. Las MOHHs son construidas a través de un proceso de aprendizaje evolutivo utilizando el NSGA-II, el cual evoluciona combinaciones de reglas condición-acción produciendo al final un conjunto de MOHHs Pareto-óptimas. Las MOHHs construidas son probadas en diferentes conjuntos de problemas y los resultados obtenidos son presentados aquí.

Palabras clave. Híper-heurísticas, optimización multi-objetivo, computación evolutiva, problemas de corte.

 

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Acknowledgements

This research was supported in part by ITESM under the Research Chair CAT-144 and the CONACYT Project under grant 99695 and the CONACYT postdoctoral grant 290554/37720. A shorter versión of the paper has already appeared inMICAI2010.

 

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