A robust design of simulated annealing approach for mixed-model sequencing

doi:10.1016/j.cie.2004.12.005

Computers & Industrial Engineering

Volume 48, Issue 4, June 2005, Pages 753-764

https://doi.org/10.1016/j.cie.2004.12.005 Get rights and content

Abstract

The effectiveness of the solution method based on simulated annealing (SA) mainly depends on how to determine the SA-related parameters. A scheme as well as parameter values for defining an annealing schedule should be appropriately determined, since various schemes and their corresponding parameter values have a significant impact on the performance of SA algorithms. In this paper, based on robust design we propose a new annealing parameter design method for the mixed-model sequencing problem which is known to be NP-hard. To show the effectiveness of the proposed method, extensive computation experiments are conducted. It was found that the robust designed method outperforms the SA algorithm by McMullen and Frazier [McMullen, P.R., & Frazier, G.V. (2000). A simulated annealing approach to mixed-model sequencing with multiple objectives on a just-in-time line. IIE Transactions, 32, 679–686].

Introduction

Although simulated annealing (SA) approach has already proved its usefulness in the very difficult combinatorial optimization problems, one may still face a dilemma in choosing the SA-related parameters. To apply SA to a specific problem, we have to define problem-specific parameters (representation of solutions, energy function and neighborhood structure, etc.) and determine annealing parameters (initial temperature, cooling function, epoch length and stopping condition). Several schemes maximizing the performance of SA, in terms of solution optimality or convergence speed, have been suggested and a factorial design and a simplex method have been utilized to select parameter values [Ali et al., 2002, Arts and Van Laarhoven, 1987, Huang et al., 1986, Johnson et al., 1989, Lundy and Mees, 1986, Park and Kim, 1998, Saab and Rao, 1991]. However, there exists interrelation among various schemes for defining the annealing schedule, which results in a significant impact on the performance of SA algorithms. In this paper, we propose a new annealing parameter design method based on Taguchi's robust design which primarily selects the design parameters for a product or process to minimize the effect of the noise parameters, so that the response is close to the desired target with minimum variation [Su & Hsieh, 1998].

Although the idea of the proposed method is applicable to any type of optimization problem, we will demonstrate our method by a mixed-model sequencing problem for brief explanation and concrete comparison with the results in the literature. Due to the NP-hard complexity of the mixed-model sequencing problem many heuristic approaches have been developed to solve the sequencing problem, especially efficient metaheuristics: a genetic algorithm (GA), simulated annealing and Tabu search (TS) [Celano et al., 1999, McMullen, 2001, McMullen and Frazier, 2000, Tamura et al., 1999]. With attention confined to the study on SA, we note the study of McMullen and Frazier (2000) who have presented an SA based heuristic for the mixed-model sequencing problem that simultaneously considers both the minimization of setups and the stability of parts usage rates.

The organization of this paper is as follows. In Section 2, the mixed model sequencing problem contributed by McMullen and Frazier (2000) is summarized. A robust design to improve the performance of SA algorithm is developed in Section 3. Extensive experiments are conducted based on the proposed algorithm and the results are discussed in Section 4, which is followed by the conclusion in Section 5.

Section snippets

Mixed-model sequencing problem

Mixed-model lines are used to produce several kinds of models in small lots without carrying large inventories. The production sequence for the mixed-model sequencing problem depends on the goals of the production facility. McMullen and Frazier (2000) considered two kinds of goals: usage goal and setup goal. Before presenting the mathematical representation of two goals, the following notations are defined first:

n: number of unique products to be produced
D: total number of units for all

Optimal experimental design of simulated annealing approach

In the annealing parameters, are included the initial temperature, cooling function, epoch length and stopping condition. For the annealing parameters, there are a variety of schemes provided in the literature [Ali et al., 2002, Arts and Van Laarhoven, 1987, Huang et al., 1986, Johnson et al., 1989, Lundy and Mees, 1986, Saab and Rao, 1991]. In this section, based on Taguchi's robust design method, we propose a new systematic approach to select the optimal combination of the schemes.

Numerical experiment

To evaluate the effectiveness of RD-SA, RD-SA is compared with the SA algorithm suggested by McMullen and Frazier (2000), MF-SA. Note that in our notations MF-SA is considered to simply use the schemes A₁, B₁, C₁, and D_1. Table 7 presents parameter values for MF-SA and RD-SA.

We tested three problem sets and ran both SA algorithms ten times for each problem. The results are summarized in Table 8, Table 9, Table 10, which show means and standard deviations (SD) of objective function values and

Conclusions

A new parameter design for SA algorithms to solve the mixed-model sequencing problem was proposed. The parameter design uses the robust design method, which can efficiently find the optimal level combination with less experiment. To show the effectiveness of the robust designed SA (RD-SA), several test problems were solved by two SA algorithms (RD-SA and MF-SA) and the results were compared in terms of optimality and convergence speed. It was found that RD-SA outperforms MF-SA for all problem

Acknowledgements

The authors are very grateful to the anonymous referee for his/her meticulous and painstaking review and detailed comments which greatly improved the paper. This research has been supported by Dongeui University, Korea, while H.M. Yoon was a Visiting Scholar at the Department of Urban and Environmental Engineering, Kyushu University.

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