A hybrid differential evolution approach based on surrogate modelling for scheduling bottleneck stages

doi:10.1016/j.cor.2015.08.005

Computers & Operations Research

Volume 66, February 2016, Pages 215-224

https://doi.org/10.1016/j.cor.2015.08.005 Get rights and content

Highlights

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We develop a hybrid approach for solving the BSP using surrogate modelling.
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We transform the original problem into an expensive-to-evaluate problem.
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We create a surrogate model to evaluate a given partial schedule.
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An improved adaptive proximity-based method is introduced in DE.

Abstract

Surrogate modelling based optimization has attracted much attention due to its ability of solving expensive-to-evaluate optimization problems, and a large majority of successful applications from various fields have been reported in literature. However, little effort has been devoted to solve scheduling problems through surrogate modelling, since evaluation for a given complete schedule of these complex problems is computationally cheap in most cases. In this paper, we develop a hybrid approach for solving the bottleneck stage scheduling problem (BSP) using the surrogate modelling technique. In our approach, we firstly transform the original problem into an expensive-to-evaluate optimization problem by cutting the original schedule into two partial schedules using decomposition, then a surrogate model is introduced to, quickly but crudely, evaluate a given partial schedule. Based on the surrogate model, we propose a differential evolution (DE) algorithm for solving BSPs in which a novel mechanism is developed to efficiently utilize the advantage of the surrogate model to enhance the performance of DE. Also, an improved adaptive proximity-based method is introduced to balance the exploration and exploitation during the evolutionary process of DE. Considering that data for training the surrogate model is generated at different iteration of DE, we adopt an incremental extreme learning machine as the surrogate model to reduce the computational cost while preserving good generalization performance. Extensive computational experiments demonstrate that significant improvements have been obtained by the proposed surrogate-modelling based approach.

Section snippets

Background and motivation

Bottleneck stage exists in almost all of the manufacturing facilities such as the weaving stage in textile industry, the assembly stage in mechanical industry, the photoetching stage and the diffusion stage in wafer fabrication industry. Effective scheduling on bottleneck stages can significantly improve the performance of the overall production system, as bottleneck stages are generally most influential to factory-level KPIs according to the principle of wooden barrel. This paper studies

Problem description and formulation

Scheduling of bottleneck stages is often modelled as parallel machine scheduling problem with different constraints and objectives in literature. Here we describe and formulate the studied BSP problem as below.

There are totally n independent jobs $N = {1, 2, \dots, n}$ , m parallel machines $M = {1, 2, \dots, m}$ . Jobs are required to be processed on machines to minimize some performance criterions. Each job $j \in N$ is to be processed by exactly one of the machines, and has a processing time $p_{j}$ , a weight $w_{j}$ , and an

Decomposition scheme for the problem

In our approach, the BSP problem is decomposed into two subproblems: the assignment subproblem (AP) and the sequencing subproblem (SP). The AP is to assign jobs to machines, and the SP is to sequence jobs for each machine. By solving the AP, each job is designated with a machine on which the job needs to be processed. After doing that, the SP can be regarded as multiple independent single machine scheduling problems with different sets of jobs, which are comparatively easy to solve. The

The algorithm

As stated in Section 3, the AP is an expensive-to-evaluate optimization problem, and it is generally very time-consuming or even infeasible for traditional population-based evolutionary algorithms to solve large-scale AP directly. Therefore, we incorporate a surrogate model in the DE algorithm to accelerate the evaluation speed, i.e., to crudely estimate the corresponding total weighted flow time for each solution of the AP without determining the solution of the SP. As the $1 / r_{i} / \sum^{} w_{i} f_{i}$ problem

Experimental studies

In this section, we give results of the numerical experiments to compare the proposed algorithm with the Proximity-based standard DE algorithm and some effective dispatching rules on randomly generated instances and practical production data from a large semiconductor enterprise in China.

Conclusions

This paper is focused on solving bottleneck stage scheduling problems via the surrogate modelling technique. In our approach, we firstly transform the original scheduling problem into an expensive-to-evaluate problem by cutting the original schedule into two partial schedules using decomposition, then a surrogate model is introduced to evaluate a given partial schedule. Based on the surrogate model, we present a differential evolution algorithm where a given partial schedule can be crudely

Acknowledgement

This work is supported by the National Natural Science Foundation of China, China (Nos. 61104172, 61025018, and 60834004), and the National Science and Technology Major Project of China (2011ZX02504-0088). The authors would like to thank the Information Center in Central Semiconductor Manufacturing Corporation for cooperation in experimental studies of this research.

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View full text

A hybrid differential evolution approach based on surrogate modelling for scheduling bottleneck stages

Highlights

Abstract

Section snippets

Background and motivation

Problem description and formulation

Decomposition scheme for the problem

The algorithm

Experimental studies

Conclusions

Acknowledgement

A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times

Eur J Oper Res

Parallel machine scheduling to minimize the makespan with sequence dependent deteriorating effects

Comput Oper Res

A survey of problems, solution techniques, and future challenges in scheduling semiconductor manufacturing operations

J Sched

A novel timetabling algorithm for a furnace process for semiconductor fabrication with constrained waiting and frequency-based setups

OR Spectr

A hybrid dynamic harmony search algorithm for identical parallel machines scheduling

Eng Optim

Scheduling rules to minimize total tardiness in a parallel machine problem with setup and calendar constraints

Comput Oper Res

Two branch-and-bound algorithms for the robust parallel machine scheduling problem

Comput Oper Res

An informational approach to the global optimization of expensive-to-evaluate functions

J Glob Optim

Surrogate modeling for the fast optimization of energy systems

Energy

Engineering design via surrogate modelling: a practical guide

Recent advances in surrogate-based optimization

Prog Aerosp Sci

Optimization and approximation in deterministic sequencing and scheduling: a survey

Ann Discret Math

Scheduling with release dates on a single machine to minimize total weighted completion time

Discret Appl Math

Neural networks: a comprehensive foundation

Support vector networks

Mach Learn

Least squares support vector machine classifiers

Neural Process Lett