A hybrid differential evolution approach based on surrogate modelling for scheduling bottleneck stages
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 , m parallel machines . Jobs are required to be processed on machines to minimize some performance criterions. Each job is to be processed by exactly one of the machines, and has a processing time , a weight , 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 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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