Discrete imperialist competitive algorithm for the resource-constrained hybrid flowshop problem with energy consumption

Xin-Rui Tao,Jun-Qing Li,Peng Duan,Ti-Hao Huang

doi:10.1007/s40747-020-00193-w

Xin-Rui Tao, Jun-Qing Li + Show 2 more

Open Access

https://doi.org/10.1007/s40747-020-00193-w

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Abstract

The resource-constrained hybrid flowshop problem (RCHFS) has been investigated thoroughly in recent years. However, the practical case that considers both resource-constrained and energy consumption still has rare research. To address this issue, a discrete imperialist competitive algorithm (DICA) was proposed to minimize the makespan and energy consumption. In the proposed algorithm, first, each solution was represented by a two-dimensional vector, where one vector represented the scheduling sequence and another one showed the machine assignment. Then, a decoding method considering the resource allocation was designed. Finally, we combined DICA and the simulated annealing algorithm (SA) to improve the performance of the proposed approach. Furthermore, we tested the proposed algorithm based on a randomly generated set of real shop scheduling system instances and compared with the existing heuristic algorithms. The results confirmed that the proposed algorithm can solve the RCHFS with high efficiency.

Highlights

Hybrid flowshop scheduling problem (HFSP) is a generalization of the conventional flowshop scheduling problem
The main contributions of the present paper are as follows: (1) we considered resource-constrained and energy consumption based on HFSP and proposed corresponding models
Machine allocation and operation ordering are considered in the encoding process for the two-vector-based solution representation, as they are commonly used for the standard hybrid flowshop scheduling problems

Summary

Introduction

Hybrid flowshop scheduling problem (HFSP) is a generalization of the conventional flowshop scheduling problem. Compared with other types of scheduling problems, the multi-process and multi-stage characteristics of HFSP are deemed more realistic. The main contributions of the present paper are as follows: (1) we considered resource-constrained and energy consumption based on HFSP and proposed corresponding models. To the best of our knowledge, it is the first work to consider the HFSP with resource constrained and energy consumption objective; (2) a novel DICA method was proposed to solve the RCHFS with energy consumption. Equation (4) means that only one machine can process each job at any stage. Equation (6) means that the same job must complete the current process before proceeding to the stage. Equation (7) indicates that the earlier job in the scheduling arrangement of the same stage, the earlier the processing time begins. It is evident that J2 can enter the second stage immediately after the first one is finished

II III Processing Standby

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Findings

Conclusions