Article
Adaptive Population NSGA-III with Dual Control Strategy for
Flexible Job Shop Scheduling Problem with the Consideration
of Energy Consumption and Weight
Mingliang Wu
1,2
, Dongsheng Yang
1,2
, Bowen Zhou
1,2
, Zhile Yang
3,
*, Tianyi Liu
1,2
, Ligang Li
4
,
Zhongfeng Wang
4
and Kunyuan Hu
4
Citation: Wu, M.; Yang, D.; Zhou, B.;
Yang, Z.; Liu, T.; Li, L.; Wang, Z.; Hu,
K. Adaptive Population NSGA-III with
Dual Control Strategy for Flexible Job
Shop Scheduling Problem with the
Consideration of Energy Consumption
and Weight. Machines 2021, 9, 344.
https://doi.org/10.3390/machines
9120344
Academic Editor: Yuansong Qiao and
Seamus Gordon
Received: 11 November 2021
Accepted: 1 December 2021
Published: 9 December 2021
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1
Intelligent Electrical Science and Technology Research Institute, Northeastern University,
Shenyang 110819, China; 1970754@stu.neu.edu.cn (M.W.); yangdongsheng@mail.neu.edu.cn (D.Y.);
zhoubowen@ise.neu.edu.cn (B.Z.); 2070716@stu.neu.edu.cn (T.L.)
2
Key Laboratory of Integrated Energy Optimization and Secure Operation of Liaoning Province,
Northeastern University, Shenyang 110819, China
3
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
4
Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110169, China; lilg@sia.cn (L.L.);
wzf@sia.cn (Z.W.); hukunyuan@sia.cn (K.H.)
* Correspondence: zl.yang@siat.ac.cn
Abstract:
The flexible job shop scheduling problem has always been the focus of research in the
manufacturing field. However, most of the previous studies focused more on efficiency and ignored
energy consumption. Energy, especially non-renewable energy, is an essential factor affecting the
sustainable development of a country. To this end, this paper designs a flexible job shop scheduling
problem model with energy consideration more in line with the production field. Except for the
processing stage, the energy consumption of the transport, set up, unload, and idle stage are also
included in our model. The weight property of jobs is also considered in our model. The heavier the
job, the more energy it consumes during the transport, set up, and unload stage. Meanwhile, this
paper invents an adaptive population non-dominated sorting genetic algorithm III (APNSGA-III) that
combines the dual control strategy with the non-dominated sorting genetic algorithm III (NSGA-III)
to solve our flexible job shop scheduling problem model. Four flexible job shop scheduling problem
instances are formulated to examine the performance of our algorithm. The results achieved by
the APNSGA-III method are compared with five classic multi-objective optimization algorithms.
The results show that our proposed algorithm is efficient and powerful when dealing with the
multi-objective flexible job shop scheduling problem model that includes energy consumption.
Keywords:
flexible job shop scheduling problem; energy consumption; makespan; NSGA-III; dual
control strategy
1. Introduction
Facing the global competition of the integration of the world economy, if the manufac-
turing industry wants to stand out from the cruel survival of the fittest, it must accelerate
its response to external changes, improve product quality and performance, reduce various
costs in the process, and provide customer-based personalized service on-demand [
1
,
2
].
At the same time, affected by the deterioration of the climate and the greenhouse effect,
society and the country have also put forward higher and higher requirements for the
green production of enterprises [
3
,
4
]. The manufacturing industry, which accounts for half
of the total carbon emissions, has also attracted the attention of society and governments at
all levels [
5
,
6
]. Therefore, ensuring a high-efficiency production rhythm in production and
processing while seeking to improve energy efficiency and reduce total carbon emissions
has become the direction of the study efforts of experts and scholars [7,8].
Machines 2021, 9, 344. https://doi.org/10.3390/machines9120344 https://www.mdpi.com/journal/machines
