Effective invasive weed optimization algorithms for distributed assembly
permutation fl owshop problem with total flowtime criterion
Hong-Yan Sang
a
,
*
, Quan-Ke Pan
b
,
*
, Jun-Qing Li
d
, Ping Wang
a
, Yu-Yan Han
a
, Kai-Zhou Gao
c
,
Peng Duan
a
a
School of Computer Science, Liaocheng University Liaocheng, 252059, PR China
b
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, PR China
c
Institute of Systems Engineering, Macau University of Science and Technology, Macau 999078, PR China
d
School of Information Science and Engineering, Shandong Normal University, 250014, PR China
ARTICLE INFO
Keywords:
Flowshop
Assembly system
Meta-heuristics
Invasive weed optimization
ABSTRACT
Distributed assembly permutation flowshop scheduling problem (DAPFSP) has important applications in modern
assembly systems. In this paper, we present three variants of the discrete invasive weed optimization (DIWO ) for
the DAPFSP with total flowtime criterion. For solving such a problem, we present a two-level representation that
consists of a product permutation and a number of job sequences. We introduce neighbourhood operators for both
the product permutation and job sequences. We design effective local search procedures respectively for product-
permutation-based neighbourhood and job-sequence-based neighbourhood. By combining the problem-specific
knowledge and the idea of invasive weed optimization, we present three DIWO-based algorithms: a two-level
discrete invasive weed optimization (TDIWO), a discrete invasive weed optimization with hybrid search opera-
tors (HDIWO), and a HDIWO with selection probability. The algorithms explore the two neighbourhoods in quite
a different way. We calibrate the presented DIWO algorithms by means of the design of experimental method, and
carry out a comprehensive computational campaign based on the 810 benchmark instances in the literature. The
numerical experiments show that the presented DIWO algorithms perform significantly better than the other
competing algorithms in the literature. Among the proposed algorithms, HDIWO is the best one.
1. Introduction
In the past decades, assembly systems have been widely used for their
practical interest. Production scheduling, which deals with the allocation
of resources to jobs over time with one or several optimization objectives,
plays a key role in improving the effectiveness and efficiency of the as-
sembly systems [1]. Assembly permutation flowshop scheduling problem
(APFSP) is an important scheduling problem [2–7], which can be
regarded as a combination of the flowshop scheduling problem and as-
sembly scheduling problem. APFSP consists of two stages: production
and assembly. In the production stage, the jobs are processed through a
flowshop formed by a series of machines. In the assembly stage, the jobs
are assembled into products at a single assembly machine. The applica-
tions of APFSP can be found in the fire engine assembly plat [8], the
personal computer production [9], the distributed database system [10],
and many others.
With the intensification of market competition and the general trend
of economic globalization, production systems with more than one pro-
duction center are becoming more and more common. For example,
instead of producing all the components needed for the final product,
more and more enterprises buy them from different types of suppliers and
assemble them. This outsourcing strategy in production is widely used in
automobiles and electronics. Companies such as Dell, Lucent, Cisco and
HP outsource most of their components. The multiple production centers
or distributed manufacturing systems can reduce production costs and
management risks while increasing the product quality [11]. Scheduling
problems in the distributed assembly systems become much more
important and complex [12]. It is of significance to provide effective,
efficient, and advanced algorithms for the scheduling problems in
distributed assembly systems for enterprises to become competitive in
the twenty-first century global markets [13].
This paper considers a distributed assembly permutation flowshop
scheduling problem (DAPSFP) [14], which is a generalization of APSFP
in the distributed production environments. In this problem, a set of n
* Corresponding authors.
E-mail address: sanghongyan@lcu-cs.com (H.-Y. Sang).
Contents lists available at ScienceDirect
Swarm and Evolutionary Computation
journal homepage: www.elsevier.com/locate/swevo
https://doi.org/10.1016/j.swevo.2018.12.001
Received 9 November 2017; Received in revised form 5 November 2018; Accepted 3 December 2018
Available online 4 December 2018
2210-6502/© 2018 Published by Elsevier B.V.
Swarm and Evolutionary Computation 44 (2019) 64–73