A new history-guided multi-objective evolutionary algorithm based on decomposition for batching scheduling
Introduction
Scheduling on batch processing machines (BPMs) (Ahmadi, Ahmadi, Dasu, & Tang, 1992) is an important branch of classical scheduling and exists in manufacturing systems of most industries, such as casting industry, furniture manufacturing, metal manufacturing, aeronautical manufacturing, pharmaceutical industry and logistics freight (Mathirajan & Sivakumar, 2006). In parallel batch scheduling, one typical model of scheduling on BPMs, several jobs are grouped into one batch and processed simultaneously. Once the processing begins, the batch cannot be interrupted. The longest processing time of all jobs in a batch is regarded as the processing time of the batch (Potts & Kovalyov, 2000).
Although makespan is a common objective related to productivity, it cannot represent the needs in just-in-time (JIT) production adequately. With the increasing importance of time-related competition and JIT needs, production performance based on due-dates becomes more significant (Lee, Do Chung, Jeon, & Chang, 2017). Customer satisfaction and work-in-process inventory, besides productivity, have consequently gained much attention from manufacturers. If the orders are completed before their due dates, the delay penalties can be avoided. However, if the completion times of orders are much earlier than their due dates, this will also lead to huge inventory cost. Thus, with the fierce competition and the increasing importance of JIT needs, production performance related to due date becomes more important. JIT needs can be represented by minimizing both earliness and tardiness of jobs (Hamidinia, Khakabimamaghani, Mazdeh, & Jafari, 2012). Since different orders have different degrees of delay penalties and inventory costs in real production, the total weighted earliness/tardiness penalty (TWET) is considered as one optimization objective of the studied problem.
Recently, more and more attention has been paid to environmental pollution and energy consumption in industries, where 54 percent of global delivered energy is consumed. Moreover, its energy consumption has grown by an average of 1.2 percent every year since 2012. At the same time, world energy related to carbon dioxide (CO2) was 32.3 billion metric tons in 2012, and is likely to grow to 43.2 billion metric tons in 2040 (Conti etal., 2016). For sustainable development of modern industries, it is vital to improve utilization efficiency of energy and resources. For most small-scaled and medium-scaled enterprises, reducing processing time of machines through scheduling is a feasible method to reduce energy consumption. Therefore, the total energy consumption (TEC) is optimized as another objective of the studied problem. In addition, with technology update, the advanced machines and the low-performance equipments are run simultaneously in the same factory. Advanced machines generally have faster processing speed and more energy consumption per unit time than those with low performance, which makes production scheduling more difficult (Zhou, Li, Du, Pang, & Chen, 2018).
Although the above three objectives have been widely investigated in the literature, most of these studies only involve one or two objectives (Fang, Lin, 2013, Luo, Du, Huang, Chen, Li, 2013, Naderi, Zandieh, Roshanaei, 2009). Moreover, the real production environment is often more complicated. Decision makers of electronics manufacturing facilities, tire production plants and metal working industries, generally consider not only production efficiency and energy consumption (Zhou etal., 2018), but also whether the products can be delivered on time. Therefore, a parallel batch scheduling problem with different job sizes, processing time and unequal due dates is investigated to minimize makespan, TWET and TEC, simultaneously.
Aiming at the studied problem, there are two issues to be noted. First, the solutions to this problem have specific structural features, which are preferable for addressing the problem. For instance, the jobs grouped into a batch can determine the utilization and processing time of this batch. Moreover, the order of processing batches can influence the earliness/tardiness penalty of jobs in batches. Second, the structural features of the studied problem, a NP-hard constrained combinatorial optimization (CCO) problem, are tough to be formulated and utilized effectively. Therefore, based on the above considerations, a history-guided evolutionary algorithm based on decomposition with local competition (HGEA/D-L) is proposed.
There are two novel strategies in the proposed HGEA/D-L algorithm, that is, local competition and internal replacement. The proposed local competition strategy is based on two presented structural indicators, called wasted ratio of batches (Chen, Du, & Huang, 2011) and weighted earliness/tardiness penalty (WET) of jobs, respectively. The two indicators can be used to direct the adjustment of job positions and find better neighboring individuals that can compete with the existing individuals. In the strategy of internal replacement, an elitist preservation based on decomposition assigns all the individuals into the sub-populations aggregating into the whole objective space. Moreover, one half of the population can be uniformly selected from different sub-populations as elites. The other half of the population is replaced by the new individuals generated under the guidance of historical information updated with the structural features extracted from the elites. As a result, the above two parts of the individuals constitute the population of the next generation.
The rest of this paper is organized as follows: Section 2 introduces the related work of the batch scheduling problems and multi-objective optimization algorithms. Section 3 presents the studied problem. Section 4 describes the proposed HGEA/D-L algorithm in detail. Experimental results and comparison are provided in Section 5. The conclusions of this study and future research directions are presented in Section 6.
Section snippets
Literature review
A review of the literature related to the studied problem and the proposed algorithm is presented in this section. The research on production scheduling problems considering the related optimization objectives is reviewed in Section 2.1. And the literature related to multi-objective optimization evolutionary algorithms (MOEAs) based on decomposition is presented in Section 2.2.
Problem description
According to the standard 3-field notation (Graham, Lawler, Lenstra, & Kan, 1979), the studied problem can be denoted as Qm∣p-batch, pj, sj, dj, αj, βj, vi, ei, C∣(Cmax, TEC, TWET). Suppose there are n jobs to be grouped into b batches which are scheduled on m machines. Each job has five attributes, i.e., processing time pj, job size sj, due date dj, earliness unit cost αj and tardiness unit cost βj. The generated batch set is denoted by B. Each batch contains
Proposed algorithm
In this section, a history-guided evolutionary algorithm based on decomposition with local competition is introduced. After the main framework of the proposed algorithm HGEA/D-L is presented, two main strategies, local competition and internal replacement, are described in detail, respectively. Finally, the computational complexity of the HGEA/D-L is analyzed.
Computational experiments
To evaluate the performance of the proposed algorithm comprehensively, two groups of comparative experiments are designed. Firstly, the HGEA/D-L is compared with two well-known multi-objective optimization algorithms based on decomposition, i.e., the NSGA-III and the RVEA, to verify the overall performance of HGEA/D-L and the effectiveness of strategies in the HGEA/D-L, respectively. In order to apply the NSGA-III and the RVEA to the studied problem, some modifications are required. On the one
Conclusions
In this paper, a history-guided multi-objective evolutionary algorithm based on decomposition with local competition, called HGEA/D-L, is proposed to address the studied just-in-time scheduling problem on parallel BPMs, to minimize the makespan, the total weighted earliness/tardiness penalty and the total energy consumption, simultaneously. In order to solve this problem efficiently, two novel strategies are designed to make full use of valuable structural features of existing individuals. As
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
CRediT authorship contribution statement
Zhao-hong Jia: Conceptualization, Methodology, Writing - review & editing, Resources, Project administration, Funding acquisition. Le-yang Gao: Methodology, Software, Validation, Validation, Investigation, Data curation, Writing - original draft, Writing - original draft. Xing-yi Zhang: Writing - review & editing.
Acknowledgments
This work was supported by the National Natural Science Foundation (71601001); the Humanity and Social Science Youth Foundation of Ministry of Education of China (15YJC630041); the Natural Science Foundation of Anhui Province (1608085MG154); and Natural Science Foundation of Anhui Provincial Department of Education (KJ2015A062).
References (48)
- et al.
A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction
Journal of Manufacturing Systems
(2011) - et al.
Parallel-machine scheduling to minimize tardiness penalty and power cost
Computers and Industrial Engineering
(2013) - et al.
Multi-objective unit commitment with introduction of a methodology for probabilistic assessment of generating capacities availability
Engineering Applications of Artificial Intelligence
(2015) - et al.
Optimization and approximation in deterministic machine scheduling: A survey
Annals of Discrete Mathematics
(1979) - et al.
A genetic algorithm for minimizing total tardiness/earliness of weighted jobs in a batched delivery system
Computers and Industrial Engineering
(2012) - et al.
Bi-criteria ant colony optimization algorithm for minimizing makespan and energy consumption on parallel batch machines
Applied Soft Computing
(2017) - et al.
A dynamic control approach for energy-efficient production scheduling on a single machine under time-varying electricity pricing
Journal of Cleaner Production
(2017) - et al.
Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan
European Journal of Operational Research
(2011) - et al.
Hybrid flow shop scheduling considering machine electricity consumption cost
International Journal of Production Economics
(2013) - et al.
Makespan minimization in flowshop batch processing problem with different batch compositions on machines
International Journal of Production Economics
(2017)