An improved multi-objective whale optimization algorithm for the hybrid flow shop scheduling problem considering device dynamic reconfiguration processes

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Abstract

Manufacturing industries frequently encounter production scheduling problems containing device dynamic reconfiguration processes (DRP). DRP refers to dynamic device adjustments (such as replacement of tools), leading to changes in the devices’ actual processing time. It has a severe impact on the production schedule. Nevertheless, there is scarcely research upon hybrid flow shop scheduling problem (HFSP) with DRP. Besides, it is necessary to consider multiple conflict objectives in the HFSP. Thus, the multi-objective HFSP with DRP (MOHFSP-DRP) is significant in both theoretical research and application. This paper first proposes a multi-objective mathematical model (MOHFSP-DRP) that simultaneously considers the DRP and devices’ adjustable processing modes. The bi-objective of this model is to minimize both the makespan and the whole device’s energy consumption. This study then proposes an improved multi-objective whale optimization algorithm (IMOWOA) to solve the MOHFSP-DRP and obtain the Pareto-based optimal solution set. After that, to verify the proposed method’s effectiveness, numerical experiments are implemented based on the real-world cases in a Chinese company’s digital hot-rolling workshop. Results denote that the presented IMOWOA is superior to SPEA2 and NSGA-II. Finally, the MOHFSP-DRP model and IMOWOA are applied to a real-world hot-rolling shop successfully. The real-world cases verify the proposed IMOWOA can tackle the presented MOHFSP-DRP very well.

Introduction

Hybrid Flow Shop Scheduling Problem (HFSP) (Garey et al., 1976, Campos et al., 2014, Tang et al., 2016, Zhaoet al., 2019, Gonget al., 2020) has drawn extensive attention due to widespread applications in industrial production. Usually, the traditional HFSP (Dugardin et al., 2010, Lei and Guo, 2015, Zhang et al., 2017, Lv and Lei, 2018) considers the machining order of the workpiece and the selection of machining equipment at each stage. Nevertheless, the processing time for every operation in traditional models is usually predetermined and immutable. However, many factors or destabilizations in practical production processes affect devices’ actual processing time. For example, devices need to reconfigure their tools when tools’ life use up, making the processing time dynamically changing. Besides, a flexible device can adjust its actual processing time by adjusting its processing mode. Such above factors lead to severe deviations between the scheduling scheme and the practical production. Thus, the main problem confronting us is considering such dynamic characteristics to construct dynamic scheduling models in a realistic production environment (Jolai, Rabiee, & Asefi, 2012). It is a new scheduling issue since it considers workpiece order and machine allocation and the processing mode allocation of devices with DRP. These features make it unique and complex, compared with traditional HFSP (Alidaee & Ahmadian, 1993).

HFSP in the practical production environment is a multi-objective problem with extensive research (Behnamianet al., 2009, Pargar et al., 2018, Burdett et al., 2020). For example, Behnamian et al. put forward a three-phase method for solving the MOHFSP with the same equipment and setup time at each stage. Moreover, Wang proposes a multi-objective memory algorithm (X. Wang & Tang, 2017). Nevertheless, the above literature does not consider such dynamic factors, including DRP. To the best of the authors' knowledge, few studies focus on MOHFSP-DRP. Most research upon MOHFSP mainly focuses on improving the optimization efficiency in a static production environment rather than constructing a dynamic MOHFSP model with such above factors much closer to real-life production conditions. Therefore, to fill the research gaps, it is imperative to study MOHFSP-DRP concerning modeling theory and practical application.

This paper regards the minimum of makespan and the workshop’s total energy consumption as conflicting optimization objectives. And this paper adopts a Pareto-based (Bader & Zitzler, 2011) strategy to solve the presented MOHFSP-DRP. As stated earlier, dynamic factors in MOHFSP-DRP make conflict objectives have two unique relationships: (1) Makespan (Lu, Li, Gao, Liao, & Yi, 2017) can be decreased by choosing a higher processing mode of devices, but that increases extra device energy consumption (Tseng, Liao, & Huang, 2009). (2) Makespan and the total energy consumption rises respectively when the dynamic reconfiguration processes take place in a particular device. To the author’s knowledge, the current research on these relationships is relatively rare.

As stated earlier, meta-heuristic algorithms (Nagano et al., 2014, Bu et al., 2018, Burdettet al., 2019, Burdett and Kozan, 2018) are efficient methods to solve optimization problems, including ABC (Zhang, Cheng, Shi, Gong, & Zhao, 2019), GWO, and Whale Optimization Algorithm (WOA) (Mirjalili & Lewis, 2016). WOA is a new metaheuristic algorithm to solve continuity problems inspired by the humpback whales hunting behavior. Besides, results prove that WOA is predominant in traditional algorithms, such as PSO and GA. WOA is a high-efficiency algorithm with a few parameters, a simple search mechanism, which has the advantage of good convergence. Good convergence owes to WOA’s hypercube mechanism and internal adaptive strategy. WOA’s unique hyper-cube mode rapidly re-positions the whale population around. It defines a search space in the neighborhood of the best solution to make search agents quickly exploit potential optimal value via using the current best record inside that domain. The adaptive strategy, which smoothly transits between exploration and exploitation, contributes to obtain the optimal global solution rapidly. These reasons make WOA advantageous and competitive for solving optimization problems concerning global search capability and convergence performance. Many engineering fields, such as optimal single mobile robot scheduling (Petrović, Miljković, & Jokić, 2019), have successfully applied WOA to solve optimization issues.

Nevertheless, there is no WOA-based method or research to solve HFSP considering dynamic reconfiguration processes. No free lunch theorem denotes any two optimization algorithms are equivalent when their mean performance across all possible problems. That implies the importance of using the specific issue’s nature to guide the algorithm’s search process (Lu et al., 2017). But current relevant researches on using problem nature to improve algorithms’ performances are relatively limited. The above reasons prompt us to exploit an excellent multi-objective WOA-based approach according to the problematic nature of MOHFSP-DRP.

The paper organizes the rest of the context as follows. Section II formulates a mathematical model of MOHFSP-DRP. Then Section III proposes an improved multi-objective optimization WOA-based algorithm (IMOWOA). Section IV performs numerical experiments from a real-life digital hot-rolling workshop. A real-world case is then described in Section V. Finally, Section VI gives some discussions on the conclusions and discusses future research work.

Section snippets

MOHFSP-DRP statements

Fig. 1 depicts the production processes of MOHFSP-DRP. Jobs enter the first processing stage in a specific order (X1). There are multiple devices (hypothesis 3) in each processing stage. Allocate Jobs sequentially to each device. The number (hypothesis 4) of jobs is commonly more enormous than the number of devices. Thus, the idle equipment that completed the preceding prior processing tasks will process the remaining jobs successively. Each job immediately moves to the next stage after being

Original whale optimization algorithm

Inspired by the humpback whales hunting behavior, Mirjalili & Lewis develop WOA to solve optimization issues. Like other swarm algorithms, it is with an exploration/exploitation ability (Mirjalili & Lewis, 2016).

(1) The exploitation phase of WOA (A1)

When hunting, humpback whales swim spirally beneath the water's surface to generate plenty of circle bubbles to encircle and attack prey. To mimic that whales' unique predatory behavior, there are the mathematical models of shrinking encircling

Numerical experiments design based on real-world cases

The section evaluates performances of IMOWOA concerning solving MOHFSP-DRP, which consists of five parts: (1) Experiment design (2)Performance indexes (3) Parameter setting (4)The validity evaluation of optimization strategies (5)The comparisons between IMOWOA with other states of the art algorithms.

The following algorithms are all programmed by Matlab. The test environment is a computer with Intel Core i7, clocked at 1.99ghz, 8 GB RAM, and Windows 10 operating system.

The application of IMOWOA in a real-world case

This study applies the presented models to solve real-world cases from a digital-twin-based hot rolling workshop from a factory.

Conclusions and research in the future

This study formulates a real-life MOHFSP-DRP considering the device reconfiguration process and devices' multiple processing mode constraints. This model can dynamically schedule production tasks by perceiving and predicting DRP, narrowing the gaps between the theoretical model and the practical production. This paper then put forward an energy consumption evaluation approach under DRP and devices' multiple processing mode constraints to calculate a digital production line's energy consumption.

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.

Acknowledgments

The presented work was supported by the National Science and Technology Innovation 2030 of China Next-Generation Artificial Intelligence Major Project (no. 2018AAA0101800).

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