Decomposition-based bi-objective optimization for sustainable robotic assembly line balancing problems

Highlights

• A novel bi-objective optimization model for a sustainable robotic assembly line balancing problem.

• Comprehensive energy consumption models classified into four categories.

• An adaptive infeasibility-driven MOEA/D is proposed to minimize total energy consumption and workstations simultaneously.

• A problem specific local search is incorporated to improve the algorithm performance.

• Managerial insights to make tradeoffs between productivity and energy consumption.

Abstract

Due to the increasing greenhouse gas emissions and the energy crisis, the manufacturing industry which is one of the most energy intensive sector is paying close attention to the improvement of environmental performance efficiency. Therefore, in this paper the automated assembly line is balanced in a sustainable way which aims to optimize a green manufacturing objective (the total energy consumption) and a productivity-related objective (similar working load) simultaneously. A comprehensive total energy consumption of each processing stage was analyzed and modeled. To make the model more practical, a sequence-based changeover time and robots with different efficiencies and energy consuming rates are considered and optimized. To properly solve the problem, the proposed novel optimal solution takes the well-known MOEA/D as a base and incorporates a well-designed coding scheme and a problem-specific local search mechanism. Computational experiments are conducted to evaluated each improving strategies of the algorithm and its superiority over two other high-performing multi-objective optimization methods. The model allows decision makers to select more sustainable assembly operations based on their decision impacts in both productivity and energy-saving.

Introduction

Owing to the continuous increasing energy consumption, global energy crisis and climate change, the sustainable development of modern society has become one of the most serious challenges facing human race. Economy, society, and environment are considered as the three pillars of sustainability. However, the industries have traditionally focused on the first aspect, i.e., improving the quality and efficiency of production, but the environmental or social aspects were with little regard. Seeing into industrial energy consumption, the production processes and manufacturing activities play the major roles, which are responsible for approximately 90 % of the total [1]. These facts inevitably led the researchers and manufactures to pay serious attention to improve energy efficiency and control greenhouse gas emissions in the industrial production process, instead of giving high priority to production efficiency and cost.

Differ from the traditional manufacturing, the accelerating utilization of industrial robots in automatic production lines brings lots of benefits, but meanwhile consumes a significant amount of electrical energy. It motivates us to pay close attention to the energy efficiency in robotic assembly lines. According to the International Federation of Robotics, by 2018, global sales of industrial robots have accelerated reaching an all-time high of more than 380,000 units, twice as much as in 2013. These industrial robots are used to perform various operations which are physically demanding, highly repetitive or high-risk, such as assembly, stamping, die casting, forging and welding, due to their high precision and capability. As a result, the electrical energy consumed by robots becomes one of the primary forms of energy consumption in the manufacturing. Fysikopoulos et al. indicated that the energy cost during a car manufacturing process contributes about 9–12 % of the total manufacturing cost, and 20 % reduction in energy consumption can result in about 2–2.4 % saving in the final manufacturing cost [2]. Therefore, considering energy efficiency in robotic lines will contribute significantly to both the economy and the environment, also making the enterprises more competitive and sustainable in the market.

Nowadays, it is widely believed that there can be tremendous opportunities in developing novel optimization techniques and strategies for sustainable manufacturing, by simultaneously including both economic criterions and energy efficiency criterions (e.g., controlling GHG emissions, decreasing total costs and greening the industry) [3,4]. These challenges spread among the optimization of manufacturing activities in various levels such as machining processes (e.g. [5]), scheduling (e.g. [6]), production planning (e.g. [1]), line balancing, supply chain (e.g. [7]) and so forth. If the robotic assembly line, as one of the most cost intensive and energy related processes during manufacturing, was balanced in a sustainable way, the benefits could be enormous. In this paper, we proposed an optimization method of a bi-objective Sustainable Robotic Assembly Line Balancing Problem (SRALBP), which put emphasis on the potential benefits for involving the energy efficiency criterion into traditional robotic line balancing problem, and established a more comprehensive model with energy consumption falling into four categories. Specifically, we considered the sequence-based changeover of fixtures and tools, which accounts for a non-ignorable part of both workstation time and energy consumption when a robot performs various tasks within a workstation. Since the traditional ALBP is an assigning problem, which does not regard the sequencing of tasks assigned to the stations, the proposed mathematical model also take the task sequence into consideration.

The assembly line balancing problem (ALBP) is one of the most studied problems in the industrial engineering literature. In ALBP, a set of required tasks are assigned to a serious of workstations in order to produce a product and some objective functions should be optimized subjected to a set of constraints. General Assembly Line Balancing Problems (GALBPs) regard further specification, such as parallel stations (e.g., [8,9]), product diversity (e.g., [10,11]), stationary resources (e.g. [12]), equipment selection (e.g. [13]), or space constraints (e.g., [14]), among others. Extensive reviews on ALBP are done by Becker and Scholl [15], and Battaïa and Dolgui [16].

In manual assembly lines, the actual processing times for activities vary considerably and can hardly obtain the optimal balance; while the performance of robotic assembly lines is rather predictable, which gives rise for improving the system performance through appropriate line balancing and robot assignment [17]. Assembly lines using robots are called robotic assembly lines. Since there are different types of robots available in the market, which can execute the same task with different capabilities and efficiencies, the allocation of robots to workstations has great influence on the performance of assembly lines. First formulated by Rubinovitz and Bukchin based on ALBPs, the Robotic Assembly Line Balancing Problems (RALBPs) concern not only assigning tasks to workstations but also allocating the best fitting robot for each workstation so as to improve the productivity [18]. RALBPs can be classified into two types. In RALBP-I type, it aims at minimizing the number of workstations and the cycle time is fixed, while RALBP-II type deals with minimizing the cycle time with a given number of workstations [19].

A larger number of solution methods have been developed to solve the RALBP, including mathematical programming approaches, heuristic and meta-heuristic algorithms. Since assembly line balancing problem is NP-hard, the computational time of an exact method to find an optimum solution will be much greater than any heuristic method to yield a good near optimum solution [20]. For studies focused on single-objective robotic assembly line balancing problems, both optimum and heuristic algorithms can be found. A branch-and-bound algorithm designed by Rubinovitz et al. [18], an integer programming model with a simulation-based adjustment technique used by Tsai and Yao [21], and a cutting plane algorithm proposed by Kim and Park [22] were used to balance the robotic assembly line. However, the algorithm still requires huge amount of computational resources even heuristic rules are incorporated, which is only suitable for small problems. Gao et al. proposed a genetic algorithm which was hybridized with a local search for type-II RALBP [19]. Zhou et al. proposed a genetic algorithm with the mechanism of simulated annealing for balancing robotic weld assembly lines [23]. Nilakantan and Ponnambalam proposed bio-inspired search algorithms, PSO algorithm and a hybrid cuckoo search-PSO to minimize the cycle time [24].

During the last decades, more complex ALBPs with several conflicting objective functions have aroused extensive academic interests. Pareto Front based approximation methods and aggregative methods, especially meta-heuristic algorithms, have been used to solve the multi-objective problems. Yoosefelahi et al. formulated a multi-objective mixed integer linear programming model to minimize the cycle time, robot setup costs and robot costs [25]. An evolution algorithm was used to solve the problem. Rabbani et al. proposed a model to minimize robot purchasing costs, robot setup costs, sequence dependent setup costs, and cycle time for type II robotic mixed-model assembly line balancing problem [26]. They used NSGA-II and multi-objective particle swarm optimization (MOPSO) to solve the problem. Zhou and Wu used an improved immune clonal selection algorithm to solve the bi-objective RALBP considering time and space constraints [27].

However, the studies on RALBP mentioned above so far has focused on traditional objectives, such as minimizing cycle time, minimizing number of workstations and maximizing assembly line efficiency. To the best of authors’ knowledge, researches which take into consideration the sustainability in the robotic assembly line systems is relatively limited. There exist only a few studies concerning energy consumption or carbon footprint, which will be discussed in this paragraph. Nilakantan et al. investigated the energy consumption in straight robotic assembly lines and developed two models to minimize the cycle time and energy consumption [28]. They utilized particle swarm optimization (PSO) to solve the problem. Nilakantan et al. minimized the energy consumption of a U-shaped robotic assembly line [29]. Li et al. subsequently investigated the reduction of total energy consumption in two-sided robotic assembly lines and developed a multi-objective restarted simulated annealing algorithm to obtain Pareto solutions [30]. Their results indicated that the optimization of line balancing and the minimization of energy consumption in some situations were conflicting. Zhou and Kang presented a mathematical model with three objectives of minimizing the cycle time, the sum of energy consumption, and the total cost of robots of assembly lines [31]. They developed a multi-objective hybrid imperialist competitive algorithm with nondominated sorting strategy to solve the problem.

One of the limitations of the existing researches on RALBP lies in the lack of practical features of real-life manufacturing systems. It can be observed that the existing researches on energy-optimized assembly line problems are highly concentrated on optimizing the energy consumption during operating and standby process. However, the transport of workpieces between workstations and changeover between tasks are also non-negligible processes in the assembly line. On one hand, transportation and changeover also generate considerable energy consumption. On the other hand, the changeover time has significant influence on both workstation time and standby energy consumption. In many assembly lines, such as car body welding lines, the operation time for the tasks is comparatively short. The number of changeovers makes a big difference to the total workstation time. Therefore, a comprehensive energy optimization considering operating, standby, transportation and changeover during the balancing of robotic assembly lines urgently needs to be studied.

Another limitation lies in the requirement of incorporating problem-specific strategies to guarantee satisfactory performance [32]. Notice that our robotic assembly line balancing problem SRALBP is a multi-objective optimization problem bounded by the industrial related constraints. When solving these constrained multi-objective optimization problems (CMOPs), it is important to maintain a balance among convergence, diversity and feasibility of a population. And there are two major aspects to achieve this balance, which are the multi-objective optimization method and the constraint-handling technique [33].

In terms of optimization method, multi-objective evolutionary algorithms (MOEAs) are widely used to solve multi-objective optimization problems in manufacturing systems [[34], [35], [36], [37], among others], since MOEAs can produce a set of well distributed non-dominated solutions in a single run. According to the selection strategy used in the evolutionary process, MOEAs can be classified into different types. Most of existing MOEAs are dominance-based MOEA, which uses a selection strategy based on Pareto domination. For instance, the most popular NSGA-II adopts a non-dominated sorting and elitism-preserving strategy [38]. Another type of MOEAs is the decomposition-based MOEA, which has attracted much attention in recent years. It decomposes a multi-objective optimization problem into a number of single-objective optimization problems, and use different weight vectors and aggregation functions. One of the major advantages of MOEA/D over Pareto dominance based MOEAs is that single objective local search techniques can be readily used in MOEA/D [39]. Therefore, a MOEA/D is adopted in this paper to solve the proposed SRALBP considering energy consumption and changeovers. Meanwhile, a local search mechanism is designed and implemented in the MOEA/D. By exploring the properties of proposed problem, more focuses on the optimization of energy consumption is placed during the design of the search mechanisms to guarantee more satisfactory performance.

As for the constraint-handling technique, the majority of existing methods for ALBPs are feasibility-driven methods, where the feasible solutions are always better than infeasible solutions. However, the method may lead to being trapped in local optima. In this paper, an infeasibility-driven strategy is adopted to trade off the feasibility and convergence. A small proportion of infeasible solutions is maintained in the population to take full advantage of the useful information contained in the infeasible solutions. The improvement in search ability and convergence of the algorithm is verified through experiments.

The aim of this paper is to effectively apply the enhanced MOEA/D and infeasibility-driven strategy to a practical robotic assembly line balancing problem, optimizing the comprehensive energy optimization in a robotic assembly line when balancing the work load and assigning the best fitting robots to workstations, so that the energy efficiency and sustainability of the assembly line can be improved. In comparison with the existing studies, the contributions of this paper are as follows:

• In order to optimize the robotic assembly line toward a sustainable trend, a Type-I SRALBP considering the energy consumption of each process was analyzed and modeled, in which the objective is to minimize the total energy consumption and number of workstations simultaneously.

• In the proposed model, the energy consumption was more comprehensively modeled, divided into the four parts: operating energy, standby energy, transport energy and changeover energy. Sequence-dependent changeover is incorporated to achieve a better modelling of the real robotic assembly lines balancing problem. Number of changeovers is optimized to reduce the unproductive time and reduce the number of workstations.

• In this paper, an enhanced decomposition-based multi-objective algorithm (MOEA/D) has been proposed to address the proposed constrained multi-objective optimization problem. A constraint-handling technique which reserves informative infeasible individuals during the evolution process and an adaptive PBI method with regard to the infeasible individual distribution are integrated to improve its convergence and distribution.

• Taking into account the features of the proposed SRALBP, a problem-specialized local search enhancement is integrated to strengthen the search capability. The dedicated energy-related local search further optimizes the total energy consumption and accelerate the search process.

The rest of this paper is organized as follows. The description of a sustainable robotic assembly line balancing and the model formalization is carried out in Section 2. In Section 3, the detailed mechanism of the proposed enhanced MOEA/D is discussed. Computational experiments are carried out to validate and evaluate the performance of the algorithms in Section 4. Finally, conclusions are drawn and the prospect of future research is provided in Section 5.