多目标拆卸线平衡问题的Pareto细菌觅食算法*

拆卸线平衡问题的优化涉及多个目标,为克服传统方法在求解多目标拆卸线平衡问题时不能很好处理各子目标间冲突及易于早熟等不足,提出了一种多目标细菌觅食优化算法。算法采用Pareto非劣排序技术对种群进行分级,并结合拥挤距离机制评价同级个体的优劣。为提高算法收敛性能,在趋向性操作结束后引入精英保留策略保留优秀个体,并采用全局信息共享策略引导菌群不断向均匀分布的Pareto最优前沿趋近。通过不同规模算例的对比验证表明了算法的有效性与优越性。     

Multi-objective optimization of a stochastic assembly line balancing: A hybrid simulated annealing algorithm

This paper deals with multi-objective optimization of a single-model stochastic assembly line balancing problem with parallel stations. The objectives are as follows: (1) minimization of the smoothness index and (2) minimization of the design cost. To obtain Pareto-optimal solutions for the problem, we propose a new solution algorithm, based on simulated annealing (SA), called m_SAA. m_SAA implements a multinomial probability mass function approach, tabu list, repair algorithms and a diversification strategy. The effectiveness of m_SAA is investigated comparing its results with those obtained by another SA (using a weight-sum approach) on a suite of 24 test problems. Computational results show that m_SAA with a multinomial probability mass function approach is more effective than SA with weight-sum approach in terms of the quality of Pareto-optimal solutions. Moreover, we investigate the effects of properties (i.e., the tabu list, repair algorithms and diversification strategy) on the performance of m_SAA.     

Evolutionary optimization using epsilon method for resource-constrained multi-robotic disassembly line balancing

This paper concentrates on a resource-constrained multi-robotic disassembly line balancing (RC-MDLB) problem. In this RC-MDLB problem, different types of end-of-life products are disassembled simultaneously on the same line under the following conditions: allocating multiple robots to a workstation to simultaneously process the disassembly tasks that have no precedence relationship with each other, each robot needs a fixed number of limited resources to process tasks, and the total resources for each workstation is fixed. A mathematical model is presented for the RC-MDLB problem to minimize the cycle time and the number of robots being occupied simultaneously. A constrained multi-objective evolutionary algorithm framework and a constrained NSGA-II (E-NSGA-II) algorithm with epsilon method are proposed to handle the constraints of the RC-MDLB problem. The proposed E-NSGA-II is applied to a set of RC-MDLB problem instances introduced in this paper and compared with five representative multi-objective evolutionary algorithms. The experimental results reveal that the proposed E-NSGA-II presents outstanding performance on most of the cases analyzed.     

Model review and algorithm comparison on multi-objective disassembly line balancing

As the disassembly of end-of-life products is affected by several dynamic and uncertain issues, many mathematical models and solution approaches have been established. However, with more extended objectives, constraints and different methods of disassembly, inconsistent models relating to product representations and types of disassembly lines have become the main barriers for the transfer of research to practise. In this paper, a systematic overview of recent models to summarise the input data, parameters, decision variables, constraints and objectives of disassembly line balancing are presented. After discussing the adaptation and extensibility of these models for different environments, a unified encoding scheme is designed to apply typical multi-objective evolutionary algorithms on this problem with extensive decision variables and seven significant objectives. Algorithm comparison on four typical cases is then carried out based on seven commonly used products to verify the optimisation process for the integrated version of existing models and demonstrate the overall performance of the typical multi-objective evolutionary algorithms on this problem. Experimental results can be a baseline for further algorithm design and practical algorithm selection on these disassembly line balancing scenarios.     

Multi-objective partial disassembly optimization based on sequence feasibility

A sustainable manufacturing system integrates production systems, consumer usage behavior, and End-of-Life (EoL) product value recovery activities. Facilitating multi-objective disassembly planning can be a step toward analyzing the tradeoffs between the environmental impact and profitability of value recovery. In this paper, a Genetic Algorithm (GA) heuristic is developed to optimize partial disassembly sequences based on disassembly operation costs, recovery reprocessing costs, revenues, and environmental impacts. EoL products may not warrant disassembly past a unique disassembly level due to limited recovered component market demand, minimal material recovery value, or minimal functional recovery value. The effectiveness of the proposed GA is first verified and tested using a simple disassembly problem and then applied to the traditional coffee maker disassembly case study. Analyses are disaggregated into multiple disassembly network optimization problems, one for each product subassembly, resulting in a bottom-up approach to EoL product partial disassembly sequence optimization.     

拆卸线平衡问题的改进细菌觅食优化算法

拆卸是产品回收过程中最重要的环节,拆卸过程高效与否直接影响产品的回收效率。为克服传统算法求解拆卸线平衡问题时性能不稳定的缺陷,在构建基于工作站利用率、负荷均衡,尽早拆卸有危害、高需求的零件,最小化拆卸成本等方面的拆卸线平衡问题多目标优化模型的基础上,提出一种改进的细菌觅食优化算法对问题求解。通过改进细菌的移动规则扩大搜索空间,引入全局信息共享策略增强算法收敛性能,定义了一种自适应驱散概率防止驱散操作中解的退化。在对不同规模算例的对比分析中,验证了该算法的有效性。     

模糊作业时间的拆卸线平衡Pareto多目标优化

针对实际拆卸作业的复杂性,建立了考虑模糊作业时间的多目标拆卸线平衡问题的数学模型,提出了一种基于Pareto解集的多目标遗传模拟退火算法进行求解。改进了模拟退火操作的Metropolis准则,使其能够求解多目标优化问题。采用拥挤距离评价非劣解的优劣,保留了优秀个体,并通过精英选择策略,将非劣解作为遗传操作的个体,引导算法向最优方向收敛。基于25项拆卸任务算例,通过与现有的单目标人工蜂群算法进行对比,验证了所提算法的有效性和优越性。最后将该算法应用于某打印机拆卸线实例中,求得8种可选平衡方案,实现了求解结果的多样性。     

A solution approach based on beam search algorithm for disassembly line balancing problem

The disassembly line balancing (DLB) problem is the process of allocating a set of disassembly tasks to an ordered sequence of workstations in such a way that optimizes some performance measures (e.g., cycle time, number of stations). Since DLB problems belong to the class of NP hard, many heuristic and meta-heuristic algorithms are applied to cope with the complexity of the DLB problems in order to obtain acceptable solutions in a reasonable amount of time. In this study, a beam search (BS) based approach for the DLB problem is proposed. Minimization of number of workstations is used as the performance measure. The proposed algorithm is compared with the optimal solutions of well-known real cases and generated test problems. The results indicate that the proposed approach based on BS is a very competitive and promising tool for further researches.     

Artificial bee colony algorithm for solving sequence-dependent disassembly line balancing problem

In this paper, we consider a sequence-dependent disassembly line balancing problem (SDDLBP) with multiple objectives that requires the assignment of disassembly tasks to a set of ordered disassembly workstations while satisfying the disassembly precedence constraints and optimizing the effectiveness of several measures. Since the complexity of SDDLBP increases with the number of parts of the product, an efficient methodology based on artificial bee colony (ABC) is proposed to solve the SDDLBP. ABC is an optimization technique which is inspired by the behavior of honey bees. The performance of the proposed algorithm was tested against six other algorithms. The results show that the proposed ABC algorithm performs well and is superior to the other six algorithms in terms of the objective values performance.     

Multi-objective partial parallel disassembly line balancing problem using hybrid group neighbourhood search algorithm

To reduce waste during disassembly production and improve disassembly efficiency, this study investigates a type of partial parallel disassembly line applicable for the simultaneous disassembly of different products. A multi-objective mathematical model for a partial parallel disassembly line balancing problem is built considering four optimisation goals, namely, the minimisation of the cycle time, number of workstations, idle index, and quantity of disassembly resources. In addition, a novel multi-objective hybrid group neighbourhood search algorithm is proposed. First, a certain set of neighbourhood individuals (from the current population of individuals) is generated via neighbourhood search mechanisms based on optimal embedding and exchange operations. Then, a Pareto filtering process is performed on a mixed population composed of the individuals of the current population and all neighbourhoods. Subsequently, the current population individuals are renewed based on the mixed population. To prevent the algorithm from falling into a local optimum and to enhance the algorithm’s global search performance, we conduct a local search strategy based on a simulated annealing operation on the newly generated population individuals. The effectiveness and superiority of the proposed algorithm are proven by solving two complete disassembly line balancing problems at different scales and a partial disassembly line balancing problem, and also by comparison with several algorithms investigated in existing literature. Finally, the proposed model and algorithm are applied to a partial parallel disassembly line designed for the simultaneous disassembly of two types of waste products in a household appliance disassembly enterprise. The results of the partial parallel disassembly line are compared with those of an initial single-product straight disassembly line, and the comparison results show that the solution results of the optimisation goals for the partial parallel disassembly line are more superior than those of the initial single-product straight disassembly line.     

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

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.     

一种保持群体多样性的多目标遗传算法

提出一种保持群体多样性的多目标遗传算法.该算法采用一种基于信息熵的测度,以衡量群体在多日标空间下的多样性,并利用该测度将群体当前的进化状态(多样性)与算法的运行机制相关联,设计了若干种增强算法探索力度的策略,有效地开拓了算法的搜索范围,提高了进化过程中群体的多样性,防止了算法早熟收敛.对所提出算法的计算复杂度进行了理论分析.仿真实验表明,所提出的算法具有较好的收敛性能和分布特性.     

Disassembly line balancing under high variety of end of life states using a joint precedence graph approach

Disassembly is an important aspect of end of life product treatment, as well as having products disassembled in an efficient and responsible manner. Disassembly line balancing is a technique that enables a product to be disassembled as efficiently and economically viable as possible; however, considering all possible end of life (EOL) states of a product makes disassembly line balancing very difficult. The EOL state and the possibility of multiple recovery options of a product can alter both disassembly tasks and task times for the disassembly of the EOL product. This paper shows how generating a joint precedence graph based on the different EOL states of a product is beneficial to achieving an optimal line balance where traditional line balancing approaches are used. We use a simple example of a pen from the literature to show how a joint disassembly precedence graph is created and a laptop example for joint precedence graph generation and balancing. We run multiple scenarios where the EOL conditions have different probabilities and compare results for the case of deterministic task times. We also consider the possibility where some disassembly task times are normally distributed and show how a stochastic joint precedence graph can be created and used in a stochastic line balancing formulation.     

An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem

The consideration of this paper is given to address the straight and U-shaped assembly line balancing problem. Although many attempts in the literature have been made to develop deterministic version of the assembly line model, the attention is not considerably given to those in uncertain environment. In this paper, a novel bi-objective fuzzy mixed-integer linear programming model (BOFMILP) is developed so that triangular fuzzy numbers (TFNs) are employed in order to represent uncertainty and vagueness associated with the task processing times in the real production systems. In this proposed model, two conflicting objectives (minimizing the number of stations as well as cycle time) are considered simultaneously with respect to set of constraints. For this purpose, an appropriate strategy in which new two-phase interactive fuzzy programming approach is proposed as a solution method to find an efficient compromise solution. Finally, validity of the proposed model as well as its solution approach are evaluated though numerical examples. In addition, a comparison study is conducted over some test problems in order to assess the performance of the proposed solution approach. The results demonstrate that our proposed interactive fuzzy approach not only can be applied in ALBPs but also is capable to handle any practical MOLP models. Moreover, in light of these results, the proposed model may constitute a framework aiming to assist the decision maker (DM) to deal with uncertainty in assembly line problem.     

Assembly line balancing under uncertainty: Robust optimization models and exact solution method

This research deals with line balancing under uncertainty and presents two robust optimization models. Interval uncertainty for operation times was assumed. The methods proposed generate line designs that are protected against this type of disruptions. A decomposition based algorithm was developed and combined with enhancement strategies to solve optimally large scale instances. The efficiency of this algorithm was tested and the experimental results were presented. The theoretical contribution of this paper lies in the novel models proposed and the decomposition based exact algorithm developed. Moreover, it is of practical interest since the production rate of the assembly lines designed with our algorithm will be more reliable as uncertainty is incorporated. Furthermore, this is a pioneering work on robust assembly line balancing and should serve as the basis for a decision support system on this subject.     

Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge

Particle swarm optimisation (PSO) is an evolutionary metaheuristic inspired by the swarming behaviour observed in flocks of birds. The applications of PSO to solve multi-objective discrete optimisation problems are not widespread. This paper presents a PSO algorithm with negative knowledge (PSONK) to solve multi-objective two-sided mixed-model assembly line balancing problems. Instead of modelling the positions of particles in an absolute manner as in traditional PSO, PSONK employs the knowledge of the relative positions of different particles in generating new solutions. The knowledge of the poor solutions is also utilised to avoid the pairs of adjacent tasks appearing in the poor solutions from being selected as part of new solution strings in the next generation. Much of the effective concept of Pareto optimality is exercised to allow the conflicting objectives to be optimised simultaneously. Experimental results clearly show that PSONK is a competitive and promising algorithm. In addition, when a local search scheme (2-Opt) is embedded into PSONK (called M-PSONK), improved Pareto frontiers (compared to those of PSONK) are attained, but longer computation times are required.     

A mathematical model and a genetic algorithm for two-sided assembly line balancing

A two-sided assembly line is a type of production line where tasks are performed in parallel at both sides of the line. The line is often found in producing large products such as trucks and buses. This paper presents a mathematical model and a genetic algorithm (GA) for two-sided assembly line balancing (two-ALB). The mathematical model can be used as a foundation for further practical development in the design of two-sided assembly lines. In the GA, we adopt the strategy of localized evolution and steady-state reproduction to promote population diversity and search efficiency. When designing the GA components, including encoding and decoding schemes, procedures of forming the initial population, and genetic operators, we take account of the features specific to two-ALB. Through computational experiments, the performance of the proposed GA is compared with that of a heuristic and an existing GA with various problem instances. The experimental results show that the proposed GA outperforms the heuristic and the compared GA.     

Simultaneously solving the transfer line balancing and buffer allocation problems with a multi-objective approach

Two of the most researched problems on transfer line, transfer line balancing problem (TLBP) and buffer allocation problem (BAP), are usually solved separately, although they are closely interrelated. When machine tools have different reliability, the traditional balancing approaches lead to a deviation of the production rate from the actual throughput, which is used as the objective of the following optimization on BAP. This may not only reduce the solution space of BAP, but also bring about a biased overall result.In this paper, the simultaneous solution of these two problems is presented, which includes transfer line balancing problem, BAP, and selection of line configuration, machine tools and fixtures. Production rate computed through simulation software and total cost considering machine tools and buffer capacities are used as two objective functions. The problem is solved applying a multi-objective optimization approach. Two well-known evolutionary algorithms are considered: Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO). A real case study related to automotive sector is used to demonstrate the validity of the proposed approach.     

Line balancing of PCB assembly line using immune algorithms

Printed Circuit Boards (PCBs) are widely used in most electronic devices. Typically, a PCB design has a set of components that needs to be assembled. In a broad sense, this assembly task involves placing PCB components at designated location on a PCB board; fixing PCB components; and testing the PCB after assembly operation to ensure that it is in proper working order. The stringent requirements of having a higher component density on PCBs, a shorter assembly time, and a more reliable product prompt manufacturers to automate the process of PCB assembly. Frequently, a few placement machines may work together to form an assembly line. Thus, the application of more than one machine for component placement on a PCB presents a line-balancing problem, which is basically concerned with balancing the workload of all the machines in an assembly line. This paper describes the application of a new artificial intelligence technique known as the immune algorithm to PCB component placement as well as the line balancing of PCB assembly line. It also includes an overview of PCB assembly and an outline of the assembly line balancing problem. Two case studies are used to validate the IA engine developed in this work. The details of IA, the IA engine and the case studies are presented.     

Robust assembly line balancing with heterogeneous workers

Assembly lines are manufacturing systems in which a product is assembled progressively in workstations by different workers or machines, each executing a subset of the needed assembly operations (or tasks). We consider the case in which task execution times are worker-dependent and uncertain, being expressed as intervals of possible values. Our goal is to find an assignment of tasks and workers to a minimal number of stations such that the resulting productivity level respects a desired robust measure. We propose two mixed-integer programming formulations for this problem and explain how these formulations can be adapted to handle the special case in which one must integrate a particular set of workers in the assembly line. We also present a fast construction heuristic that yields high quality solutions in just a fraction of the time needed to solve the problem to optimality. Computational results show the benefits of solving the robust optimization problem instead of its deterministic counterpart.