求解装配线平衡问题的蚁群算法研究
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摘要
装配线平衡问题是指将操作分配至各个工位,使得某些目标达到最优的一系列优化决策问题。平衡装配线可缩短产品的生产周期,提高产品的生产效率,具有重要的现实意义。另一方面装配线平衡问题是一类典型的NP难问题,研究其有效求解算法具有重要的理论意义。
求解装配线平衡问题的方法主要有三类：启发式算法、精确算法和元启发式算法。第一类方法求解效率很高,但效果难以保证；第二类方法适合求解小规模算例的精确解,但在求解大规模问题时效率低下；元启发式算法则两方面比较均衡,是当前求解装配线平衡问题的主流算法。在众多元启发式算法中,蚁群算法由于遍历求解的过程与装配线的设计过程相似性极高,能充分地利用问题的特性,故利用该算法求解装配线平衡问题的研究是一个重要的发展方向。
论文针对第2类单边装配线平衡问题,提出了一种改进蚁群算法。(1)引入了一种新的启发式因素：可释放后继操作数。如果某项操作一旦被分配,便有较多的操作被释放成为候选操作,显然该项操作应被优先分配以增强蚁群的多样性；(2)给出了合理、有效的操作选择、分配机制以顾全全局搜索和局部寻优之间的平衡。选择机制以有利于后续工位分配的原则确定操作的选择权值,顾全全局优化,而操作分配机制则侧重于当前工位的优化,为局部寻优；(3)综合考虑局部信息和全局信息的贡献定义了两种信息素,分别刻画工位和操作间的优化组合与同一工位中操作间的优化组合,后者可自组织实现操作间的组合。数值实验结果显示该算法对第1类和第2类装配线平衡问题都有较优的求解效果。
分析装配线平衡问题的平衡特性,针对第2类单边装配线平衡问题提出了一种工位蚁群算法。(1)将优化指标分解到每个工位,利用各个工位的局部优化逼近全局优化；(2)提出了一种定界策略,根据当前的最好解,增加(或减小)工位时间的下界(或上界),缩小工位时间的变化范围,提高算法的求解速度；(3)利用精英复制策略在当前的优秀蚂蚁(精英蚂蚁)中随机选择一只,复制其局部解取代不满足定界条件的局部解。实验结果显示,工位蚁群算法能求得大部分算例的最优节拍,求解结果优于其它元启发式算法所得的最好节拍,也优于前面所提的改进蚁群算法。将三种策略应用于第1类装配线平衡问题的求解,提出了第1类问题的工位蚁群算法。实验结果显示,该算法也能有效求解第1类装配线平衡问题。
针对第2类双边装配线平衡问题提出了一种改进蚁群算法。(1)提出了一个启发式权值的计算公式。在公式中引入了两种新的启发式因素：操作所在边的位置和闲置时间,前者使得单边操作以较大概率被优先选择,为后续工位保留了更多的双边操作,后者使得所选择的操作不再仅局限于闲置时间为0或最小的操作,这两个启发式因素的提出增强了蚁群的多样性；(2)给出了一种边工位的确定原则,使得两边工位的工位时间尽可能以相同的速度增加,以保证伴随工位内部的平衡性,同时可减少因两边工位分配的不均衡性造成的闲置时间的增加；(3)给出了一种动态更新步长的定界策略,在操作分配机制中给出了新的工位时间下界的定界规则,定义了三种理想分配操作并设定不同的优先级别,选择合适的理想操作组合分配至工位。数值实验结果验证了该算法的有效性。
The decision problem of optimally partitioning the assembly works among the stations to achieve some objective is known as the assembly line balancing problem (ALBP). Balancing assembly line can shorten the production cycle, and improve production efficiency, which is of important practical significance. On the other hand, it is a typical NP-hard problem, and the research of effective algorithm for it has important theoretical significance.
The methods for solving ALBP are mainly classified into three groups:heuristic approach, exact method and meta-heuristic algorithm. The first method can efficiently solve problem, but its effectiveness is difficult to guarantee; the second one is suitable for solving the exact solution of small-scale examples, but it is inefficient for solving the large-scale problems. Meta-heuristic algorithm is relatively balanced in effectiveness and efficiency. So it becomes the mainstream algorithm for solving ALBP. Among many meta-heuristic algorithms, ant colony optimization algorithm becomes an important development for solving ALBP, because of the high similarity between the traversal solution process and the assembly design process.
An improved ant colony optimization is proposed to address the type2of the simple assembly line balancing problem (SALBP-2).(1) A novel heuristic factor:the number of release tasks, is introduced to select tasks. Among the candidate tasks, if a task is assigned to station, many tasks will be released to be the candidate task, this task should be chosen with priority to increase the diversity of ant colony.(2) A task selection strategy and an assignment mechanism are proposed to assign tasks, which is rational and effective for balancing the global optimization and the local optimization. The selection strategy is applied to calculate the selection weights of candidate tasks, which in view of the global optimization, yet the assignment mechanism is emphasized to optimize the current station, which belongs to the local optimization.(3) Two pheromones are defined to describe the combination relationship between stations and tasks and that among tasks in the same station, considering the contribution of global information and local information, respectively. The latter can adaptively combine tasks. The computational results indicate the better effect of the proposed algorithm for solving SALBP-2and the type1of the simple assembly line balancing problem (SALBP-1).
Analysis the balance characteristic of ALBP, a station ant colony algorithm (SACO) is proposed to address SALBP-2.(1) The objective of SACO is decomposed to each station, and approach the global optimization through each local optimization.(2) A bound strategy is proposed to increase/decrease the lower bound/upper bound of station times according to the current best solution, and narrow the variation range of all station times.(3) An elite copy strategy is applied to randomly select one from the current superior ants (Elite Ants), and copy its partial solution to replace the one, which is not satisfied the constraints of bound strategy. The computational results show that SACO can obtain the optimal of most instances, and all obtained results are better than those of other existing meta-heuristic algorithms, including the proposed ACO. Three strategies are also applied to address SALBP-1. Computational results demonstrate that the algorithm is effective for solving SALBP-1.
An improved ACO is also proposed to address the type2of two-sided assembly line balancing problem (TALBP-2).(1) A novel formulation is introduced to calculate the heuristic weight. In the formulation, two new heuristic factors:the side of candidate tasks and the idle time of them are introduced. The one-sided task can be chosen in greater probability according to the first factor, thus keeping more either-tasks to the following stations. The second one can make the chosen tasks are no longer limited to the tasks, whose idle time is0or the minimum. Two factors can increase the diversity of optional tasks.(2) A determination rule of station direction is proposed to make two-sided station time increase at the same speed as possible, which can improve the balance between the accompany stations and decrease the idle times caused by imbalance of two stations.(3) A bound strategy with variable-step and a new lower bound rule of station times are introduced in the task assignment mechanism. Three ideal tasks with different priority are defined to choose the suitable ideal task combination for the current station. Computational results verify the validity of proposed approaches.
求解装配线平衡问题的方法主要有三类：启发式算法、精确算法和元启发式算法。第一类方法求解效率很高,但效果难以保证；第二类方法适合求解小规模算例的精确解,但在求解大规模问题时效率低下；元启发式算法则两方面比较均衡,是当前求解装配线平衡问题的主流算法。在众多元启发式算法中,蚁群算法由于遍历求解的过程与装配线的设计过程相似性极高,能充分地利用问题的特性,故利用该算法求解装配线平衡问题的研究是一个重要的发展方向。
论文针对第2类单边装配线平衡问题,提出了一种改进蚁群算法。(1)引入了一种新的启发式因素：可释放后继操作数。如果某项操作一旦被分配,便有较多的操作被释放成为候选操作,显然该项操作应被优先分配以增强蚁群的多样性；(2)给出了合理、有效的操作选择、分配机制以顾全全局搜索和局部寻优之间的平衡。选择机制以有利于后续工位分配的原则确定操作的选择权值,顾全全局优化,而操作分配机制则侧重于当前工位的优化,为局部寻优；(3)综合考虑局部信息和全局信息的贡献定义了两种信息素,分别刻画工位和操作间的优化组合与同一工位中操作间的优化组合,后者可自组织实现操作间的组合。数值实验结果显示该算法对第1类和第2类装配线平衡问题都有较优的求解效果。
分析装配线平衡问题的平衡特性,针对第2类单边装配线平衡问题提出了一种工位蚁群算法。(1)将优化指标分解到每个工位,利用各个工位的局部优化逼近全局优化；(2)提出了一种定界策略,根据当前的最好解,增加(或减小)工位时间的下界(或上界),缩小工位时间的变化范围,提高算法的求解速度；(3)利用精英复制策略在当前的优秀蚂蚁(精英蚂蚁)中随机选择一只,复制其局部解取代不满足定界条件的局部解。实验结果显示,工位蚁群算法能求得大部分算例的最优节拍,求解结果优于其它元启发式算法所得的最好节拍,也优于前面所提的改进蚁群算法。将三种策略应用于第1类装配线平衡问题的求解,提出了第1类问题的工位蚁群算法。实验结果显示,该算法也能有效求解第1类装配线平衡问题。
针对第2类双边装配线平衡问题提出了一种改进蚁群算法。(1)提出了一个启发式权值的计算公式。在公式中引入了两种新的启发式因素：操作所在边的位置和闲置时间,前者使得单边操作以较大概率被优先选择,为后续工位保留了更多的双边操作,后者使得所选择的操作不再仅局限于闲置时间为0或最小的操作,这两个启发式因素的提出增强了蚁群的多样性；(2)给出了一种边工位的确定原则,使得两边工位的工位时间尽可能以相同的速度增加,以保证伴随工位内部的平衡性,同时可减少因两边工位分配的不均衡性造成的闲置时间的增加；(3)给出了一种动态更新步长的定界策略,在操作分配机制中给出了新的工位时间下界的定界规则,定义了三种理想分配操作并设定不同的优先级别,选择合适的理想操作组合分配至工位。数值实验结果验证了该算法的有效性。
The decision problem of optimally partitioning the assembly works among the stations to achieve some objective is known as the assembly line balancing problem (ALBP). Balancing assembly line can shorten the production cycle, and improve production efficiency, which is of important practical significance. On the other hand, it is a typical NP-hard problem, and the research of effective algorithm for it has important theoretical significance.
The methods for solving ALBP are mainly classified into three groups:heuristic approach, exact method and meta-heuristic algorithm. The first method can efficiently solve problem, but its effectiveness is difficult to guarantee; the second one is suitable for solving the exact solution of small-scale examples, but it is inefficient for solving the large-scale problems. Meta-heuristic algorithm is relatively balanced in effectiveness and efficiency. So it becomes the mainstream algorithm for solving ALBP. Among many meta-heuristic algorithms, ant colony optimization algorithm becomes an important development for solving ALBP, because of the high similarity between the traversal solution process and the assembly design process.
An improved ant colony optimization is proposed to address the type2of the simple assembly line balancing problem (SALBP-2).(1) A novel heuristic factor:the number of release tasks, is introduced to select tasks. Among the candidate tasks, if a task is assigned to station, many tasks will be released to be the candidate task, this task should be chosen with priority to increase the diversity of ant colony.(2) A task selection strategy and an assignment mechanism are proposed to assign tasks, which is rational and effective for balancing the global optimization and the local optimization. The selection strategy is applied to calculate the selection weights of candidate tasks, which in view of the global optimization, yet the assignment mechanism is emphasized to optimize the current station, which belongs to the local optimization.(3) Two pheromones are defined to describe the combination relationship between stations and tasks and that among tasks in the same station, considering the contribution of global information and local information, respectively. The latter can adaptively combine tasks. The computational results indicate the better effect of the proposed algorithm for solving SALBP-2and the type1of the simple assembly line balancing problem (SALBP-1).
Analysis the balance characteristic of ALBP, a station ant colony algorithm (SACO) is proposed to address SALBP-2.(1) The objective of SACO is decomposed to each station, and approach the global optimization through each local optimization.(2) A bound strategy is proposed to increase/decrease the lower bound/upper bound of station times according to the current best solution, and narrow the variation range of all station times.(3) An elite copy strategy is applied to randomly select one from the current superior ants (Elite Ants), and copy its partial solution to replace the one, which is not satisfied the constraints of bound strategy. The computational results show that SACO can obtain the optimal of most instances, and all obtained results are better than those of other existing meta-heuristic algorithms, including the proposed ACO. Three strategies are also applied to address SALBP-1. Computational results demonstrate that the algorithm is effective for solving SALBP-1.
An improved ACO is also proposed to address the type2of two-sided assembly line balancing problem (TALBP-2).(1) A novel formulation is introduced to calculate the heuristic weight. In the formulation, two new heuristic factors:the side of candidate tasks and the idle time of them are introduced. The one-sided task can be chosen in greater probability according to the first factor, thus keeping more either-tasks to the following stations. The second one can make the chosen tasks are no longer limited to the tasks, whose idle time is0or the minimum. Two factors can increase the diversity of optional tasks.(2) A determination rule of station direction is proposed to make two-sided station time increase at the same speed as possible, which can improve the balance between the accompany stations and decrease the idle times caused by imbalance of two stations.(3) A bound strategy with variable-step and a new lower bound rule of station times are introduced in the task assignment mechanism. Three ideal tasks with different priority are defined to choose the suitable ideal task combination for the current station. Computational results verify the validity of proposed approaches.
引文
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