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资料来源：文章名：一种基于分枝定界算法的注塑模架基工艺规划系统书刊名：Advanced Manufacturing Technology作 者： P. Y. Gan, K. S. Lee and Y. F. Zhang出版社：Department of Mechanical Engineering, National University of Singapore, Singapore章 节：A Branch and Bound Algorithm Based Process-Planning System for Plastic Injection Mould Bases页 码：10.1007/s0017001一种基于分枝定界算法的注塑模架基工艺规划系统 70022 文 章 译 名： A Branch and Bound Algorithm Based Process-Planning System for Plastic Injection Mould BasesP. Y. Gan, K. S. Lee and Y. F. ZhangDepartment of Mechanical Engineering, National University of Singapore, SingaporeThis paper describes the use of artificial intelligence in the process planning of plastic injection mould bases. The com- puter-aided process-planning system, developed for IMOLD will extract and identify the operations required for machining. These operations are considered together with their precedence constraints and the available machines before the process plan for the mould base plate is generated. The process plan is optimised by a branch and bound based algorithm. Overall machining time has been proposed as the objective function for optimisation. The ability of this algorithm to search intelli- gently for a feasible optimised solution is illustrated by an industrial case study. A brief comparison with a genetic algor- ithm based process planning system is also made. The result of this development will allow users to optimise process plans easily for any given mould base, with options to suit dynamic changes on the manufacturing shop floor.Keywords: Branch and bound algorithm; Computer-aided process-planning (CAPP); Optimisation; Plastic injection mould base1. IntroductionComputer-aided process planning (CAPP) has received much attention in recent years. It has long been identified as the bridge between computer-aided design (CAD) and computer- aided manufacturing (CAM) systems to achieve a fully auto- mated factory. Despite the need, insufficient CAPP systems have been developed for the different industries requiring them. This work focuses on developing a CAPP system for mould base makers. At present, most process planning for the pro- duction of mould bases is done manually. The process plans depend very much on the decisions of the process planner. The introduction of CAPP systems should ensure consistently good process plans with more comprehensive consideration ofCorrespondence and offprint requests to: K.-S. Lee, Department of Mechanical and Production Engineering, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. E-mail: .sgthe manufacturing parameters. CAPP systems are required in industry for the following reasons:1. Mould base companies are receiving an increasing number of requests to manufacture customised mould bases, in which additional features are added to a standard mould base. Therefore, extra operations are required to create these new features. Usually, standard mould bases have a predetermined process plan, which is optimised for the amount of machining required. As new operations are added, this optimised process plan is disrupted and manual process planning is unable to keep up with the changes. CAPP systems are able to re-optimise the process plan constantly to ensure optimality of the process plans used.2. Overall shop floor conditions should be taken into account during process planning. Manual process planning is unable to consider all shop floor changes and apply them efficiently. Only CAPP systems allow rigorous consideration of optimis- ation.The goal of this work is to develop a CAPP system for process planning mould bases. IMOLD (Intelligent Mold Design) is a knowledge-based application software developed at the Department of Mechanical Engineering, NUS to facilitate plastic injection mould design. The system is an addition to IMOLD, and it process plans the mould bases created using IMOLD. Databases of machines, tools, precedence constraints, and the model part file are read together with real-time inputs of machine availability during process planning. An operator is required to enter the customised features and a process plan is then generated using some form of artificial intelligence. The branch and bound technique is the chosen search algor- ithm here.This paper presents the operation of a flexible CAPP system aimed at assisting process planners in more comprehensive considerations during operations planning. A brief literature survey is provided of some forms of artificial intelligence used in process planning and related work in this field. Problem formulation and the branch and bound algorithm implemented are included in the following sections. Lastly, a case study demonstrates the usability and potential of this system. A comparison between branch and bound based CAPP and genetic algorithm based CAPP is shown in a second case study. 2. BackgroundProcess planning is the preparation of a set of detailed instruc- tions for all the steps required to create the final product from a piece of raw material 1. The quality of a process plan depends very much on the skills of the process planner, as extensive knowledge of the available tools, the machines and the operations needed to create a part is required 2. A CAPP system is therefore seen as an important tool for assisting in process planning.A CAPP system should optimise a part for all possible methods of manufacturing. However, many reported CAPP systems are not able to generate globally optimised process plans 3. As a result, there has been an increasing use of artificial intelligence to search for global solutions 4,5. Many of the reported methods involve only feature sequencing with- out including details of the operations required 6,7. Details of the operations are necessary for allocating shop floor resources for performing the operations.The performance measure is the objective function to be maximised or minimised in all optimisation problems. For process planning, the objective is either to minimise time, cost, or sometimes both. There is a variety of work done using cost as the performance measure 8. However, there is also a range of cost models that can be used to consider and calculate cost 9,10, but there is no universal method to account for costs. It is known that to minimise work-in-progress and the flow- time of jobs in a job shop, process plans with the least overall machining time should be used 11. We therefore use time, as it is a more definite basis on which to quantify the quality of generated process plans. This choice is further justified, as the delivery time of mould bases is very important in mould- making industries.An exhaustive sequential search for a process plan solution leads to unacceptable computation times when a large number of operations are required. This work uses a branch and bound algorithm to search intelligently for the optimal or near optimal process plan. The branch and bound algorithm is a well-known search algorithm for implicit enumeration of the search space 12. Its use as an artificial intelligence method has been reported widely in the areas of scheduling, process planning, and problem solving 13.Some work has been reported using the branch and bound technique for process planning 1416. However, the nature of process plans in those works is different from the process planning required for the mould making industry. This work uses the branch and bound technique to process plan all the operations considering all tool access directions on all the available machines and tools for each mould base plate. To the best of our knowledge, such a level of consideration has not been dealt with in other related studies.3. Problem FormulationA process-planning problem is constrained to the number of operations, precedence relations, machines, machining direction, and tools. The optimised solution is a way to sequence theoperations with their associated machines to produce a process plan, which takes the least possible production time.3.1 Process Planning ModelThe information required for optimisation is extracted from mould bases modelled using IMOLD. This database of oper- ations, machines, machining direction, tools, and precedence constraints is used for process planning together with machine availability. A schematic representation of this model is shown in Fig. 1 and the following assumptions are made:1. Only one operation can be processed by one machine at a time.2. All the machines can access the part at only one particular face. If machining is to be done on another face, the part has to be taken down and set-up time has to be incurred to replace the part facing a different direction.3. Cranes or robots are available at all times. No waiting time is allowed for time wasted while waiting for machinery or labour to move the parts.Customised features require the process planner to input the necessary data manually. This is because a single feature can be created by many possible methods and this allows the process planner more control over the system. The assigned operations and the final generated process plan should satisfy the following conditions:1. The features of the mould base plate are recognised with the operations assigned to them. The operations assigned should produce the desired shape, dimension, tolerance, and finish to the feature.Fig. 1. The process planning model.2. The sequence of operations obtained from the process plan should not violate any precedence relations governing the operations.machining direction, but no change of machine between the two operations. It is defined as,3n13. Operations can only be carried out on available machines with the available tools, which are capable of machiningMDST =i=1(K(MDi+1,MDi)that particular feature.The process plan obtained should include the number of operations to be carried out, the sequence of these operations, the machines, machining direction, and corresponding tools used. Such details are necessary so that time can be saved for operations to be carried out on a particular machine using the same set-up. For example, a blind hole must be drilled in the+x direction whereas a through hole can be drilled from the+x or x directions. It can be seen by considering just these two operations, that the process plan should try to perform these two operations on the same machine from the +x direc- tion so that extra set-up time is not incurred.3.2 The Objective FunctionTo quantify the objective function, which is the overall machin- ing time (OMT), we use a calculation framework similar to that used by Zhang et al. 17. The objective function is calculated for each successive sequence of the process plans, and the sequence that yields the minimum OMT will be taken as the final process plan. There are 3 areas which contribute to the calculation of OMT, and they are machine set-up times, machining direction set-up times, and machining times.3.2.1 Machine Set-up Time3Machine set-up time (MST) is considered whenever there is a change of machines between two operations. It is defined as the time required to move between machines and the set-up time of the mould baseplate onto the machine in a particular direction. It is defined for a total of all n operations as,n11 K(Mi+1,Mi) MDSTIi+1)(3)MDi is the machining direction selected to process operation i and MDSTIi is the machining direction set-up time index for the machine used in operation i. MDSTIi and MSTIi are related by the difference in time to move the part between the old and new machine.MSTIi = MDSTIi(4)+ (Time to move part between machines)As no waiting time for the cranes or robots is assumed, we take MDSTIi and MSTIi to be the same.3.2.3 Machining Time3Machining time MT is the actual time to perform all machining operations such as drilling, milling, or grinding on the assigned machines with the respective tools.ni iMT =(MTM ,T )i(5)i=1The machining time for a single operation can vary according to the assigned machine and tool selected. From this, there exists one or more possible MTi for a single operation.3.2.4 Overall Machining TimeOverall machining time is the total of all machine change set- up times, machining direction change set-up times and all machining times.OMTmin = (MST + MDST + MT)optimised sequence(6) The objective is to produce a sequence of operations that willMST =where,i=1(K(Mi+1,Mi) MSTIi+1)(1)K(Mi+1,Mi) =1 if i = 11 if Mi+1 G Mi (i 1)(2)0 if Mi+1= Mi(i 1)require the least OMT.Table 1. Types of machines, MSTI, MDSTI and types of suitable tool.Machines (M)MSTI, MDSTI(min)Tool types Suitable (T)1. FARTWARTH VBM-5VL5, 51vertical surface miller2. HAMAI-4DS horizontal gang6, 61surface miller3. Manual chamfering machine2, 254. OKAMATO grinding machine4, 425. HUACHONG grinding3, 32machine6. Radial drilling machine2, 24, 67. MORI SEIKI MV65-503, 31,3,4,6,7,8,9vertical CNC milling8. MAKINO MC98 vertical4, 41,3,4,6,7,8,9Mi refers to the machine selected to process operation i,MSTIi refers to the machine set-up time index for the machineused in operation i, and n is the number of operations selected for the whole series of operations identified from the mould fea- tures.3.2.2 Machining Direction Set-up TimeCNC millingMachining direction set-up time (MDST) is the time required to change the orientation of the mould baseplate on the same machine. MDST is calculated only when there is a change in1. Face mill cutter; 2. Grinding wheel; 3. End mill; 4. NC spot drill;5. Edge-grinding wheel; 6. Drill; 7. Reamer; 8. Boring tool; 9. Tap drillFig. 2. Customised core plate part with 11 additional operations.4. Branch and Bound AlgorithmA branch and bound algorithm was chosen as the search algorithm to be used as it has a proven track record in this area. Its robust and enumerative nature should yield an optimal or near optimal solution. The search space of most branch and bound algorithms is inherently large and computationally complex. This means that effective heuristic and efficient lower bound calculations are important for decreasing search space to help arrive at a good solution earlier.4.1 Implemented AlgorithmThe algorithm starts by sequencing one of the available oper- ations and this is called branching the node. By branching a node, a new node is formed and the node is kept in the search space if its lower bound value is better than the upper bound value or vice versa. A heuristic is used to schedule the remaining operations for every node and the best solution found so far will be recorded as the upper bound value. The next node to be branched is the one with the best lower bound value, as it is deemed to have the best potential. As more nodes are branched, more and more operations will be sequenced, and the upper bound value will become smaller and smaller. Thealgorithm stops when the upper bound value is smaller than all lower bound values and the process plan is the sequence that yields the upper bound solution.To balance the quality of the solution and the computation time, a termination condition is set such that the program will exit when there is no more improvement to the upper bound value after a certain number of cycles (Xc). For most problems, it was found that a value of about 10 000 for Xc will yield near optimal solutions while giving a computation time of less than 10 min.To explain the branch and bound algorithm better, we use the conventions of the A* algorithm. The mathematical rep- resentation of the lower bound function f(Sa) for sequence Sa is defined asf(Sa) = g(Sa) + h(Sa)(7)where g(Sa) is the cost incurred to reach Sa and h(Sa) is a function that calculates the estimated cost of reaching the final schedule. When all the operations are sequenced, h(Sk(final) = 0, the objective function can then be calculated as f(Sk(final) = g(Sk(final). The implemented branch and bound algorithm can be briefly summarised as follows:beginStep 1. S0 Initial situation (no operation sequenced) Open S0doStep 2. Choose in Open, a node with sequence Sa, which has the best lower boundOpen Open SaStep 3. Sequence all the possibilities starting from Safor each possibility SkStep 4. Use a heuristic to schedule the remaining operationsSk(final)objective function = g(Sk(final)Step 5. Update the upper bound valueif g(Sk(final) is betterthen upper bound = f(Sk(final)Step 6. Calculated the lower boundfor each possibility k, f(Sk) = g(Sk) + h(Sk)Step 7. Include branched node into search spaceif f(Sk) better than upper boundthen Open Open + SkendStep 8. Discard all nodes in Open with f(S) worse than, or equal to, upper boundwhile Termination condition G OR Open G end4.2 Constant Machine / Machining Direction HeuristicA good heuristic will help to generate good solutions as early as possible. When good solutions are generated early, the upper bound value will become lower and has a higher chance of rejecting unpromising nodes with higher lower bound values. This will reduce the search space so that time can be spent more efficiently on nodes, which might give a better solution than the current best. However, when a heuristic becomes too complex and computationally intensive, it causes each branch to take a much longer time and can significantly increase the overall running time. There is thus a need to use a simple and effective heuristic.When a process planner plans for a particular job, operations that require both the same machine and machining direction will usually be grouped and carried out together. To build on that behaviour, the heuristic will keep looking for the sub- sequent operation that has the same machine and machining direction as the previous one. The heuristic can be briefly summarised as:doStep 1. To determine operation i+1,for all other operations, which can be processed using, machine Michoose the operation with a corresponding machine and machining direction which will yield the lowest added time (AT = MDSTi+1 + MSTi+1 + MTi+1)Step 2. if no operation is chosen, i.e. none of the remaining available operations can be processed by machine Mi, choose the operation with the lowest ATwhile there are still unassigned operations, i = i + 1endThe heuristic will choose an available operation that has the same machine and machining direction as the previous oper- ation if the time is shorter. In cases where time is saved by carrying out that operation on a faster machine, the faster machine is chosen. By having a heuristic like this, the process plan will not always force operations to be carried out on the same machine and in the same machining direction but rather allow different machines to be used if time can be saved.4.3 Lower Bound CalculationThe lower bound value is an estimate of the best possible solution that can arise from the current sequence of a node. A simple way of calculating the lower bound would be to add up the minimum process times for all remaining operations. However, that will underestimate the lower bound value of that node as no set-up time is included in the estimate. Underestimating lower bound values causes many unpromising nodes to be branched and hence wastes time. To obtain best possible solution, we included the set-up when necessary into the lower bound calculations. It is found that by including set- up times, the search space is reduced significantly especially for large problems.5. Results and DiscussionThe algorithm is programmed in the C language and was run on a workstation. For the case study, we used the available machines from a local mould base maker as the pool of machines. Details of the machine database are shown in Table 1.5.1 Standard and Customised Mould Base PlatesFigure 2 shows a Hoppt 3 plate-D type customised mould baseplate created using IMOLD. The operations required to produce the mould baseplate are recorded in a database, as shown in Table 2. The CAPP system is used to process plan the mould baseplate for a few scenarios to show the versatility of the system. Xc was set to 10 000 and the scenarios are as follows:1. Standard mould baseplate (up to operation 29).2. Standard mould baseplate when machine 7 is unavailable.3. Customised mould baseplate (all operations).Tables 3, 4, and 5 show the process plans for the three scenarios. From the solutions, it can be seen that the generated process plans try to maintain the same machine and machining direction where it is possible to save machining time. Where machine 7 is unavailable, the process plan will continue without the use of this machine. It can also be observed that as the number of available machines decreases, OMT increases, as shown in Table 4. The increase in OMT is accounted for by a reduction in search space when the number of machines decreases. When extra operations are added, the process plan includes and fits the operations in the best possible way soTable 2. Operations identified for a Hoppt 3 plate-D type customised mould base in Fig. 3.FeaturesOperationsPredecessorsMachinesToolDirections(OPR)(M)Types (T)(MD)F1 machining to thickness1 Milling1, 7, 81+zF2 machining to thickness2 Milling1, 7, 81zF3 machining side3 Milling2, 7, 81+xF4 machining side4 Milling2, 7, 81xF5 machining side5 Milling2, 7, 81+yF6 machining side6 Milling2, 7, 81yF7 edge chamfering7 Chamfer grinding1, 2, 3, 4, 5, 635All edgesF8 cavity8 Rough milling1, 2, 3, 4, 5, 67, 83+zF9 cavity9 Fine milling87, 83+zF10 machining of top face10 Grinding84, 52+zF11 machining of bottom11 Grinding1, 24, 52z12 U-drillling176, 7, 86+z,zF12 support pin holes ( 4)13 Reaming127, 87+z,z14 Boring137, 88+z,z15 U-drilling3, 4, 5, 67, 86+z,zF13 guide pin holes ( 4)16 Reaming8, 157, 87+z,z17 Boring167, 88+z,zF14 return pin holes ( 4)18 U-drilling3, 4, 5, 66, 7, 86+z,z19 Boring187, 88+z,zF16 screw bolt hole ( 4)20 Spot drilling1, 2, 3, 4, 5, 66, 7, 84z21 Drilling226, 7, 86zF18 hole thread F16 ( 4)22 Tapping236, 7, 89zF19 hole thread F2223 Tapping317, 89+xF20 hole thread F2324 Tapping337, 89xF21 counterbore holes ( 4)25 Counterbore drilling157, 83zF22 eye bolt hole26 Spot drilling1, 2, 3, 4, 5, 66, 7, 84+x27 Drilling306, 7, 86+xF23 eye bolt hole28 Spot drilling1, 2, 3, 4, 5, 66, 7, 84x29 Drilling326, 7, 86xAdditional features for core plate (CB) customisation shown in Fig. 4F24 cooling holes ( 2)30 Drilling5, 6, 116, 7, 86+xF25 cooling holes ( 2)31 Milling3, 4, 116, 7, 86yF26 cooling holes ( 2)32 Drilling5, 6, 116, 7, 86+xF27 cooling holes ( 2)33 Drilling86, 7, 86+zF28 inlet/outlet holes ( 4)34 Counterbore drilling34, 366, 7, 83+xF29 hole threads ( 4)35 Tapping387, 89+xF30 plug holes ( 2)36 Counterbore drilling356, 7, 83yF31 ejector pin holes ( 3)37 Drilling97, 86+z,zF32 slider slot38 Milling1, 2, 3, 4, 5, 67, 83+y, +zF33 slider slot hole39 Drilling9, 427, 86+yF34 interlock holes ( 2)40 Milling9, 10, 117, 83+zTable 3. Details of best process plan found for standard mould base core plate.Number123456789101112131415OPR561234287181589191617M777778837777777MD+yy+zz+xxxAE*+z+z+z+z+z+z+zT111111456633878Number1617181920212223242526272829OPR1213262723292425202122141011M77777777777755MD+z+z+x+x+xxxzzzzz+zzT67469693469822Number of nodes branched = 10 000 (computation time = 2 min 54 s) Number of M and MD changes = 13OMT = 94.81 min译文：一种基于分枝定界算法的注塑模架基工艺规划系统作者：P.Y.Gan，K.S.Lee和Y.F.Zhang本文介绍了在注塑模具基座的工艺规划中使用人工智能。 为IMOLD开发的计算机辅助加工计划系统将提取并识别加工所需的操作。 在产生模具底板的工艺计划之前，将这些操作与其优先约束和可用机器一起考虑。 流程计划通过基于分支和界限的算法进行优化。 已经提出整体加工时间作为优化的目标函数。 工业案例研究说明了该算法智能地搜索可行的优化解决方案的能力。 与基于遗传算法的工艺规划系统进行了简单的比较。 这一发展的结果将使用户能够轻松优化任何给定模具基地的工艺计划，并可选择适合生产车间的动态变化。关键词：分支定界算法; 计算机辅助进程计划（CAPP）; 优化; 注塑模具基地1.简介 计算机辅助工艺规划（CAPP）近年来备受关注。 它一直被认为是计算机辅助设计（CAD）和计算机辅助制造（CAM）系统之间的桥梁，以实现完全自动化的工厂。 尽管需要，CAPP系统不足以满足不同行业的要求。 这项工作专注于为模具制造商开发CAPP系统。 目前，大多数生产模具基地的工艺规划都是人工完成的。 流程计划非常依赖流程计划员的决定。 CAPP系统的引入应该保证始终如一的良好工艺计划，并且需要更全面的考虑制造参数。 工业界需要CAPP系统，原因如下： 1.模具基地公司正在接受越来越多的制造定制模具基地的要求，其中附加功能被添加到标准模具基地。 因此，需要额外的操作来创建这些新功能。 通常，标准模架具有预定的工艺计划，针对所需的加工量进行了优化。 随着新操作的添加，此优化的流程计划会中断，而手动流程计划无法跟上这些更改。 CAPP系统能够不断重新优化流程计划，以确保所用流程计划的最优化。 2.工艺规划时应考虑整体车间条件。 手动流程计划无法考虑所有车间变更并有效应用。 只有CAPP系统能够严格考虑优化。 这项工作的目标是开发工艺规划模具基地的CAPP系统。 IMOLD（智能模具设计）是NUS机械工程系开发的基于知识的应用软件，用于塑料注塑模具设计。 该系统是对IMOLD的补充，并且它使用IMOLD处理计划模具库。 机器，工具，优先约束和模型部件文件的数据库与过程规划期间机器可用性的实时输入一起被读取。 要求操作员输入定制特征，然后使用某种形式的人工智能生成过程计划。 分支定界技术是这里选择的搜索算法。 本文介绍了灵活的CAPP系统的操作，旨在帮助流程计划人员在运营规划期间进行更全面的考虑。 本文对工艺规划和相关工作中使用的某些形式的人工智能进行了简要的文献调查。 以下部分包括问题描述和实施的分支定界算法。 最后，一个案例研究展示了这个系统的可用性和潜力。 第二个案例研究显示了基于分枝界限的CAPP和基于遗传算法的CAPP的比较。2.背景 工艺规划是为了从一块原料生产最终产品所需的所有步骤准备的一套详细说明1。 过程计划的质量很大程度上取决于过程计划员的技能，因为需要对可用工具，机器和创建零件所需的操作有广泛的了解2。 CAPP系统因此被视为协助工艺规划的重要工具。 CAPP系统应该为所有可能的制造方法优化零件。 然而，很多报道的CAPP系统无法产生全球优化的工艺计划3。 因此，越来越多地使用人工智能来搜索全球解决方案4,5。 许多报道的方法只涉及特征排序，包括所需操作的细节6,7。 操作细节对于分配车间资源以执行操作是必需的。 当需要大量操作时，对流程计划解决方案进行详尽的顺序搜索会导致不可接受的计算时间。 本工作使用分支定界算法智能地搜索最佳或接近最佳的工艺计划。 分支定界算法是用于隐式枚举搜索空间的众所周知的搜索算法12.它作为一种人工智能方法在调度，过程规划和问题解决等领域被广泛13。 已经有报道使用分支定界技术进行工艺规划14-16。 但是，这些工程中的工艺计划的性质与模具制造行业所需的工艺规划不同。 这项工作使用分支和绑定技术来处理所有操作的计划，考虑到每个模具底板上所有可用机器和工具上的所有工具访问方向。 就我们所知，在其他相关研究中尚未处理这样的考虑。3.问题表述 与相关机器进行操作以制定工艺计划，从而尽可能缩短生产时间,流程规划问题受限于数量操作，优先关系，机器，加工方向,和工具。 优化的解决方案是一种排序方法 .3.1工艺规划模型优化所需的信息是从使用IMOLD建模的模具中提取的。 该操作数据库，机器，加工方向，工具和优先约束与机器可用性一起用于工艺规划。 该模型的示意图如图1所示，并做出以下假设：1.一台机器一次只能处理一项操作。2.所有机器只能在一个特定的面上访问零件。 如果要在另一个面上进行加工，则必须拆下该零件，并且需要花费设置时间来更换朝向不同方向的零件。3.起重机或机器人随时可用。 在等待机器或劳动力移动零件时，不允许等待时间浪费时间。 定制功能要求流程计划人员手动输入必要的数据。 这是因为可以通过许多可能的方法创建单个功能，并允许流程计划人员更好地控制系统。 分配的操作和最终生成的流程计划应该满足以下条件：1.模具底座的特征通过分配给他们的操作来识别。 分配的操作应产生所需的形状，尺寸，公差和完成特征。 picture1 2.从流程计划中获得的操作顺序不应违反任何有关操作的优先关系。3.只能使用可用工具在可用机器上执行操作，这些工具能够加工该特定功能。 获得的工艺计划应包括要执行的操作数量，这些操作的顺序，机器，加工方向以及所使用的相应工具。 这些细节是必要的，这样可以节省时间，以便在使用相同设置的特定机器上执行操作。 例如，必须在1x方向钻一个盲孔，而从1x或2x方向钻一个通孔。 通过考虑这两个操作可以看出，流程计划应该尝试在1x方向上在同一台机器上执行这两个操作，这样就不会产生额外的设置时间。3.2目标函数 为了量化目标函数，即整体加工时间（OMT），我们使用与Zhang等人使用的计算框架类似的计算框架。17。 针对每个连续的工艺计划序列计算目标函数，并将产生最小OMT的序列作为最终工艺计划。 有三个有助于计算OMT的区域，它们是机器设置时间，加工方向设置时间和加工时间。 3.2.1机器设置时间机器设置时间（MST）在两次操作之间发生机器更换时被考虑。 它被定义为在机器之间移动所需的时间以及模具底板在机器上沿特定方向的安装时间。 它被定义为所有n个操作的总和， Mi表示选择用于处理操作i的机器，MSTIi表示用于操作i的机器的机器建立时间指数，n表示针对从模具特征确定的整个系列操作选择的操作的数量。 3.2.2加工方向设置时间加工方向设置时间（MDST）是更改同一机器上模具底板方向所需的时间。 MDST仅在有变化时计算加工方向，但两次操作之间机床不变。 它被定义为，N21MDST 5（V（MDi11，MDi）I513 1 2 V（Mi11，Mi） 3 MDSTIi11）（3）MDi是选择用于处理操作i的加工方向，MDSTIi是用于操作i的机器的加工方向设置时间索引。 MDSTIi和MSTIi通过时间差异来移动旧机器和新机器之间的部件。MSTIi 5 MDSTIi（4）1（在机器间移动部分的时间）由于没有考虑起重机或机器人的等待时间，我们认为MDSTIi和MSTIi是相同的。3.2.3加工时间加工时间MT是执行所有加工操作的实际时间，例如使用相应工具在指定机器上进行钻孔，铣削或磨削。?MT 5（MTMi，Ti）i（5）I51单次操作的加工时间可能会根据所选机器和工具的不同而有所不同。 由此，对于单个操作存在一个或多个可能的MTi。3.2.4整体加工时间总加工时间是所有机床更换设置时间，加工方向更改设置时间和所有加工时间的总和。 目标是产生一系列的操作需要最少的OMT。表1.机器类型，MSTI，MDSTI和合适工具的类型。picture24.分支定界算法选择分支定界算法作为搜索算法，因为它在该领域具有公认的记录。 其强大和枚举性质应该产生一个最佳或接近最佳的解决方案。 大多数分支定界算法的搜索空间本质上很大且计算复杂。 这意味着有效的启发式和有效的下界计算对于减少搜索空间以帮助早日达成一个好的解决方案非常重要。4.1实现的算法该算法首先对可用操作之一进行排序，这称为分支节点。通过分支一个节点，形成一个新的节点，并且如果其下限值优于上限值，则该节点保持在搜索空间中，反之亦然。启发式用于调度每个节点的剩余操作，迄今为止找到的最佳解决方案将记录为上限值。下一个要分支的节点是具有最佳下限值的节点，因为它被认为具有最好的潜力。随着越来越多的节点分支，越来越多的操作将被排序，并且上限值将变得越来越小。该算法在上限值小于所有下限值时停止，并且进程计划是生成上限解决方案的序列。为了平衡解决方案的质量和计算时间，设置