Optimal allocation of index positions on tool magazines using an ant colony algorithmAbstract Generation of optimal index positions of cutting tools is an important task to reduce the non-machining time of CNC machines and for achievement of optimal process plans. The present work proposes an application of an ant colony algorithm, as a global search technique, for a quick identification of optimal or near optimal index positions of cutting tools to be used on the tool magazines of CNC machines for executing a certain set of manufacturing operations. Minimisation of total indexing time is taken as the objective function.Keywords Indexing time . Automatic tool change .CNC machine . Optimization . Ant colony algorithm1 IntroductionIn today?s manufacturing environment, several industries are adapting flexible manufacturing systems (FMS) to meet the ever-changing competitive market requirements. CNC machines are widely used in FMS due to their high flexibility in processing a wide range of operations of various parts and compatibility to be operated under a computer controlled system. The overall efficiency of the system increases when CNC machines are utilized to their maximum extent. So to improve the utilization, there is a need to allocate the positions of cutting tools optimally on the tool magazines.The cutting tools on CNC machines can be changed or positioned automatically when the cutting tools are called within the part program. To do this turrets are used in CNC lathe machines and automatic tool changers (ATC) in CNC milling machines. The present model can be used either for the ATC magazines or turrets on CNC machines.The indexing time is defined as the time elapsed in which a turret magazine/ATC moves between the two neighbouring tool stations or pockets. Bi-directional indexing of the tool magazine is always preferred over uni-directional indexing to reduce the non-machining time of the machine. In this the magazine rotates in both directions to select automatically the nearer path between the current station and target station. The present work considers bi-directional movement of the magazine. In bidirectional indexing, the difference between the index numbers of current station and target station is calculated in such a way that its value is smaller than or equal to half of the magazine capacity.Dereli et al. 1 formulated the present problem as a “traveling salesmanproblem”(TSP), which is NP complete. They applied genetic algorithms (GA) to solve the problem. Dorigo et al. 2, 3 introduced the ant colony algorithm (ACA) for solving the NP-complete problems. ACA can find the superior solution to other methods such as genetic algorithms, simulated annealing and evolutionary programming for large-sized NP-complete problems with minimum computational time. So, ACA hasbeen extended to solve the present problem.2 MethodologyDetermination of the optimal sequence of manufacturing operations is a prerequisite for the present problem. This sequence is usually determined based on minimum total set-up cost. The authors 4 suggested an application of ACA to find the optimal sequence of operations. Once the sequence of operations is determined, the following approach can be used to get the optimal arrangement of the tools on the magazine.Step 1 Initially a set of cutting tools required to execute the fixed (optimal) sequenceof the manufacturing operations is assigned. Each operation is assigned a single cutting tool. Each tool is characterized by a certain number. For example, let the sequence of manufacturing operationsM1-M4-M3-M2-M6-M8-M9-M5-M7-M10 be assigned to the set of cutting tools T8-T1-T6-T4-T3-T7-T8-T2-T6-T5. The set of tools can be decoded as 8-1-6-4-3-7-8-2-6-5. Here the manufacturing operation M1 requires cutting tool 8, M4 requires 1 and so on. In total there are eight different tools and thus eight factorial ways of tool sequences possible on the tool magazine.Step 2 ACA is applied as the optimization tool to find the best tool sequence that corresponds to the minimum total indexing time. For every sequence that is generated by the algorithm the same sequence of index positions (numbers) is assigned. For example, let the sequenceof tools 4-6-7-8-2-5-3-1 be generated and hence assigned to the indexing positions 1-2-3-4-5-6-7-8 in the sequential order, i.e. tool 4 is assigned to the 1st position, tool 6 to the 2nd position and so on.Step 3 The differences between the index numbers of subsequent cutting tools are calculated and then totaled to determine the total number of unit rotations for each sequence of cutting tools. Absolute differences are to be taken while calculating the number of unit rotations required from current tool to target tool. This following section describes an example in detail.The first two operations M1 and M4 in the pre-assumed fixed sequence of operations require the cutting tools 8 and 1, respectively. The tool sequence gener