1、A note onoptimization of multi-pass turning operations using ant colony systemAbstractAn article by Vijayakumar et al. Optimization of multi-pass turning operations using ant colony system, International Journal of Machine Tools and Manufacture 43(15) (2003) 16331639 proposed an ant colony optimizat
2、ion methodology for determining the machining parameters in a multi-pass turning operation model. By using the problem of Chen and Tsai A simulated annealing approach for optimization of multi-pass turning operations, International Journal of Production Research 34(10) (1996) 28032825, they conclude
3、d that their ant colony approach outperformed the other optimization techniques proposed by other researchers. This note discusses an illustrative multi-pass turning problem, which was used in several literatures and demonstrates that the optimal solution as found by Vijayakumar et al. 1 is not vali
4、d.Keywords: Multi-pass turning operations; Ant colony algorithm; Optimization techniques1. IntroductionSelecting proper values for machining parameters such as cutting speed, feed rate, and depth of cut directly affects the machining economics in metal-cutting processes 3.Several cutting constraints
5、 must be considered in machining operations. In turning operations, a cutting process can possibly be completed with a single pass or by multiple passes. Multi-pass turning is preferable over single-pass turning in the industry for economic reasons 2. A multipass cutting operation involves several r
6、oughing cuts and a single finishing cut. That makes the problem of determining the optimal cutting conditions more difficult and complicated. Machining parameters can be determined based on the machine operators experience or by following the cutting handbook supplied by the equipment manufacturer.
7、However, those data are not guaranteed to be optimal or even good for a particular cutting environment. Therefore, developing mathematical models for multi-pass turning operations has become a useful tool for determining the optimal cutting conditions. The main objective of this note is to review pa
8、st research work for solving a popular multi-pass turning operation model and to demonstrate that the optimal solution arrived at by Vijayakumar et al. 1 for an illustrative problem is impracticable.2. Multi-pass turning modelVijayakumar et al. proposed an ant colony optimization methodology for det
9、ermining the machining parameters in a multi-pass turning operation model, which originally was developed by Shin and Joo 4 and has been extended by Chen and Tsai 2. All the notations used in this paper are the same as those in Vijayakumar et al. 1. The minimum unit production cost criterion is adop
10、ted as the objective of the proposed model. The production cost for machining one unit piece is represented by the sum of the following four terms:Minimize ， （1）， （2）， （3）， （4）， （5）Six constraints are considered for the rough cutting operation.， （6）， （7） ， （8） ， （9） ， （10）， （11）In addition, the othe
11、r six constraints plus another constraint for roughness are considered for the finish cutting operation， （12）， （13） ， （14）， （15）， （16） ， （17） ， （18）Shin and Joo provided an example and decomposed the optimization problem into two separate sub-problems.They dealt with these two sub-problems separatel
12、y using an approach combining the Fobonacci search and dynamic programming.The minimum production cost they found was $2.385/unit. Chen and Tsai 2 proposed an approach that combined the simulated annealing algorithm and a pattern search technique. The minimum production cost they arrived at was $2.2
13、974/unit. Chen and Tsai then extended the multi-pass turning operation model of Shin and Joo by adding seven more constraints including stable cutting region constraints, chiptool interface temperature constraints, and roughing and finishing parameter relations. These seven constraints are expressed
14、 as follows.Stable cutting region constraints:， （19）， （20）Chiptool interface temperature constraints:， （21）， （22）Constraints for roughing and finishing parameter relations:， （23）， （24）， （25）Based on the same machining data of the problem used by Shin and Joo 4, the minimum production cost obtained b
15、y Chen and Tsai is $2.2959/unit. Onwubulu and Kumalo 5,6 proposed a technique based on a genetic algorithm to determine the optimal machining parameters for the extended model of Chen and Tsai. They arrived at a production cost of $1.761/unit, which was substantially lower than that of Chen and Tsai 2. Vijayakumar et al. 1 proposed an ant colony optimization method to solve the same problem. They claimed that their ant colony-based approach found an even
