Machining parameter optimization using ant colony system.

Zuperl, Uros ; Cus, Franc ; Balic, Joze 等

1. INTRODUCTION

The selection of optimal cutting parameters is a very important issue for every machining process. In workshop practice, cutting parameters are selected from machining databases or specialized handbooks, but they don't consider economic aspects of machining.

Optimization of cutting parameters is a difficult work (Cus & Balic, 2000), where the following aspects are required: knowledge of machining; empirical equations relating the tool life, forces, power, surface finish, etc., to develop realistic constrains; specification of machine tool capabilities; development of an effective optimization criterion; and knowledge of mathematical and numerical optimization techniques.

Optimization of machining parameters is complicated when a lot of constraints are included, so it is difficult for the non-deterministic methods to solve this problem. Consequently, non-traditional techniques were used in the optimization problem (Liu & Wang, 1999). (Zuperl & Cus, 2003) have described the multi objective technique of optimization of cutting conditions for turning process by means of the neural networks. Further genetic algorithm and simulated annealing techniques have been applied to solve the continuous machining profile problem by (Milfelner et al., 2004).

In this paper, a multi-objective optimization method, based on combination of ANFIS and ACO evolutionary algorithms, is proposed to obtain the optimal parameters in turning processes.

2. MACHINING MODEL FORMULATION

The objective of this optimization machining model is to determine the optimal machining parameters including cutting speed, feed rate and depth of cut in order to minimize the operation cost and to maximize production rate (represented by manufacturing time ([T.sub.p]) and cutting quality ([R.sub.a]).

[C.sub.p] = [T.sub.p] x ([C.sub.t]/T + [C.sub.1] + x [C.sub.0]) (1)

where [C.sub.t], [C.sub.1] and [C.sub.0] are the tool cost, the labour cost and the overhead cost respectively; T is tool life. The objectives used in this work are determined according to (Zuperl & Cus, 2003). In order to ensure the evaluation of mutual influences and the effects between the objectives and to be able to obtain an overall survey of the manufacturer's value system the multi attribute function of the manufacturer (y) is determined. The cutting parameter optimization problem is formulated as the following multi-objective optimization problem: min [T.sub.p] (v, f, a), min [C.sub.p] (v, f, a), min [R.sub.a] (v, f, a)

y = 0,42 x [e.sup.(-0,22Tp)] + 0,17 x [e.sup.(-0,26Ra)] + 0,05/ (1 + 1,22 x [T.sub.p] x [C.sub.p] x [R.sub.a]) (2)

A multiattribute value function is defined as a real-valued function that assigns a real value to each multiattribute alternative, such that more preferable alternative is associated with a larger value index than less preferable alternative.

The following limitations are taken into account: Permissible range of cutting conditions: [v.sub.min] [less than or equal to] v [less than or equal to] [v.sub.max], [f.sub.min] [less than or equal to] f [less than or equal to] [f.sub.max], [a.sub.min] [less than or equal to] a [less than or equal to] [a.sub.max]; Implied limitations issuing from the tool characteristics and the machine capacity; The limitations of the power and cutting force are equal to: P(v, f, a) [less than or equal to] [P.sub.max], F(v, f, a) [less than or equal to] [F.sub.max].

The proposed approach consists of two steps. First, experimental data are prepared to train and test ANFIS system to represent the objective function (y). Finally, an ACO algorithm is utilized to obtain the optimal objective value. Figure 1 shows the flowchart of the approach.

[FIGURE 1 OMITTED]

3. OBJECTIVE FUNCTION MODELLING

First step uses an adaptive neuro fuzzy inference system (ANFIS) to model the response (manufacturer's implicit multiattribute) function (y). The variables of this problem are velocity, feed rate and depth of cut, which can have any continuous value subject to the limits available. The ANFIS system needs three input neurons for three parameters: v, f and a. The output from the system is a real value (y). Figure 2 shows the fuzzy rule architecture of ANFIS when the triangular membership function is adopted, respectively. The architectures shown in Figure 2 consist of 32 fuzzy rules. During training in ANFIS, 140 sets of experimental data were used to conduct 400 cycles of training. ANFIS has proved to be an excellent universal approximator of non-linear functions. If it is capable to represent the manufacturer's implicit multiattribute function.

[FIGURE 2 OMITTED]

4. ANT COLONY OPTIMIZATION (ACO)

Special insects like ants, termites, and bees that live in a colony are capable of solving their daily complex life problems. These behaviours which are seen in a special group of insects are called swarm intelligence. Swarm intelligence techniques focus on the group's behaviour and study the decartelized reactions of group agents with each other and with the environment. The swarm intelligence system includes a mixture of simple local behaviours for creating a complicated general behaviour and there is no central control in it. Ants have the ability to deposit pheromone on the ground and to follow, in probability, pheromone previously deposited by other ants. By depositing this chemical substance, the ants leave a trace on their paths. By detecting this trace, the other ants of the colony can follow the path discovered by other ants to find food. For finding the shortest way to get food, these ants can always follow the pheromone trails. The first ACO algorithm, called ant system (AS) has been applied to the travelling salesman problem (TSP). (Dorigo, 1996) proposed an ant colony optimization methodology for machining parameters optimization in a multi-pass turning model, which originally was developed by (Vijayakumar et al., 2002).

4.1 Ant colony algorithm

An ACO utilizes bi-level procedures which include local and global searches. Local search ants select a local trail I with a probability [P.sub.i](t) = [[tau].sub.i](t)/[SIGMA][[tau].sub.k](t), where i is the region index and [t.sub.i](k) is the pheromone trail on region i at time t. After selecting the destination, the ant moves through a short distance ([DELTA](T,R) = R(1 - [r.sup.10(1-T)]), where R is maximum search radius, r is a random number from [0,1], T is the total number of iterations of the algorithm. A global search is done sequentially by crossover and mutation operations. The subsequent values of the variables of the child are set to the corresponding value of a randomly chosen parent with a crossover probability ([P.sub.c]). Mutation operation adds or subtracts a value to/from each variable with mutation probability ([P.sub.m]). The mutation step size is the same as the above distance [DELTA](T,R). Performing an ACO, ants are repeatedly sent to trail solutions in order to optimize the objective value. The total number of ants (denoted by A) is set as half the total number of trail solutions (denoted by S). The number of global ants (denoted by G) and the number of local ants (denoted by L) are set as 80% and 20% of the total number of ants, respectively. The ACO algorithm:

Step 1. Set parameter values including: S, A, [rho], [[tau].sub.0], [P.sub.c], [P.sub.m], T, R, and bounds of each control factor.

Step 2. Create S trail solutions (v, f, a). Estimate the objective value of the trail solutions through the ANFIS model (y).

Step 3. Set the initial pheromone value of all trails.

Step 4. Repeat steps 6-9 until the stopping criteria has reached.

Step 5. Send L ants to the selected trail solutions for local search.

Step 6. If the solution is improved, move the ants to the new solution and update the pheromone value.

Step 7. Send G ants to global trails and generate their offspring by crossover and mutation.

Step 8. Evaporate pheromone for all trails.

5. RESULTS AND DISCUSSION

The ant colony optimization method combined with ANFIS prediction system was tested. Proposed ACO approach was compared with Method using ANN routine, genetic algorithms and LP technique. The results revelled that the proposed method significantly outperforms the GA and LP approach. The proposed approach found an optimal solution of 0.30 for as low as 1-18 runs the genetic-based approach require as much as 900-1300 runs to find an solution of 0.4 This means that the proposed approach has 8.1% improvement over the solution found by GA approach and 17.3% over LP approach.

6. CONCLUSION

In this work, non-conventional optimization techniques ACO has been studied for the optimization of machining parameters in turning operations. The ACO algorithm is completely generalized and problem independent so that it can be easily modified to optimize this turning operation under various economic criteria. The algorithm can also be extended to other machining problems such as milling operations and threading operations.

7. REFERENCES

Cus, F. & Balic, J. (2000). Selection of cutting conditions and tool flow in flexible manufacturing system. The international journal for manufacturing science & technology, Vol. 2, pp. 101-106

Dorigo, E. (1996). The ant system: Optimization by a colony of cooperating agents. IEEE Transaction on Systems, Man and Cybernetics, Vol. 26, pp. 1-13.

Liu, Y. & Wang, C. (1999). Neural Network based Adaptive Control and Optimisation in the Milling Process. International Journal of Advanced Manufacturing Technology, Vol. 15, pp. 791-795

Milfelner, M.; Zuperl, U. & Cus, F. (2004). Optimisation of cutting parameters in high speed milling process by GA. Int. j. simul. model., Vol. 3, pp. 121-131

Vijayakumar, K.; Prabhaharan, P.; Asokan, R. & Saravanan, M. (2002). Optimization of multi-pass turning operations using ant colony system. International Journal of Machine Tools and Manufacture, Vol. 3, pp. 633-639

Zuperl, U. & Cus, F. (2003). Optimization of cutting conditions during cutting by using neural networks. Robot. comput.-integr. manuf., Vol. 19, pp. 189-199