Optimization of Straight Cylindrical Turning Using Artificial Bee Colony (ABC) Algorithm

Abstract

Artificial bee colony (ABC) algorithm, that mimics the intelligent foraging behavior of honey bees, is increasingly gaining acceptance in the field of process optimization, as it is capable of handling nonlinearity, complexity and uncertainty. Straight cylindrical turning is a complex and nonlinear machining process which involves the selection of appropriate cutting parameters that affect the quality of the workpiece. This paper presents the estimation of optimal cutting parameters of the straight cylindrical turning process using the ABC algorithm. The ABC algorithm is first tested on four benchmark problems of numerical optimization and its performance is compared with genetic algorithm (GA) and ant colony optimization (ACO) algorithm. Results indicate that, the rate of convergence of ABC algorithm is better than GA and ACO. Then, the ABC algorithm is used to predict optimal cutting parameters such as cutting speed, feed rate, depth of cut and tool nose radius to achieve good surface finish. Results indicate that, the ABC algorithm estimated a comparable surface finish when compared with real coded genetic algorithm and differential evolution algorithm.

Appendix

The pseudo code of ABC algorithm [13] is presented below:

• 1. Initialize the Colony Size (CS), Number of Food Sources (SN), Number of dimensions to each solution (D), Modification Rate (MR), Scout Production Period-limit (SPP)

• 2. Initialize the population of solutions x _i,j where i = 1… SN and j = 1… D

• 3. Evaluate the population

• 4. cycle = 1

• 5. REPEAT

• 6. Produce a new solution v _i for each employed bee by using Eq. (2) and evaluate it, if R _j  < MR, otherwise x _ij .

  [∅ _ij —is a random number in the range [−1, 1]. k ∈ {1, 2… SN} (SN: Number of solutions in a colony) is randomly chosen index. Although k is determined randomly, it has to be different from i. R _j is a randomly chosen real number in the range [0, 1] and j ∈ {1, 2,… D} (D: Number of dimensions in a problem). MR, modification rate, is a control parameter.]

• 7. Apply greedy selection process for the employed bees between the v _i and x _i

• 8. Calculate the probability values P _i using Eq. (3) for the solutions x _i

• 9. For each onlooker bee, produce a new solution v _i by using (2) in the neighbourhood of the solution selected depending on P _i and evaluate it.

• 10. Apply greedy selection process for the onlooker bees between the v _i and x _i

• 11. If Scout Production Period (SPP) is completed, determine the abandoned solutions by using “limit” parameter for the scout, if it exists, replace it with a new randomly produced solution using Eq. (4)

• 12. Memorize the best solution achieved so far

• 13. cycle = cycle +1

• 14. UNTIL (Max Cycle Number or Max CPU time)