1. Optimization of multi-pass turning operations using ant colony system Authors: K. Vijayakumar, G. Prabhaharan, P. Asokan, R. Saravanan 2003 Presented by: Kent Fairbourn 10-31-07

2. Purpose Compare the Ant colony algorithm with the Genetic algorithm and simulated annealing. Compare the Ant colony algorithm with the Genetic algorithm and simulated annealing. Find a faster method for producing a global optimization Find a faster method for producing a global optimization Optimize per unit cost for turning operations Optimize per unit cost for turning operations Handbooks are insufficient – do not consider economic aspects of machining Handbooks are insufficient – do not consider economic aspects of machining

3. Genetic Algorithm Used to find exact or approximate solutions to optimization problems Used to find exact or approximate solutions to optimization problems Population of solutions evolves toward a better solution Population of solutions evolves toward a better solution Each generation involves mutation (combination) of “fit” solutions Each generation involves mutation (combination) of “fit” solutions Terminates at set number of generations or a solution of predetermined fitness Terminates at set number of generations or a solution of predetermined fitness Weaknesses : Finds local rather than global solutions. Can’t adjust for long term benefit. Weaknesses : Finds local rather than global solutions. Can’t adjust for long term benefit.

4. Simulated Annealing Approximated a global optimum for a given search function Approximated a global optimum for a given search function Solutions are mixed as parts and compared to nearby solutions Solutions are mixed as parts and compared to nearby solutions Compares all solutions to one another Compares all solutions to one another Time consuming – Many iterations required Time consuming – Many iterations required

5. Real Life Ant Colony Behavior Ant wander for food, find it and return to their colony, leaving a pheromone trail Ant wander for food, find it and return to their colony, leaving a pheromone trail Other ants follow same trail Other ants follow same trail Longer trails lose pheromone density Longer trails lose pheromone density Shorter trails prevail and are used by all Shorter trails prevail and are used by all

6. Ant Colony Optimization (ACO) Each virtual ant takes a random path Each virtual ant takes a random path Paths are evaluated and mutated or replaced Paths are evaluated and mutated or replaced Values associated with successful solutions receive more virtual pheromones (Trail Value) Values associated with successful solutions receive more virtual pheromones (Trail Value)

7. Governing Equations UC = C M + C i + C R +C T UC = C M + C i + C R +C T Goal = Max F(X) = -UC(X,n,d) Goal = Max F(X) = -UC(X,n,d) (X is the machining parameter set, n is the number of passes, and d is the depth of cut)

8. Optimization Parameters Cut Speed Cut Speed Feed Rate Feed Rate Depth of Cut Depth of Cut Tool Life Tool Life Operating Constraints Operating Constraints Power Power Stable Cutting Region Stable Cutting Region Chip-Tool Interface Chip-Tool Interface Finish Machining Finish Machining Surface Finish Surface Finish

9. Parameters Used

10. Parameter Values Each parameter has an upper and lower bound for the virtual ants to choose from. Each parameter has an upper and lower bound for the virtual ants to choose from. Values taken from Chen and Tsai’s Simulated Annealing Model Values taken from Chen and Tsai’s Simulated Annealing Model

11. ACO

12. ACO

13. ACO applet Example courtesy of Mark Sinclair Example courtesy of Mark Sinclair Example courtesy of Mark Sinclair Example courtesy of Mark Sinclair

14. Results ACO vs. SA vs. GA Method Unit Cost ($) # Runs Difference ACO1.62621-15------ GA1.76101-100-7.65% SA2.2959901-1000-8.28% Cutting Speed (m/min) Feed (mm/rev) Roughing Cut 103.050.9 Finishing Cut 162.020.24 ACO Optimum Machining Parameters

15. Conclusions ACO obtains a near optimal solution among a large solution base in reasonable time ACO obtains a near optimal solution among a large solution base in reasonable time Superior to GA and SA Superior to GA and SA Generic algorithm can be applied to varying parameters and constraints Generic algorithm can be applied to varying parameters and constraints Also applicable to Milling and Threading Operations Also applicable to Milling and Threading Operations

16. References