Multi-Objective Ant Colony Optimization for Solving the Twin- Screw Extrusion Configuration Problem

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1 Multi-Objective Ant Colony Optimization for Solving the Twin- Screw Extrusion Configuration Problem Cristina Teixeira*, J. A. Covas*, Thomas Stützle** and A. Gaspar-Cunha* *IPC/I3N-Institute for Polymer and Composites, University of Minho, Campus de Azurém, Guimarães, Portugal **Université Libre de Bruxelles, IRIDIA, 50 Av. F. Roosevelt, CP 194/6, B-1050 Brussels, Belgium [Teixeira]; [Covas]; [Stützle]; [Gaspar-Cunha] Abstract: The Twin-Screw Configuration Problem (TSCP) consists in defining the best location of a set of available screw elements along a screw shaft. Due to its combinatorial nature, it can be seen as a sequencing problem. In addition, different conflicting objectives may have to be considered when defining a screw configuration and, thus, the problem is usually tackled as a multiobjective optimization problem. In this research, a multi-objective ant colony optimization (ACO) algorithm was adapted to deal with the TSCP. The influence of different parameters of the ACO algorithm was studied and its performance was compared with that of a previously proposed multi-objective evolutionary algorithm. The results produced showed that ACO algorithms have a significant potential for solving this type of problems. Keywords: multi-objective; ant colony optimization; evolutionary algorithms, polymer extrusion; twin-screw extrusion Supplementary file

Roosevelt, CP 194/6, B-1050 Brussels, Belgium E-mail: cteixeira@dep.uminho.

2 5. Results and Discussion Table 3. Screw elements used in each of the four instances TSCP1 to TSCP4. Instances Length TSCP1 Pitch KB Length TSCP2 Pitch KB Length TSCP3 Pitch KB- KB Length TSCP4 Pitch KB- KB- KB Table 4. Case studies for each of the four instances of Table 1. Given are the optimization criteria, the aim of optimization and the feasible ranges of the objectives. Case study Criteria Aim Xmin Xmax Average Strain Maximization Specific Mean Energy (SME) Minimization Average Strain Maximization Viscous Dissipation Minimization Specific Mean Energy (SME) Minimization Viscous Dissipation Minimization Table 5. MOACO components studied. ACO Component Values tested pheromone evaporation rate 0.1, 0.2, 0.3, 0.4 and 0.5 pheromone information position vs relation pheromone update strategy best-so-far vs iteration-best assignment order sequential vs importance-based number of pheromone matrices one vs several pheromone summation rule with vs without number of colonies one vs three weight aggregation linear vs power

5 120 45 60 30 30 30 60 30 120 30 120 37.5 60 60 30 TSCP3 Pitch 45 30 45 30-20 60 30 20 KB- KB- 60 30 30 60 20 45 30 20 Length 97.5 120 45 60 30 30 30 60 30 120 30 120 37.5 60 60 30 TSCP4 Pitch 45 30 45 30-20 60 30 20 60 30 30 60 KB- KB- KB- 30 45 30 20 Table 4.

3 Table 6. Best parameters MO-ACO values accomplished. ACO Component Best Values pheromone evaporation value 0.2 pheromone information Relation pheromone update strategy best-so-far assignment order Sequentially number of pheromone matrices Several pheromone summation rule Without number of colonies Three weight aggregation Power

2 pheromone information Relation pheromone update strategy best-so-far assignment

4 Figure 4. Influence of the pheromone evaporation value (ρ equal to 0.2 and 0.3).

5 Figure 5. Influence of the pheromone information (position versus relation).

6 Figure 6. Influence of the pheromone update strategy (best so far versu iteration best).

7 Figure 7. Influence of the assignment order using sequence with position pheromone (information versus importance)

8 Figure 8. Influence of the assignment order using sequence with a relation pheromone (information versus importance).

9 Figure 9. Influence of the number of matrices (single matrix versus one for each objective).

10 Figure 10. Influence of the pheromone summation rule using a position pheromone information (with versus without).

11 Figure 11. Influence of the number of colonies (one colony versus three colonies).

12 Figure 12. Influence of the weight aggregation method (linear versus power).

13 Figure 13. Comparison between pheromone evaporation value 0.1 and 0.2

14 Figure 14. Comparison between pheromone evaporation value 0.1 and 0.3

15 Figure 15. Comparison between pheromone evaporation value 0.1 and 0.4

16 Figure 16. Comparison between pheromone evaporation value 0.1 and 0.5

17 Figure 17. Comparison between pheromone evaporation value 0.2 and 0.3

18 Figure 18. Comparison between pheromone evaporation value 0.2 and 0.4

19 Figure 19. Comparison between pheromone evaporation value 0.2 and 0.5

20 Figure 20. Comparison between pheromone evaporation value 0.3 and 0.4

21 Figure 21. Comparison between pheromone evaporation value 0.3 and 0.5

22 Figure 22. Comparison between pheromone evaporation value 0.4 and 0.5

23 Figure 23. Comparison between MOACO and RPSGA for TSCP1 instance.

24 Figure 24. Comparison between MOACO and RPSGA for TSCP2 instance.

25 Figure 25. Comparison between MOACO and RPSGA for TSCP3 instance.

26 Figure 26. Comparison between MOACO and RPSGA for TSCP4 instance.

27 Figure 27. Comparison between MOACO and TPLS for TSCP1 instance.

28 Figure 28. Comparison between MOACO and TPLS for TSCP2 instance.

29 Figure 29. Comparison between MOACO and TPLS for TSCP3 instance.

30 Figure 30. Comparison between MOACO and TPLS for TSCP4 instance.

Ant Colony Optimization and Constraint Programming

Ant Colony Optimization and Constraint Programming Christine Solnon Series Editor Narendra Jussien WILEY Table of Contents Foreword Acknowledgements xi xiii Chapter 1. Introduction 1 1.1. Overview of the