A multiobjective memetic ant colony optimization algorithm (MACS) is proposed to solve the time and space assembly line balancing problem (TSALBP) variant where the objectives are to minimize station area and number of stations. The algorithm combines a global search using MACS with two local search methods. It is compared against a GRASP algorithm on 9 problem instances, with no clear winner between the two approaches. Future work plans to design new evolutionary and memetic algorithms for the problem and add interactive preference methods.

1. A Multiobjective Memetic Ant Colony OptimizationAlgorithm for the 1/3 Variant of the Time andSpace Assembly Line Balancing Problem 12th April 2011 Manuel Chica, ÓscarCordón, Sergio Damas, Joaquín Bautista

2. Summary Introduction SALBP and TSALBP The memetic MACS proposal General structure The MACS global search Local search operators Experiments Conclusions and future work 01 02 03 04 05 06 07

3. Introduction 02 03 04 05 06 07 08 The optimization of assembly lines is of great importance in the production and operation research context. The time and space assembly line balancing problem (TSALBP) is a realistic extension of the well-known simple assembly line balancing problem (SALBP). We present a memetic MACS proposal with two multiobjective (MO) local search (LS) methods to solve the 1/3 variant of the TSALBP. The new proposal results are compared with a GRASP algorithm using multiobjective performance indicators in 9 problem instances.

4. SALBP and TSALBP (I) An industrial process is divided into a set V of n tasks. Each task j requires an operation time tjand has a set of direct predecessors (problem constraint). The SALBP involves grouping these tasks in m workstationsminimizing the cycle time (C) or the number of stations (m). 03 04 05 06 07 08 09

5. SALBP and TSALBP (II) Importance of the area in assembly line balancing. TSALBP formulations include: The area of each task, aj ; j=1,…,n The available area for any station, A Hence, TSALBP has a multicriteria nature involving three different objectives: The cycle time of the plant (C) The number of stations (m) The available area (A) 04 05 06 07 08 09 10

6. SALBP and TSALBP (III) The existence of these three objectives creates the following problem taxonomy: 05 06 07 08 09 10 11 There are 4 TSALBP multiobjective variants One of the most realistic variants in the automotive industry: TSALBP-1/3 (A and m)

7. Memeticmetaheuristicshave demonstrated its good performance because of the combination of global search behaviour and the local optimizer. We present a multiobjective memetic algorithm: With a powerful global search metaheuristic: MACS. A MO local search approach with two local search methods, one per objective. The set of constraints associated to TSALBP encourages the use of constructive memeticmetaheuristics to solve it. 06 07 08 09 10 11 12 Thememetic MACS proposal

8. 07 08 09 10 11 12 13 General structure (I)

9. General structure (II) The function to be optimised by the local search is a scalarization of the objective function vector: Weights are created at randomforsolution:λ1, λ2 Ifλ1 > λ2then LS operatorforobjectiveAisapplied. Otherwise, LS operatorforobjectivem. If no minimization, theotherisalsolaunchedafterwards. 08 09 10 11 12 13 14

10. A TSALBP solution is an assignment of tasks to different stations satisfying the constraints. We have to give a sequence of tasks and how these tasks are split up into different stations to fully specify the assignment. 09 10 11 12 13 14 15 The MACS global search (I)

11. The MACS global search (II) 10 11 12 13 14 15 16 Pareto-based MOACO algorithms have shown good performance in several problems. MACS is an extension of the ACS which considers an external Pareto archive. The pseudo-random transition rule is considered: Sametransition rules as ACS

12. The MACS global search (III) 11 12 13 14 15 16 17 The pheromone trail information is associated to a pair (task, station). The initial pheromone value 0 is obtained from two single-objective greedy algorithms. No heuristic information used!

13. A new mechanism to close a station is used to induce diversity, following a multi-colony approach: The MACS global search (IV) 12 13 14 15 16 17 18

14. Local search operators (I) 13 14 15 16 17 18 19 Both LS operators are based on movements of tasks between their feasible stations. Repeated 20 iterations on each solution obtained by MACS.

15. Local search operators (II) 14 15 16 17 18 19 20

16. Local search operators (III) 15 16 17 18 19 20 21

17. Experiments (I) Nine real-like problem instances with different features have been selected: arc111, barthol2, barthold, scholl… Multiobjective performance indicators: unary HVR, binary C, and graphical representation of the aggregated Pareto fronts. 16 17 18 19 20 21 22

18. Experiments (II) We compare the new proposal with MACS (no memetic). Also against a multiobjectiveGRASP algorithm : Builds the solution with a random selection of the next task to be included in the current station between the candidates using heuristic information. Makes use of an external Pareto archive and a restricted candidate list (RCL) . A mechanism to close stations using different thresholds. Two similar LS operators applied when solution is built. 17 18 19 20 21 22 23

19. Experiments (III) 18 19 20 21 22 23 24 Binary C performance indicator No cleardominance in P4, P5, P6 and P8 MACS Memetic MACS P1 and P9 GRASP isbetter GRASP Memetic MACS Clear dominace of Memetic MACS P2, P3 and P7 memetic MACS isbetter

20. Experiments (IV) According to HVR, memetic MACS and GRASP are the best algorithms depending on the problem instance. Memetic MACS is better than GRASP in P2, P3, P7 and P8. But worse in P1, P4, P5, and P6. MACS is obviously worse than GRASP and memetic MACS. 19 20 21 22 23 24 HVR performance indicator

21. Experiments (V) 20 21 22 23 24 21 22

22. A novel memetic MACS was developed and applied to tackle the TSALBP-1/3. Its behaviour is clearly superior to the MACS global search. However, thereis no clearconclusionaboutwhichalgorithmisbetterregardingthecomparisonbetween GRASP and memetic MACS. As future work, we will consider: Designing new EMO and memetic algorithms. Adding interactive procedures to include preferences. Application of Wilcoxon statistical tests to the results. Conclusions and futurework 21 22 20 21 22 21 22

23. Thanks for your attention