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A Multi-objective Ant Colony Algorithm for the 1/3 Variant of the

Time and Space Assembly Line Balancing Problem

Manuel Chica, Óscar Cordón, Sergio Damas

Joaquín Bautista

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Summary

Introduction SALBP and TSALBP The Multiple Ant Colony System (MACS) Our MACS-based approach Experiments Current work Concluding remarks Future work

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Introduction The Time and Space Assembly Line Balancing Problem

(TSALBP) is a realistic extension of the well-known Simple Assembly Line Balancing Problem (SALBP). The multi-objective variants of this problem have never been tackled in the literature.

Since this problem has a lot of constraints, a constructive approach may be a good way to solve it. Thus, we have successfully applied a Multi-objective ACO algorithm, MACS, to the multi-objective variant of TSALBP, obtaining promising results.

Our MACS approach was tested in different problem instances and compared with other algorithms by means of multi-objective metrics of performance.

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SALBP and TSALBP (1)

An industrial process is divided into a set V of n tasks. Each task j requires an operation time tj, and has a set of direct predecessors (constraint of the problem).

The SALBP consists of grouping these tasks in m workstations minimising the cycle time of them (C).

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SALBP and TSALBP (2)

In the automotive industry, a very important issue is the area of the plant. To model this situation, the TSALBP arises to include area information (aj) to the tasks and the area for the formed stations, A.

As many real-world problems, TSALBP has a multi-criteria nature, presenting 3 variables to be minimised: the cycle time of the plant (C), the number of stations (m) and their area (A).

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SALBP and TSALBP (3)

The existence of these 3 objectives causes a problem taxonomy, shown in this table:

There are 4 TSALBP multi-objective variants.

We have selected the 1/3 variant, which minimises the number of stations, m, and their area, A, given a fixed cycle time limit.

We made this decision because it is the most realistic variant in the automotive industry.

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The Multiple Ant Colony System (MACS) (1)

The Multiple Ant Colony System (MACS) proposed by Barán et al. is a multi-objective extension of the ACS. Every non-dominated solution found by the algorithm is included in an external Pareto archive.

It has a pheromone matrix and several heuristic matrixes, one per heuristic information. The transition rule is: λ weights the importance of

the heuristic information of each ant, and β weights the heuristic information with respect to the pheromone trail

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The Multiple Ant Colony System (MACS) (2)

The initial pheromone is calculated from the costs of the two objective functions, and it is not fixed during the run of the algorithm. Its value changes according to the objective values of the found non-dominated solutions:

There is a local pheromone update applied to each arc:

And a global update only performed with each solution of the Pareto archive:

Average of the non-dominated solutions

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Our MACS-based approach (1)

A TSALBP solution is an assignment of tasks to different stations satisfying all the constraints.

Giving only a sequence of tasks does not fully specify the assignment. We need to include additional information about how the sequence is split up into different stations:

task a task c task e task dtask b task ftask g task h

station 1 station 2 station 3

A = 20 C = 12 A = 16 C = 11 A = 24 C = 12

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Our MACS-based approach (2)

A new mechanism is used to close an station by means of a probability:

MACS works with two heuristic information:The first one is related with the required time of the task and the number of successors:

The second one related with the required area of the task and the number of successors:

Tasks having a large value of time and area and a high number of successors, are preferred to be allocated first.

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Our MACS-based approach (3)

The pheromone trail information has to memorise which tasks are the most appropiate to belong to a station. Hence, it is associated to a pair (task, station)

The initial value of pheromone, 0,, is obtained from two different single-objective heuristic algorithm, one per heuristic.

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Experiments (1)

We have used four well-known problem instances from www.assembly-line-balancing.de:

Originally, these instances only had time information, but we have created their area information from the latter by reverting their precedence graph to make them bi-objective:

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Experiments (2)

As this is the first time that a multi-objective variant of the TSALBP is tackled, there are not previous contributions to the problem.

We have designed two algorithms to compare our MACS approach:

Random search algorithm: it randomly creates a task sequence. Separators between stations are put at random satisfying all the precedece and cycle limit constraints.

ACS: it was designed according to the original version of Dorigo et al. We tackled the multi-objective problem by means of a weighted rule for the aggregation of the two objectives into one:

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Experiments (3)

We have used the following parameters to run the different algorithms:

In addition, multi-objective metrics have been used to measure the real performance of them:

Unary metrics: S (convergence), M2* (diversity) and M3* (extension).

Binary metric: C metric to compare each pair of algorithms. Graphical representation of the Pareto fronts.

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Experiments (4)

According to the C metric, the solutions of the Random Search are clearly dominated by the MACS variants.

Among the MACS variants, MACS 0.2 is better than 0.5 and 0.8. Hence a diversity scheme seems to be more appropiate to solve the problem.

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Experiments (5)

With respect to the unary metrics, the MACS algorithm with q0=0.2 achieves better and more vast Pareto fronts, with more diversity and better convergence than in the others.

The graphical representacion is clear as well. MACS 0.2 outperforms the other variants, and for sure, the Random search and the ACS algorithm.

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Current work (1)

We have been working on improving the MACS algorithm to provide the constructive scheme with more diversity.

A new approach was built by introducing a multi-colony philosophy: each ant of the colony behaves in a different way by using different filling threshold.

station 3

A m

station 1

mA

station 2

mA

0.2

0.5

0.9

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Current work (2)

The incorporation of preferences is highly important in multi-criteria real-world problems.

In our case, some problem-specific knowledge is included before the search of the algorithm (a priori approach). It is used to discriminate between solutions with the same objective values.

We applied our MACS approach with preferences to the assembly line of the Nissan Pathfinder engine (industrial plant of Barcelona).

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Current work (3)

As can be seen, MACS with preferences not only reduce the number of equally-preferred solutions, but it is able to converge better to the optimal Pareto set.

Results are even better with the Nissan instance, which has a large number of solutions with the same objective values.

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Concluding remarks

From the obtained results we have found out that the yield of the MACS approach is good enough to solve the problem. The algorithm works better when we use 0.2 as q0 parameter (more diversity).

Now, we have developed a new MACS using a multi-colony technique to get more diverse non-dominated solutions. In addition, preferences have been included in the algorithm to reduce the number of equally-preferred solutions.

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Future work (1)

Apart from our current developments, we would like to include mechanisms to help the MACS algorithm to reach better Pareto sets. For example, local search procedures.

We are also planning to design a novel multi-objective genetic algorithm approach with a constructive generation of the solution to improve the results.

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Future work (2)

However, our most innovative research topic is the inclusion of preferences prior the search to provide the decisor with actually useful solutions for its decision context.

Our MACS algorithm will have to tackle with different decisors from different Nissan manufacturing locations (scenarios) to get only the set of solutions which are actually interesting for a fixed scenario.

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THANKS!