Optimization methods

 

 

Date

30/05/2007

Author

F. Moussouni, T. V. Tran, S. Brisset, P. Brochet

Affiliation

L2EP – EC Lille – France

Email

fouzia.moussouni@ec-lille.fr, tran.tuan-vu@ec-lille.fr, stephane.brisset@ec-lille.fr

Method

Exhaustive Enumeration (EE) method

References

[1]  P. Venkataraman, Applied Optimization with Matlab̉ Programming, A Wiley - Interscience publication, John Wiley & Sons, New York, 2001.

[2]  “Distributed computing Toolbox for use with Mathlab̉ ”, User’s Guide version 3, The MathWorks Inc, 1984-2006.

Description of the method

Exhaustive enumeration method (EE) [1] is the simplest of the combinatorial optimization techniques. The principle of this method is to evaluate all combinations of the discrete variables. The total number of evaluation ne is:

(1)

 

nd is the number of discrete variables, pi is the preestablished set of discrete values. The optimal solution obtained is thus the minimum value by scanning the list of feasible solutions. This method assures the global optimum, but the computational time is very huge.

To handle the CPU times of this approach, the Matlab® distributed computing toolbox and the Matlab® distributed computing Engine [6] are used to speeding up execution of this optimization problem.

Fig. 1. Basic Distributed Computing configuration

Using these Matlab® distributed computing product, the ne independent evaluations are executed simultaneously on a cluster of 8 computers.

Therefore 62 tasks are created for each combination of lamination and frame {a, b, c, d}. Then, the exhaustive enumeration with the remainder combinations {S1, S2, n1} is launched with every combination {a, b, c, d} or task. These tasks form a job. This job and their 62 tasks are defined and performed in a Matlab® client session. The Matlab® distributed computing engine performs the execution of the job by evaluating each of their 62 tasks and returns the result to the client session.

The job manager is the part of the engine that distributes the tasks for evaluation to the Matlab® workers. In this study, only 8 workers (or computers) are used to evaluate 246,078,000 combinations.

Publication of the method

 

 

 

 

BACK