The working of the model is illustrated as follows:
ALGORITHM 3 : COMOEATS ALGORITHM

![0_image_0.png](0_image_0.png)

The model that we propose works in three parallel components:

 The first uses a multi-objective evolutionary algorithm (SPEA) that, each time, generates a Pareto front increasingly improved. This algorithm performs global search and discovers multiple optimal solutions.

 An ITS, receives a non-dominated solution taken at random from the Pareto Front generated by the SPEA 
algorithm to be the topic of improvement. For each iteration, the neighborhood of the current solution is generated by keeping only non-dominated solutions that belong to the intensification zone fig 2. There are two cases: 
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*The neighborhood includes a solution dominating S0, which, in this case, will be the new solution of departure. 

*There isn't any solution that dominates S0, and in this case a solution from neighborhood will be taken as the one of departure. These stages will be reiterated until a maximum number of iterations are reached. 

![0_image_3.png](0_image_3.png)

 In the bi-objective case, the DTS detects the two most distant and successive points of the pareto front (either SL1 or SL2), calculates the middle vector cost of these points (Cm), 
and then marks the best solution belonging to the hatched dominant zone Cm , fig.3.

![0_image_1.png](0_image_1.png)

For all individuals generated by the DTS and ITS, a 

![0_image_2.png](0_image_2.png)

mechanism of selection decides that a new improved individual must be introduced in the population archives. This last will be taken as an initial solution for the SPEA method in the following iteration.

Fig.4: Diagram of basis of the COMOEATS model
V. EXPERIMENTAL RESULTS:
Our COMOEATS model has been programmed with Visual C++, executed on computer network using the MPI library (Message Passing Interface).

 For each 10 iterations (determined by user) of SPEA 
algorithm, the solutions of Pareto front obtained will be improved by the Intensificator and Diversificator tabu search. 

Then, new solutions will be integrated in the next population.

The parameters of the method are illustrated in the following table:

 The DTS detects a less explored zone of the search space and performs a local search in order to discover new solutions.