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TABLE.1: EXPERIMENTAL PARAMETERS

| SPEA                                                                                                                | TS                     |
|---------------------------------------------------------------------------------------------------------------------|------------------------|
| -size of the initial population: 100                                                                                | -size tabu list: 50    |
| individuals                                                                                                         | -number of iterations: |
| -size of the population archives:                                                                                   | 200                    |
| 100 individuals                                                                                                     | -Tabu life: 50         |
| - number of generations: 400 - probability of crossover: 0.9 -probability of mutation: 0.01 Binary -coding: 16 bits |                        |

| COMOEATS     | SPEA      |           |
|--------------|-----------|-----------|
| Contribution | 0 .507042 | 0.492958  |
| Entropie     | 0.367399  | 0.360803  |
| Spacing      | 0.0256606 | 0.0203861 |
| Métrique S   | 0.55787   | 0.5524335 |

We compare our COMOEATS method to SPEA method 
(experimentations are done on bi-objective test functions: ZDT1, ZDT2, and ZDT3). Then, we present and discuss the Pareto Front generated by every method for each function [7].

The following table presents a set of experimentations achieved on benchmarks. We use the following metrics:
Contribution: It evaluates the proportion of Pareto solution brought by each of the two foreheads F1 and F2 [5].

Entropy: The entropy uses the notion of nest to evaluate the distribution of solutions on the Pareto front. Closer to 1 the gotten value is, better is the distribution.

Spacing: This metric is based on a calculation of the distance between solutions. It permits to measure the uniformity of the distribution of points of the compromise surface in the space of objectives [6]. Used with other measures, it gives an interesting indication on the convergence of the method used.

Metric S: This metric uses a reference point while calculating the hyper-volume of the multi-dimensional region comprised between the Pareto front and the reference point [6].

-ZDT1: this problem has a convex POF
TABLE.2 : METRICS FOR ZDT1 According to this representation, we notice an advantage of our model in relation to SPEA at the level of the two metrics contribution and entropy. This difference implies a better distribution of solutions on the Pareto front.

 This improvement became clearer in fig.5, where we succeeded to visit unexplored zones by SPEA and get various solutions. On the other hand, our hybrid model bust a great number of solutions that cover all the front, thence the hypervolume hand from 0.5524335 to 0.55787.

-ZDT2: this problem has a non-convex POF:
TABLE.3 : METRICS FOR ZDT2

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SPEA (Case of ZDT2)
For this type of problems, we notice a remarkable improvement particularly at the level of new solutions discovered by our model. At the same time, there remain some less discovered parts. For this reason, we must use several Diversificator tabu searches.

| COMOEATS     | SPEA      |           |
|--------------|-----------|-----------|
| Contribution | 0.507092  | 0.492958  |
| Entropie     | 0.371775  | 0.360803  |
| Spacing      | 0.0276606 | 0.0203861 |
| Métrique S   | 0.55689   | 0.5524335 |
