PSI - Issue 37

Iulian Constantin Coropețchi et al. / Procedia Structural Integrity 37 (2022) 755 – 762 Coropetchi et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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4. Results and discussion In Fig. 7 are presented some results obtained with the Greedy algorithm and the first formulation of the objective function. If we analyse the obtained results, we can certainly say that this formulation of the objective function is a weak one because it rarely reaches the known maximum point, and the obtained final distribution is very much dependent on the initial distribution.

Fig. 7. Results obtained with the first formulation of the objective function.

If we place the solutions obtained with the first formulation on the graph representing all the possible solution obtained with the brute force approach, we can see that they are not even close to the Pareto frontier and so we can say that this combination of a Greedy algorithm and this formulation of the objective function is not a recommended one for solving the proposed problems. The next step was to modify the formulation of the objective function and to test if other formulations can present better results. In Fig. 8 are presented some of the results obtained with the Greedy algorithm and the third formulation of the objective function. Unlike the previously analyzed formulation, this one behaves better because most of the times it reaches one of the best solutions or one on the Pareto frontier. The evolution of the objective function value and the distribution of the two materials for the three tests are presented. We can observe that this formulation does not provide an optimal solution in all cases (only for two presented tests the optimum solution known from brute force is reached, or very close to the maximum objective function), so we can say that the process needs further improvement to be validated as to scale it and use it without the need of a brute force approach.

Fig. 8. Results obtained with the third formulation of the objective function.