PSI - Issue 37

Alexandru Vasile et al. / Procedia Structural Integrity 37 (2022) 857–864 Vasile et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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of the objective function obtained through brute force, red dots are results from the Greedy algorithm while black and white are the results from the simulated annealing algorithms. The latter differ between them in the sense than one compares the acceptance probability of a worse solution with a random number between 0 and 1 while the other compares it with an imposed value. If the value is closer the 1 the chance of acceptance is lower, so it results a fast simulated annealing, while if the value is closer to 0, the chance of acceptance is higher so the algorithm searches for a longer time. In our study we defined a medium value of 0.5. If the value is set to 0.001 the algorithm transforms itself in a kind of brute force algorithm, but the time needed to run it also increases.

Fig. 4. Simulated annealing algorithm structure based on the Greedy algorithm.

One can notice in Fig.5 that the algorithm with the lowest score, whose points are at a lower level on the graph, is the Greedy algorithm, followed by the SA where we use a random number as acceptance trigger, which hit 3 global maxima out of 10 runs (SA algorithm (1)), and the best results were obtained through a SA where the trigger was set at 0.5, which hit 6 global maxima out of 10 runs (SA algorithm (2)).

Table 2. Comparison between the Greedy and Simulated annealing results. Values of objective functions are in MPa. Iter/ obj_fct Inital - 15.51 Iter 1 - 2739.19 Iter 2 - 2946.50 Iter 3 - 3169.86 (FINAL)

Greedy Modified

Time

106.97 s