In many global optimization techniques, the local search methods are used for different issues such as to obtain a new initial point and to find the local solution rapidly. Most of these local search methods base on the smoothness of the problem. In this study, we propose a new smoothing approach in order to smooth out non-smooth and non-Lipschitz functions playing a very important role in global optimization problems. We illustrate our smoothing approach on well-known test problems in the literature. The numerical results show the efficiency of our method.
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Figure 1.
(a) The green and solid graph is the graph of
Table 1.
The values of
Table 2. Table of minimization process of the Example 1
Table 3.
The values of
Table 4. Table of minimization process of the Example 2
Table 5. The list of non-smooth test problems
Table 6. The numerical results for the non-smooth test problems
Problem | AFA | GDA | ||||||
No. | f.eval | Time(sec) | f.eval | Time(sec) | ||||
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