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For all fixed-dimension multimodal functions, LMFO can give the best solution in terms of Best.
In addition, the convergence rate of LMFO on the fixed-dimension benchmark functions with 2-dim can be shown in Figures 16-19.
Since constraints are one of the major challenges in solving real problems and the main objective of designing the LMFO algorithm is to solve real problems, two constrained real engineering problems are employed in the next section to further investigate the performance of the MFO algorithm and provide a comprehensive study.
There are some inequality constraints in real problems, so the LMFO algorithm should be capable of dealing with them during optimization.
The results of Table 10 show that the LMFO algorithm is able to find the best optimal design compared to other algorithms.
According to this table, the LMFO and HCPS algorithms can find a design with the minimum weight for this problem.
In this paper, an improved version of MFO algorithm based on Leevy-flight strategy, which is named as LMFO, is proposed.
According to the values of Best, Worst, Mean, and Std and p values in Section 4, the LMFO algorithm significantly outperforms others in terms of numerical optimization.
As we can see in Section 4, the LMFO has been demonstrated to perform better than or highly competitive with the other algorithms.
Since the search space of these problems is unknown, these results are strong evidences for the applicability of LMFO in solving real problems.
In our study, nineteen benchmark functions have been applied to evaluate the performance of LMFO. We also test our proposed method on the real-world engineering problems.
As shown in Section 4, LMFO is very efficient with an almost exponential convergence rate and the results were compared to a wide range of algorithms for verification.
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