دانلود رایگان مقاله همگرایی الگوریتم بهینه سازی چند متغیره

Abstract

In this paper, we introduce a new global optimization method and study its global convergence property through theoretical and experimental approaches. The proposed method is named as multivariant optimization algorithm (MOA) because the intelligent searchers, which are called as atoms, not only are divided into multiple subgroups but also are variant in responsibility. That is, global atoms explore the whole solution space in the hope of finding potential areas where local atoms start the local exploitation. The proposed method is characterized by two important features. On one hand, global atoms do the global exploration in each loop to jump out from local traps. On the other hand, global and local atoms conduct the global exploration and the local exploitation according to their own responsibility, respectively. These features contribute to increasing the chance of converging to the global best. To study the convergence property of MOA, we carried out the convergence analysis, numerical optimization experiments and the shortest path planning experiments. And the results demonstrate that MOA is globally convergent and superior to the compared methods in the global convergence accuracy and probability in solving complex challenging problems which have one or more features such as deceptiveness, randomly located optimum, asymmetry or multiple traps.

6. Conclusion

We present a detailed description and convergence proofs of a new “basic” heuristic method in this paper. The proposed method is characterized by two features: global atoms explore the whole solution space in each loop; multivariant search groups carry out the global exploration and the local exploitation respectively. These features enable MOA to discourage the premature convergence and to settle the contradiction between the global exploration and the local exploitation. The global convergence property of this characteristic method is proved through the convergence analysis and the experiments. The results against some peer optimization algorithms demonstrate the superior performance of MOA in the global convergence accuracy and probability for complex challenging problems. In summary, MOA is a global convergence method for global optimization problems. As a “basic” framework, MOA is light and compact. The parameters in MOA are suggested to be set as follows: TL equals 1–2 times the dimension of problems, r equals 0.05–0.1 times the absolute difference between the high value and the low value of the search ranges. MOA is characterized by that the global and local atoms conduct the alternate global exploration and local exploitation, respectively. As a result, MOA is suitable for solving complex challenging problems, butit doesn’t do well in solving simple problems such as the unimodal problems or the simple multimodal problems with unimodal envelop. To improve the convergence accuracy of MOA, future studies will consider the integration into the presented “basic” framework of more advanced adaptive local search techniques or using other explicitly, implicitly or automatically local search intensity.