A Hybrid Method Combining Tab Search and Nelder-Mead Algorithms for Global Continuous Optimization Problems

A hybrid method combining tabu search (TS) and Simplex NeIder-Mead (NM) has been proposed for solving global continuous optimization problems. Similar to enhanced continuous tabu search (ECTS) method, the proposed method works in three sequential phases: diversification, semi-intensification and intensification. TS strategy just works in the diversification. NM strategy works not only in semi-intensification but also in intensification which is different from other hybrid methods where NM strategy is just applied in the third phase. In the first phase, we proposed four methods to generate neighbors. The first numerical experiment comparing the results of four methods of neighbor generation is carried out and three important conclusions are given. First, the proposed hybrid method has a good performance in solving the global continuous optimization problems. Second, the right direction of neighbors is more important than its right hierarchy for most functions. Third, the spiral method to generate neighbors has the moderate performance both in the robustness and in the calculation speed. To compare the proposed hybrid method to the best and the most recent other published hybrid methods, the second numerical experiment with spiral method to generate neighbors is carried out. The comparison shows that our hybrid method is better than other methods when the dimension of the functions is no more than 4. Moreover, although the dimension is more than 4, it is not worse than many of them.