Advanced strategies on update mechanism of tree-seed algorithm for function optimization and engineering design problems

Abstract

Tree-seed algorithm (TSA) is one of the meta-heuristic algorithms proposed recently. It has a simple but effective structure. However, for complex high-dimensional functions and constrained optimization problems, TSA has the defects of slow convergence rate and low optimization accuracy. To overcome these issues, an improved tree-seed algorithm (SATSA) based on Nelder-Mead simplex method is proposed. Firstly, appropriately increase the value of the control parameters that balance exploration and exploitation, thereby improving the local search ability of TSA, and introduce an adaptive stochastic component of Gaussian distribution in the seed generation formula of the local search stage. Then, set the maximum retention times of each tree, for trees that exceed the maximum retention times in continuous iterations, increase the number of seeds produced by this tree, then use a new equation based on the global optimal location to generate seeds, thereby speeding up the convergence of the algorithm. Finally, after all trees produce seeds, introduce the improvement strategy with Nelder-Mead simplex method into some poor quality solutions, so that the solution with poor quality is searched deeply in the neighborhood, speeding up the process of moving the overall solution to the optimal solution. Its convergence is proved by theoretical analysis, and certifies that the time complexity of SATSA is not increased compared to TSA. The simulation results of 6 advanced algorithms on CEC2017 test suite and 10 challenging engineering constrained optimization problems demonstrate that the three strategies proposed in this study are feasibility and effectiveness.