Parameter-free Filled Tunnel Function Methods For Solving Two Classes Of Optimization Problems

The auxiliary function method is a deterministic global optimization algorithm,which has attracted the attention of scholars because of its simple form and convenient calculation.However,most of the constructed auxiliary functions currently have parameters,the parameters are not well controlled,and improper control will restrict the efficiency of the algorithms.Therefore,the thesis mainly studies the parameter-free auxiliary function method,constructs two new classes of parameter-free auxiliary functions by combining the filled function with the tunnel function,and proposes the corresponding global optimization algorithms.The specific research content is as follows:First of all,this paper introduces the basics of global optimization problems and several global optimization algorithms.Secondly,for the continuous unconstrained global optimization problems,a new class of auxiliary functions combining the characteristics of filled and tunnel function are constructed,which are named filled-tunnel functions.This class of functions are continuously differentiable without parameters and exponential terms.Based on the filled-tunnel functions,a new global optimization algorithm is proposed,and numerical experiments are carried out on the algorithm.The numerical experiment results show that the algorithm is feasible and effective.Subsequently,for optimization problems with equality and inequality constraints,a new class of filled-tunnel functions is constructed based on the idea of penalty functions.Some properties of the new class of filled-tunnel functions are analyzed,a new global optimization algorithm based on the new filled-tunnel functions is proposed.And numerical experiments are carried out on the algorithm.The feasibility and effectiveness of the algorithm are verified by some examples.Finally,the research work of this paper is summarized,and the follow-up work is expected.