Research On Filled Function Algorithms For Global Optimization Problems

Many practical problems in social life can be transformed into numerical solutions of global optimization problems,but there are usually many local minimum points in global optimization problems,which makes it extremely difficult to find global minimum points.In view of this,many domestic and foreign researchers have put forward various solving methods.Among them,the filled function algorithm is an effective and simple global optimization method.In this paper,the relevant research of the filled function algorithms are mainly carried out for four kinds of global optimization problems.The details are as follows:1.To solve the continuous unconstrained optimization problem,a continuously differentiable parameterless filled function without exponential and logarithmic terms is constructed,and its analytical properties are analyzed.Then,combining with the appropriate local minimization method,a new filled function global optimization algorithm is proposed,and its effectiveness is verified by a large number of numerical experiments.2.For the integer unconstrained optimization problem,a parameterless filled function is constructed and its analytic properties are analyzed.Then,by combining with a discrete local minimization algorithm,the corresponding filled function algorithm is established.Numerical experiments show that the algorithm is effective and feasible,and has stronger computational power than the existing algorithms.3.Aiming at the continuous constraint optimization problem,a single parameter filled function with continuity and differentiability is constructed,so as to design a global optimization algorithm.Its parameter values should be greater than 0 and as small as possible,so that the infeasible points and feasible points with the objective function value greater than the current minimum value are filtered out.Finally,the effectiveness of the algorithm are verified by numerical experiments.4.For the integer constrained optimization problem,it is converted into an optimization problem with box constraints by a two-stage reconstruction,and a parameterless filled function with the same local minimum as the objective function is constructed for it,so as to construct a new filled function algorithm.Numerical experiment results show that the algorithm is effective and feasible.