Orthogonal successive approximation method for solving global optimization problem

Abstract

The invention provides an orthogonal successive approximation method based on orthogonal experimental design and variable metric neighborhood search. The orthogonal successive approximation method comprises the following steps of setting an initialization parameter, and selecting a proper orthogonal table according to solved problem dimensions and discrete level numbers; conducting orthogonal experiments within a feasible region by beginning from an initial point x0, and calculating each experimental scheme through evaluation by adopting a penalty function method; selecting a new iteration point from the experimental schemes; if x1 is superior to x0, then allowing x0 to be equal to x1, and enlarging the step size in search to enhance global search at the same time; otherwise, shrinking search space to enhance local search; repeating the steps, and repeatedly iterating to successively approximate a global optimal solution until convergence conditions are met. The invention provides the orthogonal successive approximation method for solving a global optimization problem, has the advantages of simple principle, fewer calculating parameters, high convergence speed and the like and can be used for rapidly acquiring the optimal solution or the approximate solution of the global optimization problem.

Description

technical field [0001] The invention relates to an orthogonal successive approximation method for solving a global optimization problem by combining an orthogonal test and a neighborhood search, and belongs to the field of optimization methods. technical background [0002] The global optimization problem is a kind of planning problem with a wide range of engineering application backgrounds, and its description is as follows: [0003] min f(x) (1) [0004] s.t.g i (x)≤0, i=1,2,...,m (2) [0005] h j (x)=0,j=1,2,...,p (3) [0006] x ∈ X ⋐ R n - - - ( 4 ) [0007] where x=(x 1 ,...,x k ,...,x n ) T ; Use S to represent the feasible region, namely [0008] S={x|g i (x)≤0; h j (x)=0} (5) [0009] Practical engineering problems usually contain complex constraints. The objective function is generally nonline...

AI Technical Summary

Problems solved by technology

[0009] Practical engineering problems usually contain complex constraints. The objective function is generally nonlinear, discontinuous, and non-differentiable, and its derivative or gradient information cannot be obtained. It is difficult to directly use traditional gradient-based optimization methods to solve it.

Evolutionary algorithms (such as genetic algorithms, particle swarm optimization, etc.) only use fitness function information without calculating directional derivatives or finite difference approximations to gradients. They have the characteristics of simple methods, strong robustness, and wide application range. Solve global optimization problems, but there are problems such as premature convergence and easy to fall into local optimum, so there is an urgent need to develop new and efficient optimization methods

Images