利用分形求约束问题的全局最优解

给出了几种基本几何图形的分形构造方法，并利用这种方法给出一种求解约束优化问题全局最优解的直接解决，算例表明，与一般的优化问题解法相比较，分形算法具有完全不依赖初始点、适用于任何以任意多边形或多面体为约束条件的非线性优化问题的优点。该方法充分利用了分形可以填满任意三角形、四面体等基本几何图形的这一特性。它可以很容易地推广到约束条件为平行四边形、平面上任意多边形以及三维以上空间中任意多面体或超多面体的优化问题上。

The solution of the restricted optimization problem with a fractal

The formation method of several basic geometric figures with fractal is given. By this method ,a new direct method for searching the global optimum of the restricted optimization problem is presented, which is called the Fractal algorithm. At the same time, a few examples show that the fractal method has the advantage over the common method, that it is not only independent of initial point but also adaptable for any nonlinear problem with an arbitrary polygon or polyhedral as the constraint condition. This algorithm makes full use of the characteristic that an arbitrary triangle, a tetrahedron or other basic geometric graphics can be filled by a fractal. It can be easily extended to an optimization problem subjected to a parallelogram, an arbitrary polygon in plane or an arbitrary polyhedral in space. Here the triangle and the tetrahedron are used as the constraint conditions.