A Global Optimization Fractal-based Algorithm And Its Application

The global optimization problem is a task which has been researched andstudied for many years. It is commonly found in all areas of real life,such asfinance,aerospace,civil engineering. The demands for optimizing is more and morehigh,and many traditional optimization methods are difficult to adapt theseproblems which are discontinuous,no-linear,or with high dimension,so seeking newoptimization method has been an important research direction of many fields.Atpresent the methods of solving optimization problems are divided into two kinds,deterministic algorithm and random algorithm,which have different scope ofapplication according to the characteristics of problems.Generally,randomalgorithm is some kind of simulation of natural phenomenon.Its’ demand for theproperties of problems’ objective function is very low,even no demandsometimes,so it can solve those hard problems. Heuristic algorithm is one kind ofrandom algorithm,and its good application speed up people’s steps to explorevarious optimization method.In recent years,some scholars used fractal in the area of optimization,andattempted to deal with complex problems using fractal.Fractal algorithm is a kindof deterministic algorithm,it search for optimal solution by dividing the feasibleregion iteratively.It is only appropriate for simple problems with low dimension.For high dimensional and complex problems in today’s society,it is almostpowerless. In order to break this situation, this paper proposes an improved fractaloptimization algorithm, this algorithm simulates the nature "fractal growth"phenomenon, changes the original algorithm segmentation strategy completely, andbrings in a growth hormone factor to accelerate convergence speed. After threeclassic function optimization experiment, we can find that fractal optimizationalgorithm is better than the original method,and is more suitable for problems withhigh dimensional.Finally,we try to resolve combinational optimization problemusing this algorithm. The actual problem is more complex than simple functionformula, and its’ solution space is discrete, the feasible region need more specialprocessing.When apply this algorithm in the traveling salesman problem,resultsshow that it is feasible and practical.