Yu Chung Sim, a lecturer at the Faculty of Applied Mathematics, has studied a method to increase the convergent speed of global optimization.
The filled function method is an effective method to get the global optimization solution to multi-dimensional optimization problems.
One of the major problems to be solved in the search for a global optimization solution to multi-dimensional optimization problems is how to escape from the given local minima into a better one.
To solve this problem, a number of methods including Orbit method and Tunneling method have been investigated. Among them the filled function method has been admitted as an effective one and thus, it has been undergoing further study.
The filled function method was first applied to unconstrained nonlinear programming problems, followed by constrained nonlinear programming problems, non-smooth optimization problems and discrete optimization problems.
At present, in order to improve the effectiveness of the global optimization solution search algorithm using a filled function, many scientists have been looking for methods to combine various methods including the filter method and the interior point method with the filled function method.
The main problem of the filled function method is how to construct an auxiliary function called filled function at the given local minima of the objective function obtained from every repetition of the algorithm.
For this, filled functions with one parameter and those with two parameters were proposed, but they are difficult to control when they have more parameters
Recently, a new filled function method that skips the process where they used to get better minima by minimizing an objective function from the local minima of the filled function in the prior algorithms is being applied to continuous optimization problems.
As seen above, you can see that the filled function method can be applied to the global optimization problems arising in practice if we introduce filled functions with few parameters in the continuous optimization problems as well as discrete optimization problems, non-convex optimization problems and non-smooth optimization problems.
Therefore, she has proposed a new filled function that comes from the idea that an objective function and a filled function have the same stationary points and applied it to finding a global minimum solution to constrained nonlinear programming.
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