A new filled function for global optimization and its deterministic efficiency in solving the facility layout/location problem

Abstract

Although many real-world problems can be modelled as optimization problems, the multimodal nature of such problems and the fact that traditional algorithms are often trapped within local minima make it very difficult to solve these problems. The filled function method is one of the highly effective deterministic global optimization techniques that can overcome such difficulties. However, it is known that the use of non-differentiable and parameter-sensitive filled functions in the solution of global optimization problems could cause high time and computational costs. In this study, a continuously differentiable filled function is proposed to overcome such disadvantages. In addition, for the first time in the literature, the solution of the facility layout problem has been introduced using the filled function method. Moreover, it has been shown in the numerical experiment that, even with more than twenty facilities, this problem can be solved within a very satisfactory time and computational cost.