利用光滑函數優化歐幾里得 κ-中心選址問題

Abstract

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Facility location is a pivotal problem in many majors, which helps optimize single or multiple facilities to adapt to the set of demand points. Some common issues have been researched and widely applied, such as 1-center and 1-median. Our research concentrates the problem of locating a single facility in R^n based on the k-centrum Euclidean criterion, known as the generalize of those above problems. Specifically, we determine k locations to minimize the maximum weighted distance to a given set of points. In this research, we apply smoothing functions to approximate the objective function.The primary contribution of this research lies in a comprehensive theoretical and numerical evaluation of various smoothing functions, which leads to the identification of more effective choices. In addition, the proposed smoothing techniques are applied to address the Euclidean K-centrum optimization problem for placing a single facility.