发表机构
Universidad de Sevilla（塞维利亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对具有 $\ell_{p}$-和 $\ell_{q}$-范数的两区域单设施选址问题，提出 $p$-曲线概念并据此改进 MFP 算法为 P-MFP，新算法结果更优。
AI 中文摘要
两点之间的距离由它们之间的测试连接路径的长度给出。然而，在空间 $R^2$ 中，达到该路径的方式并不唯一，该空间被一条直线 $L$ 分成两个区域 $\Omega_p$ 和 $\Omega_q$，分别具有 $\ell_{p}$-范数和 $\ell_q$-范数，其中 $1<p\leq q$ 且 $L\subset\Omega_q$。在本文中，给定一点 $P\in \Omega_p$，我们找到了点 $Q\in\Omega_p$ 的轨迹，称为 $p$-曲线，使得存在两种方式达到 $P$ 与 $Q$ 之间的距离。对于每个 $P\in \Omega_p$，有两条 $p$-曲线，它们是两条不同的 $p$-抛物线的两个分支。这两个分支将 $\Omega_p$ 分成三个子区域，在其中两个子区域中使用三段最短路径。给出了每条 $p$-抛物线的隐式方程。此外，通过使用 $p$-曲线，基于 MFP 算法开发了一种改进算法，称为 P-MFP，用于解决具有 $\ell_{p}$ 和 $\ell_{q}$-范数的两个区域中的单设施选址问题。新算法获得的结果优于 MFP 算法获得的结果。
英文摘要
The distance between two points is provided by the length of their test connecting path. However, there is no unique way to attain this path in the space $R^2$, which is split by a straight line $L$ into two regions, $Ω_p$ and $Ω_q$, with $\ell_{p}$- and $\ell_q$-norms, respectively, where $1<p\leq q $ and $L\subsetΩ_q$. In this paper, given a point $P\in Ω_p$, the locus of points $Q\inΩ_p$, called $p$-curve, is found, such that there are two ways to attain the distance between $P$ and $Q$. For each $P\in Ω_p$, there are two $p$-curves which are two branches of two different $p$-parabola. These two branches split $Ω_p$ into three subregions using a three-link shortest path in two of these regions. The implicit equation of each $p$-parabola is given. Furthermore, by using the $p$-curve, an improved algorithm, called P-MFP, based on the MFP algorithm, is developed in order to solve the single-facility location problem in two regions with $\ell_{p}$ and $\ell_{q}$-norms. The results obtained with the new algorithm are better than those obtained with the MFP algorithm.ike subheadings, citations, or equations are permitted.
