MIP經典問題:旅行商問題 (traveling salesman problem)
*本文主要記錄和分享學習到的知識,算不上原創。
*參考文獻見鏈接。
旅行商問題、背包問題都是0-1規劃問題中最為經典的問題。
通常來說,當我們學習並熟悉一種求解混合整數問題的技巧時,可以用這種技巧來求解旅行商問題或者背包問題,以此來驗證自己對該技巧的掌握程度。
目錄
什麽是旅行商問題
旅行商問題的數學模型
什麽是旅行商問題
定義
Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?
時間復雜度
分類
其中,sTSP是最簡單的TSP問題。
旅行商問題的數學建模
Integer programming formulation of sTSP
變量
This formulation associates a binary variable xij with each edge (i, j), equal to 1 if and only if the edge appears in the optimal tour. The formulation of TSP is as follows.
模型
Integer programming formulation of aTSP
變量
xij is a binary variable, associated with arc (i,j) and equal to 1 if and only if the arc appears in the optimal tour.
模型
參考文獻
https://en.wikipedia.org/wiki/Travelling_salesman_problem
Traveling Salesman Problem, Theory and Applications, Edited by Donald Davendra p. cm.ISBN 978-953-307-426-9
MIP經典問題:旅行商問題 (traveling salesman problem)