On Solving the Quadratic Shortest Path Problem
نویسندگان
چکیده
منابع مشابه
On Solving the Quadratic Shortest Path Problem
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order m + 1, where m is the number of arcs in the graph. We use the alternating direction method of...
متن کاملOn the Quadratic Shortest Path Problem
Finding the shortest path in a directed graph is one of the most important combinatorial optimization problems, having applications in a wide range of fields. In its basic version, however, the problem fails to represent situations in which the value of the objective function is determined not only by the choice of each single arc, but also by the combined presence of pairs of arcs in the solut...
متن کاملSpecial cases of the quadratic shortest path problem
The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP known as the adjacent QSPP. It was recently proven that the adjacent QSPP on cyclic digraphs cannot...
متن کاملThe Quadratic Shortest Path Problem and its Genetic Algorithm
The quadratic shortest path (QSP) problem is to find a path from a node to another node in a given network such that the total cost includes two kinds of costs, say direct cost and interactive cost, is minimum. The direct cost is the cost associated with each arc and the interactive cost occurs when two arcs appear simultaneously in the shortest path. In this paper, the concept of the quadratic...
متن کاملThe Quadratic Shortest Path Problem: Complexity, Approximability, and Solution Methods
We consider the problem of finding a shortest path in a directed graph with a quadratic objective function (the QSPP). We show that the QSPP cannot be approximated unless P = NP. For the case of a convex objective function, an n-approximation algorithm is presented, where n is the number of nodes in the graph, and APX-hardness is shown. Furthermore, we prove that even if only adjacent arcs play...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: INFORMS Journal on Computing
سال: 2019
ISSN: 1091-9856,1526-5528
DOI: 10.1287/ijoc.2018.0861