http://www.civil.uwaterloo.ca/iTSS/papers/2006-3%20(Review%20of%20heuristic%20SPA).pdf

Heuristic shortest path algorithms for transportation applications: state of the art

A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food

The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the time-dependent shortest-path problem. A time-dependent graph GT is a graph that has an edge-delay function, wi, j(t), associated with each edge (vi, vj), to be stored in a database. The edge-delay function wi, j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A user-specified query is to ask the minimum-travel-time path, from a source node, vs, to a destination node, ve, over the time-dependent graph, GT, with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT. The challenge of this problem is the added complexity due to the time dependency in the time-dependent graph. That is, edge delays are not constants, and can vary from time to time. In this paper, we propose a novel algorithm to find the minimum-travel-time path with the best departure time for a LTT(vs, ve, T) query over a large graph GT. Our approach outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice. We will discuss the design of our algorithm, together with its correctness and complexity. We conducted extensive experimental studies over large graphs and will report our findings.

/pdf/finding-time-dependent-shortest-paths-over-large-graphs-1hykyzjul6.pdf

Finding time-dependent shortest paths over large graphs

This paper proposes and solves the Time-Interval All Fastest Path (allFP) query. Given a user-defined leaving or arrival time interval I, a source node s and an end node e, allFP asks for a set of all fastest paths from s to e, one for each sub-interval of I. Note that the query algorithm should find a partitioning of I into sub-intervals. Existing methods can only be used to solve a very special case of the problem, when the leaving time is a single time instant. A straightforward solution to the allFP query is to run existing methods many times, once for every time instant in I. This paper proposes a solution based on novel extensions to the A* algorithm. Instead of expanding the network many times, we expand once. The travel time on a path is kept as a function of leaving time. Methods to combine travel-time functions are provided to expand a path. A novel lower-bound estimator for travel time is proposed. Performance results reveal that our method is more efficient and more accurate than the discrete-time approach.

/pdf/finding-fastest-paths-on-a-road-network-with-speed-patterns-3i1qpen9e4.pdf

Finding Fastest Paths on A Road Network with Speed Patterns

Path planning in construction sites: performance evaluation of the Dijkstra, A∗, and GA search algorithms

Shortest paths in a network with time-dependent flow speeds

A label-setting algorithm for finding a quickest path

An ε-sensitivity analysis in the primal–dual interior point method

In a hierarchical road network, all roads can be classified into two groups according to their attributes, such as their speed limit and the number of lanes. By splitting the whole network into high-level and low-level subnetworks, the size of the road network to be searched can be reduced, and more human-oriented paths can be obtained. In this paper, we define a convenient path in the hierarchical road network and propose an algorithm for finding that path. The proposed algorithm produces a convenient and approximately shortest path with little computational effort by reducing the number of nodes to be considered. The difference between the length of the paths produced by the proposed algorithm and by existing algorithms and that of the shortest path of the whole network is discussed. Some experimental results are given to show the efficiency of the proposed algorithm.

Finding a path in the hierarchical road networks

Positive sensitivity analysis (PSA) is a sensitivity analysis method for linear programming that finds the range of perturbations within which positive value components of a given optimal solution remain positive. Its main advantage is that it is applicable to both an optimal basic and nonbasic optimal solution. The first purpose of this paper is to present some properties of PSA that are useful for establishing the relationship between PSA and sensitivity analysis using optimal bases, and between PSA and sensitivity analysis using the optimal partition. We examine how the range of PSA varies according to the optimal solution used for PSA, and discuss the relationship between the ranges of PSA using different optimal solutions. The second purpose is to clarify the relationship between PSA and sensitivity analysis using an optimal basis, and the relationship between PSA and sensitivity analysis using the optimal partition. We show that sensitivity analysis using the optimal partition is a special case of PSA, and its properties can be derived from the properties of PSA. The comparison among the three sensitivity analysis methods will lead to a better understanding of the difference among sensitivity analysis methods.

/pdf/positive-sensitivity-analysis-in-linear-programming-2u7zfooil5.pdf

Soondal Park

Papers

Shortest paths in a network with time-dependent flow speeds

A label-setting algorithm for finding a quickest path

An ε-sensitivity analysis in the primal–dual interior point method

Finding a path in the hierarchical road networks

Positive sensitivity analysis in linear programming