Bi-objective Shortest Path Problem Research Articles

Shortest Path Problems with a Crash Risk Objective

With more and more data related to driving, traffic, and road conditions becoming available, there has been renewed interest in predictive modeling of traffic incident risk and corresponding risk factors. New machine learning approaches in particular have recently been proposed, with the goal of forecasting the occurrence of either actual incidents or their surrogates, or estimating driving risk over specific time intervals, road segments, or both. At the same time, as evidenced by our review, prescriptive modeling literature (e.g., routing or truck scheduling) has yet to capitalize on these advancements. Indeed, research into risk-aware modeling for driving is almost entirely focused on hazardous materials transportation (with a very distinct risk profile) and frequently assumes a fixed incident risk per mile driven. We propose a framework for developing data-driven prescriptive optimization models with risk criteria for traditional trucking applications. This approach is combined with a recently developed machine learning model to predict driving risk over a medium-term time horizon (the next 20 min to an hour of driving), resulting in a biobjective shortest path problem. We further propose a solution approach based on the k-shortest path algorithm and illustrate how this can be employed.

Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach

Consider a multiobjective decision problem with uncertainty in the objective functions, given as a set of scenarios. In the single-criterion case, robust optimization methodology helps to identify solutions which remain feasible and of good quality for all possible scenarios. A well-known alternative method in the single-objective case is to compare possible decisions under uncertainty with the optimal decision with the benefit of hindsight, i.e. to minimize the (possibly scaled) regret of not having chosen the optimal decision. In this contribution, we extend the concept of regret from the single-objective case to the multiobjective setting and introduce a proper definition of multivariate (robust) (relative) regret. In contrast to the few existing ideas that mix scalarization and optimization, we clearly separate the modelling of multiobjective (robust) regret from its numerical solution. Moreover, our approach is not limited to a finite uncertainty set or interval uncertainty and furthermore, computations or at least approximations remain tractable in several important special cases. We illustrate all approaches based on a biobjective shortest path problem under uncertainty.

Two new approaches for the bi-objective shortest path with a fuzzy objective applied to HAZMAT transportation.

This work proposes two algorithms to the Bi-objective Shortest Path (BSP) problem, considering a fuzzy objective. Such approaches originally extend two classic label setting algorithms to solve BSP, in particular, the first one using a modified Gandibleux revision of Martin's algorithm and the second one based on the A* algorithm acceleration technique. The proposed extensions differ from the previous classic approaches for two main aspects: the two methods solve BSP problems with a linear objective function and a min-max objective function; the max-min objective considered in the BSP is a fuzzy objective function. This latter aspect represents the main contribution of this paper. The proposed approaches, applied to the selection of paths for the road transport of hazardous materials, generate the set of Pareto optimal solutions among which the decision makers have to evaluate the trade-off between paths with minimum cost and paths with minimum (or min-max) risk. In this paper, a real life case study related to the delivery of petrol from a depot to refueling stations is finally illustrated to compare the effectiveness of the proposed approaches.

A biobjective Dijkstra algorithm

We generalize the Dijkstra algorithm to the Biobjective Shortest Path (BSP) problem. The proposed method keeps only one candidate label per node in a priority queue of size n. In this way, we introduce a novel algorithm to solve the one-to-all BSP problem determining all non-dominated points in the outcome space and one efficient path associated with each of them. For the case of the one-to-one BSP problem, we incorporate the classical bidirectional search scheme in the proposed algorithm to reduce the number of iterations in practice. The proposed algorithm also includes pruning strategies to avoid the computation of unnecessary labels. The result is a fast algorithm to solve the one-to-one BSP problem in large networks. A computational experiment comparing the performance of the proposed method and the state-of-the-art methods is included.

A bio-inspired algorithm for solving bi-objective shortest-path problem

The bi-objective shortest-path problem (BSP) has attracted much attention since its great theoretical significance and wide application. The solution of this problem is to seek for the Pareto-optimal set of paths between two nodes in a graph, in which the edges refer to two attributes. The traditional methods either are highly time-consuming or only find the approximate solutions. In this paper, based on the Physarum Polycephalum model, we propose an algorithm to solve the BSP. By aid of adaptability of the Physarum Polycephalum model, the proposed method can find the multi-shortest paths with a low time consuming. The Pareto-optimal set, obtained from the multi-shortest paths, is the solution of the BSP. To test the performance of the proposed method, we conduct the experiments on some simulative graphs selected from the recently related works. The results show that the proposed method is efficient.

Urban navigation beyond shortest route: The case of safe paths

Advancements in mobile technology and computing have fostered the collection of a large number of civic datasets that capture the pulse of urban life. Furthermore, the open government and data initiative has led many local authorities to make these datasets publicly available, hoping to drive innovation that will further improve the quality of life for the city-dwellers. In this paper, we develop a novel application that utilizes crime data to provide safe urban navigation. Specifically, using crime data from Chicago and Philadelphia we develop a risk model for their street urban network, which allows us to estimate the relative probability of a crime on any road segment. Given such model we define two variants of the SafePaths problem where the goal is to find a short and low-risk path between a source and a destination location. Since both the length and the risk of the path are equally important but cannot be combined into a single objective, we approach the urban-navigation problem as a biobjective shortest path problem. Our algorithms aim to output a small set of paths that provide tradeoffs between distance and safety. Our experiments demonstrate the efficacy of our algorithms and their practical applicability.

Physarum-Inspired Applications in Graph-Optimization Problems

In the past decade, we have witnessed the rapid development of a increasing body of research focused on Physarum polycephalum, which has been employed to solve many complicated problems in real-world applications. In this paper, we give an overview towards the developments of Physarum-inspired models for graph-optimization problems. Specifically, we reported the applications of Physarum in the following graph-optimization problems: influential nodes identification, shortest path tree problem, biobjective shortest path problem, improved Physarum algorithm and approximating the transport network.

An exact method for the biobjective shortest path problem for large-scale road networks

• Recursive exact algorithm that implicitly enumerates all solutions. • Fast method that works well on graphs of up to 1.2 million nodes and 2.8 million arcs. • Consistently outperformed a top-performer benchmark algorithm for real road networks. • Easily extensible to the multiobjective shortest path problem with three or more objectives. The Biobjective Shortest Path Problem (BSP) is the problem of finding (one-to-one) paths from a start node to an end node, while simultaneously minimizing two (conflicting) objective functions. We present an exact recursive method based on implicit enumeration that aggressively prunes dominated solutions. Our approach compares favorably against a top-performer algorithm on two large testbeds from the literature and efficiently solves the BSP on large-scale networks with up to 1.2 million nodes and 2.8 million arcs. Additionally, we describe how the algorithm can be extended to handle more than two objectives and prove the concept on networks with up to 10 objectives.

ALGORITHMS FOR BIOBJECTIVE SHORTEST PATH PROBLEMS IN FUZZY NETWORKS

We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the single objective problem and the third approach is based on dynamic programming. The labeling methods usually producing several nondominated paths, we propose a fuzzy number ranking method to determine a fuzzy short- est path. Illustrative examples are worked out to show the eectiveness of our algorithms.

A bi-objective approach for shortest-path network interdiction

In the literature, solution approaches to the shortest-path network interdiction problem have been developed for optimizing a single figure-of-merit of the network configuration when considering limited amount of resources available to interdict network links. This paper presents a newly developed evolutionary algorithm that allows approximating the optimal Pareto set of network interdiction strategies when considering bi-objective shortest path problems. Thus, the paper considers the concurrent optimization of two objectives: (1) maximization of shortest-path length and (2) minimization of interdiction strategy cost. Also, the paper considers the transformation of the first objective into the minimization of the most reliable path reliability. To solve these multi-objective optimization problems, an evolutionary algorithm has been developed. This algorithm is based on Monte Carlo simulation, to generate potential network interdiction strategies, graph theory to analyze strategies’ shortest path or most reliable path and, an evolutionary search driven by the probability that a link will appear in the optimal Pareto set. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate and validate the approach.

Efficient solution generation for the bicriterion shortest path problems

In this paper, we present an algorithm to compute the set of all efficient extreme solutions in the objective space for the biobjective shortest path problem (BSPP). A simplex-based algorithm that generates all the efficient extreme points and edges in the objective space rather than the decision space is developed. Since not every extreme point of the decision space corresponds to an extreme point of the objective space, the number of these efficient extreme points in the objective space cannot exceed that of the decision space. Since the coefficient matrix associated with the flow conservation equations is totally unimodular for the BSPP, the efficient frontier is the non-dominated set of its continuous relaxation.

A comparison of solution strategies for biobjective shortest path problems

We consider the biobjective shortest path (BSP) problem as the natural extension of the single-objective shortest path problem. BSP problems arise in various applications where networks usually consist of large numbers of nodes and arcs. Since obtaining the set of efficient solutions to a BSP problem is more difficult (i.e. NP -hard and intractable) than solving the corresponding single-objective problem there is a need for fast solution techniques. Our aim is to compare different strategies for solving the BSP problem. We consider a standard label correcting and label setting method, a purely enumerative near shortest path approach, and the two phase method, investigating different approaches to solving problems arising in phases 1 and 2. In particular, we investigate the two phase method with ranking in phase 2. In order to compare the different approaches, we investigate their performance on three different types of networks. We employ grid networks and random networks, as is generally done in the literature. Furthermore, road networks are utilized to compare performance on networks with a structure that is more likely to actually arise in applications.