An Algorithm for the Minimum Robust Cost Path on Networks with Random and Correlated Link Travel Times

Abstract

Transportation networks are subject to a large degree of uncertainty due to traveler behavior, recurring congestion, capacity variability (construction zones, traffic incidents), variation in demands, etc.. resulting in unstable and unpredictable trip travel times. This has led to an emphasis on travel time reliability as a key determinant of route choice and an important measure of system performance, thus motivating research on optimizing travel time reliability on such stochastic networks. In this context, this work proposes an algorithm to compute the path of minimum robust cost (defined as a weighted combination of mean squared and variance of path travel time) on a network with stochastic and correlated link travel times.The proposed approach involves transforming the robust cost objective to a link separable or sum of squares form. Based on this formulation, a related multiple objective optimization problem is defined, and it is shown that the optimal robust cost path must lie in the non-dominated solution set of the multiple objective problem. Thus, a label correcting procedure for the multicriteria shortest path problem is applied to compute the non-dominated set and hence, the path of minimum robust cost. In addition, a new criterion of dominance is proposed (permutation invariant non-dominance or PIND) to reduce the size of the non-dominated path set while maintaining optimality with respect to the robust path problem. An approximate label correcting type procedure is developed to compute this reduced path set. Empirical experiments on a real-world network indicate that the PIND path set is significantly smaller than the corresponding ND set (between 60% and 95% on tested networks). In addition, computational tests on synthetic networks of size up to 1,500 nodes (7,500 links) demonstrate the efficiency of the proposed heuristic (computational time < 35 s) in computing the path of minimum robust cost on sparse/moderately dense (links to nodes ratio < 5) networks of size less than 500 nodes. The study also underscores the role of variability, correlations, and risk attitudes on benefits obtained from minimizing robust cost, and the suboptimality of the independence assumption.