The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multiobjective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algori...

The Inverse Shortest Path (ISP) problem has recently been considered for applications involving the precise determination of unknown path costs, given only limited experts' knowledge of some shortest paths. Unlike previous approaches which are usually restrictive (such as the minimum change requirement) and algorithmically complicated, a more general but simple optimization scheme based on embe...

During the last years, impressive progress has been achieved in the field of algorithm engineering. A problem becoming more and more important is that of data dependency: the performance of an algorithm often highly depends on the input. Yet, for a given input, it is highly non-trivial to select the best solving strategy. In this work, we introduce a new methodology for evaluating speed-up tech...

Robust optimization is a widely studied area in operations research, where the algorithm takes as input range of values and outputs single solution that performs well for entire range. Specifically, robust aims to minimize regret , defined maximum difference between solution’s cost an optimal hindsight once has been realized. For graph problems P such shortest path minimum spanning tree, polyno...

In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph D = (V,A) and a set K of directed commodities, an USPR is a set of flow paths Φ(s,t), (s, t) ∈ K, such that there exists a metric λ = (λa) ∈ Z+ with respect to which each Φ(s,t) is the unique shortest ...

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality, introducing nonlinear, nonconvex constraints. We examine the Robust Two-Path Problem, which seeks to establish two paths between a source and destination node wherein...

We study the problem of finding the next-to-shortest paths in a graph. A next-to-shortest (u, v)-path is a shortest (u, v)-path amongst (u, v)paths with length strictly greater than the length of the shortest (u, v)path. In constrast to the situation in directed graphs, where the problem has been shown to be NP-hard, providing edges of length zero are allowed, we prove the somewhat surprising r...

The Delay Constrained Least Cost (DCLC) problem is to find the least cost path in a graph while keeping the path delay below a specified value. First formulated in the context of routing in computer networks, the DCLC model also applies to mission planning and other decision problems. DCLC is NP-complete and therefore many heuristic algorithms have been proposed for it. This paper presents two ...

We introduce approximation algorithms and strong NP-completeness results for interdiction problems on planar graphs. Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded graph. We give a multiplicative (1+ǫ)-approxi...