José Luis Santos

DEVIATION ALGORITHMS FOR RANKING SHORTEST PATHS

The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K>1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction in considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition – for example, to be loopless. In this paper new algorithms are proposed for the uncontrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths.

An algorithm for the quickest path problem

The quickest path problem arises when transmitting a given amount of data between two given nodes of a network, a lead time and a capacity (per unit of time) being assigned to each arc in the network. In this paper the problem is regarded as a bicriteria path problem, allowing the use of a very efficient algorithm which solves the quickest path problem for all possible values of the amount of data that has to be transmitted.

Solving bicriteria 0-1 knapsack problems using a labeling algorithm

This paper examines the performances of a new labeling algorithm to find all the efficient paths (or non-dominated evaluation vectors) of the bicriteria 0-1 knapsack problem. To our knowledge this is the first time a bicriteria 0-1 knapsack is solved taking advantage of its previous conversion into a bicriteria shortest path problem over an acyclic network. Computational experiments and results are also presented regarding bicriteria instances of up to 900 items. The algorithm is very efficient for the hard bicriteria 0-1 knapsack instances considered in the paper.

The Determination of the Path with Minimum-Cost Norm Value*

The multiobjective shortest path problem (MSPP) consists of finding the best nondominated path linking two specified nodes in a network where k > 1 different criteria are considered for the arc costs. Solving the MSPP implies determining all the nondominated paths; there may be many such paths, making the selection process a very hard task to accomplish. A traditional way of dealing with such a difficulty is using a utility function where the parameters are aggregated with different weights. In this work, an alternative utility function based on the norm value associated with each path is considered. Two algorithms for solving the minimum-cost norm path problem are then proposed and some computational results are presented.

Roadmap to spline-fitting potentials in high dimensions

The use of the theory of splines to approximate the potential energy surface in molecular dynamics is examined. It is envisaged that such an approximation should be able to accurately capture the potentials’ behavior and be computationally cost effective, both for one-dimensional and

A new approach for the multiobjective minimum spanning tree

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An Algorithm for Ranking Loopless Paths

-dimensional problems with