Modeling some real phenomena by fractional differential equations

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.

Comparison of different methods to detect genetic barriers in a small mammal population

Habitat fragmentation and the consequently the loss of connectivity between populations can reduce the individuals interchange and gene flow, increasing the chances of inbreeding, and the increase the risk of local extinction. Landscape genetics is providing more and better tools to identify genetic barriers.. To our knowledge, no comparison of methods in terms of consistency has been made with observed data and species with low dispersal ability. The aim of this study is to examine the consistency of the results of five methods to detect barriers to gene flow in a Mediterranean pine vole population Microtus duodecimcostatus: F-statistics estimations, Non-Bayesian clustering, Bayesian clustering, Boundary detection and Simple/Partial Mantel tests. All methods were consistent in detecting the stream as a non-genetic barrier. However, no consistency in results among the methods were found regarding the role of the highway as a genetic barrier. Fst, Bayesian clustering assignment test and Partial Mantel test identifyed the highway as a filter to individual interchange. The Mantel tests were the most sensitive method. Boundary detection method (Monmonier’s Algorithm) and Non-Bayesian approaches did not detect any genetic differentiation of the pine vole due to the highway. Based on our findings we recommend that the genetic barrier detection in low dispersal ability populations should be analyzed with multiple methods such as Mantel tests, Bayesian clustering approaches because they show more sensibility in those scenarios and with boundary detection methods by having the aim of detect drastic changes in a variable of interest between the closest individuals. Although simulation studies highlight the weaknesses and the strengths of each method and the factors that promote some results, tests with real data are needed to increase the effectiveness of genetic barrier detection.

Exact solutions to the short sea shipping distribution problem

Short sea shipping has several advantages over other means of transportation, recognized by EU members. The maritime transportation could be dealt like a combination of two well-known problems: the container stowage problem and routing planning problem. The integration of these two well-known problems results in a new problem CSSRP (Container stowage and ship routing problem) that is also an hard combinatorial optimization problem. The aim of this work is to solve the CSSRP using a mixed integer programming model. It is proved that regardless the complexity of this problem, optimal solutions could be achieved in a reduced computational time. For testing the mathematical model some problems based on real data were generated and a sensibility analysis was performed.

Airport ground movement

Worldwide air traffic tends to increase and for many airports it is no longer an op-tion to expand terminals and runways, so airports are trying to maximize their op-erational efficiency. Many airports already operate near their maximal capacity. Peak hours imply operational bottlenecks and cause chained delays across flights impacting passengers, airlines and airports. Therefore there is a need for the opti-mization of the ground movements at the airports. The ground movement prob-lem consists of routing the departing planes from the gate to the runway for take-off, and the arriving planes from the runway to the gate, and to schedule their movements. The main goal is to minimize the time spent by the planes during their ground movements while respecting all the rules established by the Ad-vanced Surface Movement, Guidance and Control Systems of the International Civil Aviation. Each aircraft event (arrival or departing authorization) generates a new environment and therefore a new instance of the Ground Movement Prob-lem. The optimization approach proposed is based on an Iterated Local Search and provides a fast heuristic solution for each real-time event generated instance granting all safety regulations. Preliminary computational results are reported for real data comparing the heuristic solutions with the solutions obtained using a mixed-integer programming approach.