this paper addresses the vehicle routing problem with delivery time cost. this problem aims to find a set of routes of minimal total costs including the travelling cost and delivery time cost, starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. in this research, a hybrid metaheuristic approa...

The Lead-Based Multiple Video Transmission (LMVT) problem is motivated by applications in managing the quality of experience (QoE) of video streaming for mobile clients. In an earlier work, the LMVT problem has been shown to be NP-hard for a specific bit-to-lead conversion function φ. In this work, we show the problem to be NP-hard even if the function φ is linear. We then design a fully polyno...

A new motion planning algorithm for the so-called Dubins Travelling Salesperson Problem is derived, and compared via simulations with a number of existing algorithms from the literature. In its general form, the new algorithm is dubbed “k-step look-ahead algorithm” and stems naturally from the formulation of the Dubins Travelling Salesperson Problem as a minimum-time control problem. When the m...

We consider the special case of the traveling salesman problem (TSP) in which the distance metric is the shortest-path metric of a planar unweighted graph. We present a polynomial-time approximation scheme (PTAS) for this problem.

The (Euclidean) Vehicle Routing Allocation Problem (VRAP) is a generalization of Euclidean TSP. We do not require that all points lie on the salesman tour. However, points that do not lie on the tour are allocated, i.e., they are directly connected to the nearest tour point, paying a higher (per-unit) cost. More formally, the input is a set of points P ⊂ R and functions α : P → [0,∞) and β : P ...

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We consider a variation of Voronoi diagram, or time-based Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest time-distance path from a query point to any given point in S is a path that takes the least travelling time. The travelling speeds and hence travelling times of the subpaths along the highways and in the plane are differen...

This paper is concerned with the existence of travelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration metho...

cosmic rays (cr) travel at speeds essentially indistinguishable from the speed of light. however whilst travelling through magnetic fields, both regular and turbulent, they are delayed behind the light since they are usually charged particles and their paths are not linear. those delays can be so long that they are an impediment to correctly identifying sources which may be variable in time. fu...