Related papers: Technical Note: Split Algorithm in O(n) for the Ca…
VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations.…
This paper analyzes how the presence of service stations on highways affects traffic congestion. We focus on the problem of optimally designing a service station to achieve beneficial effects in terms of total traffic congestion and peak…
We consider the Travelling Salesman Problem with Vertex Requisitions, where for each position of the tour at most two possible vertices are given. It is known that the problem is strongly NP-hard. The proposed algorithm for this problem has…
The paper represents an algorithm for planning safe and optimal routes for transport facilities with unrestricted movement direction that travel within areas with obstacles. Paper explains the algorithm using a ship as an example of such a…
We present an analytical upper bound on the number of required vehicles for vehicle routing problems with split deliveries and any number of capacitated depots. We show that a fleet size greater than the proposed bound is not achievable…
The Capacitated Location Routing Problem is an important planning and routing problem in logistics, which generalizes the capacitated vehicle routing problem and the uncapacitated facility location problem. In this problem, we are given a…
In the highway problem, we are given an n-edge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the…
The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into…
When delivering items to a set of destinations, one can save time and cost by passing a subset to a sub-contractor at any point en route. We consider a model where a set of items are initially loaded in one vehicle and should be distributed…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously…
We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2^{n/3}) ~= 1.260^n and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the…
A graph separator is a subset of vertices of a graph whose removal divides the graph into small components. Computing small graph separators for various classes of graphs is an important computational task. In this paper, we present a…
In this paper, we review the state of the art in Out-of-Distribution (OoD) segmentation, with a focus on road obstacle detection in automated driving as a real-world application. We analyse the performance of existing methods on two widely…
Original equipment manufacturers (OEMs) manufacture, inventory and transport new vehicles to franchised dealers. These franchised dealers inventory and sell new vehicles to end users. OEMs rely on logistics companies with a special type of…
We present an efficient algorithm for regularized optimal transport. In contrast to previous methods, we use the Douglas-Rachford splitting technique to develop an efficient solver that can handle a broad class of regularizers. The…
We introduce a novel approach of using important cuts which allowed us to design significantly faster fixed-parameter tractable (FPT) algorithms for the following routing problems: the Mixed Chinese Postman Problem parameterized by the…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…