Robustness of solutions to the capacitated facility location problem with uncertain demand

We investigate the properties of robust solutions of the Capacitated Facility Location Problem with uncertain demand. We show that the monotonic behavior of the price of robustness is not guaranteed, and therefore that one cannot discriminate among alternative robust solutions by simply relying on the trade-off price-vs-robustness. Furthermore, we report a computational study on benchmark instances from the literature and on instances derived from a real-world application, which demonstrates the validity in practice of our findings

The multiple vehicle balancing problem

This paper deals with the multiple vehicle balancing problem (MVBP). Given a fleet of vehicles of limited capacity, a set of vertices with initial and target inventory levels and a distribution network, the MVBP requires to design a set of routes along with pickup and delivery operations such that inventory is redistributed among the vertices without exceeding capacities, and routing costs are minimized. The MVBP is NP\u2010hard, generalizing several problems in transportation, and arising in bike\u2010sharing systems. Using theoretical properties of the problem, we propose an integer linear programming formulation and introduce strengthening valid inequalities. Lower bounds are computed by column generation embedding an ad\u2010hoc pricing algorithm, while upper bounds are obtained by a memetic algorithm that separate routing from pickup and delivery operations. We combine these bounding routines in both exact and matheuristic algorithms, obtaining proven optimal solutions for MVBP instances with up to 25 stations

A New Heuristic for the Travelling Salesman Problem with Time Windows.

Abstract not availableJRC.(ISIS)-Institute For Systems, Informatics And Safet

A new heuristic for the Traveling Salesman Problem with Time Windows

The aim of this paper is to present a new heuristic method for the Traveling Salesman Problem with Time Windows, based on the solution of an auxiliary problem. The idea is to solve an assignment problem with an ad hoc objective function, to obtain a solution close enough to a feasible solution of the original problem. Given this solution, made by a long main, tour containing the depot and few small subtours, it is easy to insert all the subtours into the main path using a greedy insertion procedure. The algorithm described applies the proposed constructive scheme and then uses a local search procedure to improve the initial solution. The computational results show the effectiveness of this approach

Use of Neural Networks to Estimate the Number of Nodes of an Edge Quadtree

The number of nodes of an edge quadtree is the measure of its space complexity. This number depends on the figure's shape, its resolution and its precision. The goal of this work is to find a function which yields the number of nodes of an edge-quadtree when these three parameters are part of the input. A unique value to represent both the resolution and the precision is used. To measure the shape of the image we use the fractal dimension. A methodology to calculate the fractal dimension and the fractal measure is proposed. These three parameters being given, we use a neural network to approximate the sought function. The computational results show the effectiveness of this approach

A Granular Tabu Search algorithm for the Dial-a-Ride Problem

In a Dial-a-Ride system, a fleet of vehicles without fixed routes and schedules carries people from their pick-up point to their delivery point. Pre-specified time windows must be respected, and service levels for passengers as well as operation costs should be optimized. The resulting routing and scheduling problem is NP-hard and can be modeled by a mixed integer linear programming formulation. In this paper, we propose a Granular Tabu Search algorithm for the static Dial-a-Ride Problem with the objective of producing good solutions in a short amount of time (up to 3 min). We evaluate the algorithm on test instances from the literature. Our new algorithm performs well in comparison with a classical Tabu Search algorithm, a Genetic Algorithm, and a Variable Neighborhood Search

A heuristic approach to the overnight security service problem

This paper introduces the overnight security service problem. The model obtained is a single-objective mixed integer programming problem. It is NP-hard in the strong sense, and exact approaches are not practicable when solving real-life instances. Thus, the model is solved heuristically, through a decomposition in two subproblem. The former is a capacitated clustering problem, the latter is a multiple travelling salesman problem with time windows. Both have a radius constraint which is unusual. The computational results prove the robustness of the approach used. Moreover, a detailed discussion of the results shows that the management objectives are satisfied, providing lower costs, a strong guarantee on the level of service and several different solutions

A Heuristic for the Vehicle Routing Problem with Time Windows

In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Windows. Its framework is a smart combination of three simple procedures: the classical k-opt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second objective function drives the search out of local optima. No parameter tuning is required and no random choice is made: these are the distinguishing features with respect to the recent literature. The algorithm has been tested on benchmark problems which prove it to be more effective than comparable algorithms

Use of Neural Networks to Estimate the Number of Nodes of an Edge Quadtree

The number of nodes of an edge quadtree is the measure of its space complexity. This number depends on the figure's shape, its resolution and its precision. The goal of this work is to find a function which yields the number of nodes of an edge-quadtree when these three parameters are part of the input. A unique value to represent both the resolution and the precision is used. To measure the shape of the image we use the fractal dimension. A methodology to calculate the fractal dimension and the fractal measure is proposed. These three parameters being given, we use a neural network to approximate the sought function. The computational results show the effectiveness of this approach

An effective and fast heuristic for the Dial-a-Ride problem

Dial-a-Ride is an emerging transport system, in which a fleet of vehicles, without fixed routes and schedules, carries people from the desired pickup point to the desired delivery point, during a pre-specified time interval. It can be modeled as an NP-hard routing and scheduling problem, with a suitable mixed integer programming formulation. Exact approaches to this problem are too limited to tackle real-life instances (hundred of trips), therefore heuristics are needed. The heuristic method proposed in this paper builds an auxiliary graph and then solves an assignment problem on this graph. The auxiliary graph is obtained by replacing pairs of nodes with a single one and associating an ad hoc cost function to the new set of arcs. Two different simple methods are employed to transform the infeasible solution given by the assignment problem into a feasible one. The proposed algorithms have been tested on instances created using the Milan network and shown to be fast and effective