Description of the Grover algorithm based on geometric considerations

This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a quadratic speedup. The algorithm requires a predefined number of runs to succeed with probability close to one.This article provides a description of the amplitude amplification quantum algorithm mechanism in a very short computational way, based on tensor products and provides a geometric presentation of the successive system states. All the basis changes are fully described to provide an alternative to the wide spread Grover description based only on matrices and complex tensor computation. Our experiments encompass numerical evaluations of circuit using the Qiskit library of IBM that meet the theoretical consideration

A GRASPxELS with Depth First Search Split Procedure for the HVRP

Split procedures have been proved to be efficient within global framework optimization for routing problems by splitting giant tour into trips. This is done by generating optimal shortest path within an auxiliary graph built from the giant tour. An efficient application has been introduced for the first time by Lacomme et al. (2001) within a metaheuristic approach to solve the Capacitated Arc Routing Problem (CARP) and second for the Vehicle Routing Problem (VRP) by Prins (2004). In a further step, the Split procedure embedded in metaheuristics has been extended to address more complex routing problems thanks to a heuristic splitting of the giant tour using the generation of labels on the nodes of the auxiliary graph linked to resource management. Lately, Duhamel et al. (2010) defined a new Split family based on a depth first search approach during labels generation in graph. The efficiency of the new split method has been first evaluated in location routing problem with a GRASP metaheuristic. Duhamel et al. (2010) provided full numerical experiments on this topic

A GRASPxELS with Depth First Search Split Procedure for the HVRP

Split procedures have been proved to be efficient within global framework optimization for routing problems by splitting giant tour into trips. This is done by generating optimal shortest path within an auxiliary graph built from the giant tour. An efficient application has been introduced for the first time by Lacomme et al. (2001) within a metaheuristic approach to solve the Capacitated Arc Routing Problem (CARP) and second for the Vehicle Routing Problem (VRP) by Prins (2004). In a further step, the Split procedure embedded in metaheuristics has been extended to address more complex routing problems thanks to a heuristic splitting of the giant tour using the generation of labels on the nodes of the auxiliary graph linked to resource management. Lately, Duhamel et al. (2010) defined a new Split family based on a depth first search approach during labels generation in graph. The efficiency of the new split method has been first evaluated in location routing problem with a GRASP metaheuristic. Duhamel et al. (2010) provided full numerical experiments on this topic

A bi-objective stochastic approach for stochastic CARP

The Capacitated Arc Routing Problem (CARP) occurs in applications like urban waste collection or winter gritting. It is usually defined in literature on an undirected graph G = (V, E) , with a set V of n nodes and a set E of m edges. A fleet of identical vehicles of capacity Q is based at a depot node. Each edge i has a cost (length) ci and a demand qi (e.g. an amount of waste), and it may be traversed any number of times. The edges with non-zero demands or tasks require service by a vehicle. The goal is to determine a set of vehicle trips (routes) of minimum total cost, such that each trip starts and ends at the depot, each task is serviced by one single trip, and the total demand handled by any vehicle does not exceed Q . To the best of our knowledge the best published method is a memetic algorithm first introduced in 2001. This article provides a new extension of the NSGA II (Non-dominated Sorting Genetic Algorithm) template to comply with the stochastic sight of the CARP. The main contribution is: - to introduce mathematical expression to evaluate both cost and duration of the longest trip and also standard deviation of these two criteria. - to use a NGA-II template to optimize simultaneously the cost and the duration of the longest trip including standard deviation. The numerical experiments managed on the thee well-known benchmark sets of DeArmon, Belenguer and Benavent and Eglese, prove it is possible to obtain robust solutions in four simultaneous criteria in rather short computation times

Integrative and comparative genomic analyses identify clinically relevant pulmonary carcinoid groups and unveil the supra-carcinoids

International audienceThe worldwide incidence of pulmonary carcinoids is increasing, but little is known about their molecular characteristics. Through machine learning and multi-omics factor analysis, we compare and contrast the genomic profiles of 116 pulmonary carcinoids (including 35 atypical), 75 large-cell neuroendocrine carcinomas (LCNEC), and 66 small-cell lung cancers. Here we report that the integrative analyses on 257 lung neuroendocrine neoplasms stratify atypical carcinoids into two prognostic groups with a 10-year overall survival of 88% and 27%, respectively. We identify therapeutically relevant molecular groups of pulmonary car-cinoids, suggesting DLL3 and the immune system as candidate therapeutic targets; we confirm the value of OTP expression levels for the prognosis and diagnosis of these diseases, and we unveil the group of supra-carcinoids. This group comprises samples with carcinoid-like morphology yet the molecular and clinical features of the deadly LCNEC, further supporting the previously proposed molecular link between the low-and high-grade lung neuroendocrine neoplasms

A GRASP x ELS for the vehicle routing problem with three-dimensional loading constraints

This paper addresses an extension of the Capacitated Vehicle Routing Problem where the client demand consists of three-dimensional weighted items (3L-CVRP). The objective is to design a set of trips for a homogenous fleet of vehicles based on a depot node which minimizes the total transportation cost. Items in each vehicle trip must satisfy the three-dimensional orthogonal packing constraints. A GRASP ELS algorithm is proposed to compute the best possible solution. We propose a new method to address the 3D packing which allows items to be rotated or not. It is based on a relaxation of the 3D problem in which items coordinates are first computed before getting compatible z-coordinates. Additional techniques are used to reduce as much as possible the time to check the 3D packing feasibility of trips. The effectiveness of our approach is evidenced through computational experiments on 3L-CVRP instances from the literature. New realistic instances are also proposed. These instances are based on the 96 French districts and encompass both small scale instances and large scale instances with up to 200 nodes

A technical note for a Shor's algorithm by phase estimation

The objective of this paper concerns at first the motivation and the method of Shor's algorithm including an excursion into quantum mechanics and quantum computing introducing an algorithmic description of the method. The corner stone of the Shor's algorithm is the modular exponentiation that is the most computational component (in time and space). Second, a linear depth unit based on phase estimation is introduced and a description of a generic version of a modular multiplier based on phases is introduced to build block of a modular exponentiation circuit. Our proposal includes numerical experiments achieved on both the IBM simulator using the Qiskit library and on quantum physical optimizers provided by IBM

Adiabatic based Algorithm : a comprehensivealgorithmic description

International audienc