In this paper, we introduce and investigate a new style of delivery in last-mile logistics, in which we merge the existing concept of conventional truck-based delivery with emerging technologies, i.e., drones and autonomous robots (autonomous transport vehicles (ATVs)). More precisely, in the Truck-Drone-ATV Routing Problem (TDA-RP), a truck, carrying several drones and ATVs as well as the parcels, departs from a depot, visits a given list of grid points, each of them at most once, and returns to the depot by the end of the mission. In addition, at each visited grid point, a set of drones and ATVs are tasked to deliver the parcels to the customers via circumjacent operations. The objective consists in serving all customers in shortest possible time. However, due to the computational complexity of the problem, we cannot solve it by exact methods. Hence, we suggest a Genetic Algorithm for solving the problem and, through our computational experiments on randomly generated instances, we show the benefits of using a mixed fleet of drones and ATVs assisting a truck.
Computing the closed convex envelope or biconjugate is the core operation that bridges the domain of nonconvex with convex analysis. We focus here on computing the conjugate of a bivariate piecewise quadratic function defined over a polytope. First, we compute the convex envelope of each piece, which is characterized by a polyhedral subdivision such that over each member of the subdivision, it has a rational form (square of a linear function over a linear function). Then we compute the conjugate of all such rational functions. It is observed that the conjugate has a parabolic subdivision such that over each member of its subdivision, it has a fractional form (linear function over square root of a linear function). This computation of the conjugate is performed with a worst-case linear time complexity algorithm. Our results are an important step toward computing the conjugate of a piecewise quadratic function, and further in obtaining explicit formulas for the convex envelope of piecewise rational functions.
In the modern world, every technology and user generate a large amount of data. Each data carries value to some degree. Therefore, the concept of big data is actively developing because the idea of big data is to generate a new value. Addressing big data is an invocation and time-demanding job that needs a large computational infrastructure to ensure successful data processing, storage, and analysis. This report is intended to compare how one of the big data storage, Clickhouse, can replace the relational database, Oracle. This paper motivation is to obtain an understanding of the benefit and drawbacks of NoSQL database, in the case of Clickhouse to supporting a huge amount of data.
In this work we describe a good approach to solve chance-constrained programming with mixed-integer variables. We replace a hard chance constrained function by a copula. We prove that Zhang’s copula family satisfies the proprieties request by outer-approximation and we use this algorithm to solve this problem with promising results.
