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A multiperiod drayage problem with customer-dependent service periods
Full text linkWe investigate a routing problem arising in the domain of drayage operations. to determine mimimum-cost vehicle routes in several periods. We adapt a set-covering model, which is solved either with all feasible routes by an off-the-shelf MIP solver, or by and a Price-and-Branch algorithm in which the pricing problem is a formulated as a collection of shortest path problems in tailor-made auxiliary acyclic networks. We propose a new arc-flow formulation based on the previous auxiliary networks and show that solving it by a MIP solver is usually preferable. Finally, we characterize how possible changes in flexibility levels affect routing costs
Standard Bundle Methods: Untrusted Models and Duality
Full text linkWe review the basic ideas underlying the vast family of algorithms for nonsmooth convex optimization known as "bundle methods|. In a nutshell, these approaches are based on constructing models of the function, but lack of continuity of first-order information implies that these models cannot be trusted, not even close to an optimum. Therefore, many different forms of stabilization have been proposed to try to avoid being led to areas where the model is so inaccurate as to result in almost useless steps. In the development of these methods, duality arguments are useful, if not outright necessary, to better analyze the behaviour of the algorithms. Also, in many relevant applications the function at hand is itself a dual one, so that duality allows to map back algorithmic concepts and results into a "primal space" where they can be exploited; in turn, structure in that space can be exploited to improve the algorithms' behaviour, e.g. by developing better models. We present an updated picture of the many developments around the basic idea along at least three different axes: form of the stabilization, form of the model, and approximate evaluation of the function
Bit Representation Can Improve SDP Relaxations of Mixed-Integer Quadratic Programs
Full text linkA standard trick in integer programming is to replace bounded integer variables with
binary variables, using a bit representation. In a previous paper, we showed that this process
can be used to improve linear programming relaxations of mixed-integer quadratic
programs. In this paper, we show that it can also be used to improve {\em semidefinite}\/
programming relaxations
Convergence of the fixed point algorithm for quasi-equilibria
Full text linkAn algorithm for solving quasi-equilibrium problems (QEPs) is proposed relying on the sequential inexact resolution of equilibrium problems. First, we reformulate QEP as the fixed point problem of a set-valued map and analyse its Lipschitz continuity under strong monotonicity assumptions. Then, a few classes of QEPs satisfying these assumptions are identified. Finally, we devise an algorithm that computes an inexact solution of an equilibrium problem at each iteration and we prove its global convergence
Optimization Methods: an Applications-Oriented Primer
Full text linkEffectively sharing resources requires solving complex decision problems. This requires constructing a mathematical model of the underlying system, and then applying appropriate mathematical methods to find an optimal solution of the model, which is ultimately translated into actual decisions. The development of mathematical tools for solving optimization problems dates back to Newton and Leibniz, but it has tremendously accelerated since the advent of digital computers. Today, optimization is an inter-disciplinary subject, lying at the interface between management science, computer science, mathematics and engineering. This chapter offers an introduction to the main theoretical and software tools that are nowadays available to practitioners to solve the kind of optimization problems that are more likely to be encountered in the context of this book. Using, as a case study, a simplified version of the bike sharing problem, we guide the reader through the discussion of modelling and algorithmic issues, concentrating on methods for solving optimization problems to proven optimality
A Matheuristic for Integrated Timetabling and Vehicle Scheduling
Full text linkPlanning a public transportation system is a complex process, which is usually broken down in several phases, performed in sequence. Most often, the trips required to cover a service with the desired frequency (headway) are decided early on, while the vehicles needed to cover these trips are determined at a later stage. This potentially leads to requiring a larger number of vehicles (and, therefore, drivers) that would be possible if the two decisions were performed simultaneously. We propose a multicommodity-flow type model for integrated timetabling and vehicle scheduling. Since the model is large-scale and cannot be solved by off-the-shelf tools with the efficiency required by planners, we propose a diving-type matheuristic approach for the problem. We report on the efficiency and effectiveness of two variants of the proposed approach, differing on how the continuous relaxation of the problem is solved, to tackle real-world instances of bus transport planning problem originating from customers of M.A.I.O.R., a leading company providing services and advanced decision-support systems to public transport authorities and operators. The results show that the approach can be used to aid even experienced planners in either obtaining better solutions, or obtaining them faster and with less effort, or both
The MPA graph problem
Full text linkGiven an undirected graph G whose vertices are associated to different subsets of colors, the MPA problem asks for partitioning G into a minimal set of monochromatic connected subgraphs. We prove that MPA is NP-hard as well as its extensions BDMPA where the vertices of G have a bounded maximum degree, PMPA where G is planar, BDPMPA where the maximum vertex degree is bounded and G is planar, and GMPA where G consists of a p × q grid
Large-scale unit commitment under uncertainty: an updated literature survey
Full text linkThe Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject
A distributed power-saving framework for LTE Het-Nets exploiting Almost Blank Subframes
No full textAlmost Blank Subframes (ABS) have been defined in LTE as a means to coordinate transmissions in heterogeneous
networks (HetNets), composed of macro and micro eNodeBs: the macro issues ABS periods, and refrains from transmitting during ABSs, thus creating interference-free subframes for the micros. Micros report their capacity demands to the macro via the X2 interface, and the latter provisions the ABS period accordingly. Existing algorithms for ABS provisioning usually share resources
proportionally among HetNet nodes in a long-term perspective (e.g., based on traffic forecast). We argue instead that this mechanism can be exploited to save power in the HetNet: in fact, during ABSs, the macro consumes less power, since it only transmits pilot signals. Dually, the micros may inhibit data transmission themselves in some subframes, and optimally decide when to do this based on knowledge of the ABS period. This allows us to define a power saving framework that works in the short term, modifying the ABS pattern at the fastest possible pace, serving the HetNet traffic at reduced power cost. Our framework is designed using only standard signaling. Simulations show that the algorithm consumes less power than its competitors, especially at low loads, and improves the UE QoS
Bitcoin Protocol Main Threats
No full textIn this paper we explain the basics of Bitcoin protocol and the state of the art of the main attacks to it. We first present an overview of digital currencies, showing what they are and the social need they aim to satisfy. We then focus on the main digital currency up to date, Bitcoin. We treat the basics of the protocol showing what are addresses and transactions and how they are used in a distributed consensus protocol to build the blockchain. After that the main part of this paper presents the state of the art of the three main attacks on the protocol: fraudulent mining techniques, double spending attempts and deanonymization attacks