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Joint Discrete Rate Adaptation and Downlink Beamforming Using mixed integer conic programming

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第7期63卷 1750-1764页

作者： Cheng, Yong Pesavento, Marius NEC Labs Europe D-69115 Heidelberg Germany Tech Univ Darmstadt Commun Syst Grp D-64289 Darmstadt Germany

Multiuser downlink beamforming for sum-rate maximization has been intensively studied in the literature assuming that the achievable data rates of the mobile stations (MSs) are continuous and strictly increasing functions of the received signal-to-interference-plus-noise ratios (SINRs). However, in practical cellular networks that employ adaptive modulation and coding, the data rates of the MSs are determined by the specific modulation and coding schemes and thus attain discrete values. We consider in this paper discrete rate adaptation and downlink beamforming (RAB), where the discrete rate assignment is jointly optimized along with the beamformer design to achieve the maximum sum-rate with minimum total transmitted power of the base station. User admission control is embedded in the discrete rate assignment procedure. We address the RAB problem using a mixed integer second-order cone program (MI-SOCP) approach, proposing a standard big-M MI-SOCP formulation that supports the branch-and-cut (BnC) method. To reduce the complexity of the BnC algorithm, we further develop an improved extended MI-SOCP formulation. We analytically show that the extended formulation generally admits strictly tighter continuous relaxations (and thus less computational complexity) than that of the big-M formulation. Efficient strategies are proposed to customize the standard BnC method for the RAB problem. For applications in large-scale networks, we develop low-complexity SOCP based inflation and deflation procedures to find suboptimal solutions of the RAB problem. Simulations show that the inflation and deflation procedures yield sum-rates that are very close to that of the optimal solutions.

关键词： Discrete rate adaptation downlink beamforming fast heuristic algorithms mixed integer conic programming

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Joint Network Optimization and Downlink Beamforming for CoMP Transmissions Using mixed integer conic programming

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第16期61卷 3972-3987页

作者： Cheng, Yong Pesavento, Marius Philipp, Anne Tech Univ Darmstadt Commun Syst Grp D-64289 Darmstadt Germany Tech Univ Darmstadt Dept Math D-64283 Darmstadt Germany

Coordinated multipoint (CoMP) transmission is a promising technique to mitigate intercell interference and to increase system throughput in single-frequency reuse networks. Despite the remarkable benefits, the associated operational costs for exchanging user data and control information between multiple cooperating base stations (BSs) limit practical applications of CoMP processing. To facilitate wide usage of CoMP transmission, we consider in this paper the problem of joint network optimization and downlink beamforming (JNOB), with the objective to minimize the overall BS power consumption (including the operational costs of CoMP transmission) while guaranteeing the quality-of-service (QoS) requirements of the mobile stations (MSs). We address this problem using a mixed integer second-order cone program (MI-SOCP) framework and develop an extended MI-SOCP formulation that admits tighter continuous relaxations, which is essential for reducing the computational complexity of the branch-and-cut (BnC) method. Analytic studies of the MI-SOCP formulations are carried out. Based on the analyses, we introduce efficient customizing strategies to further speed up the BnC algorithm through generating tight lower bounds of the minimum total BS power consumptions. For practical applications, we develop polynomial-time inflation and deflation procedures to compute high-quality solutions of the JNOB problem. Numerical results show that the inflation and deflation procedures yield total BS power consumptions that are close to the lower bounds, e. g., exceeding the lower bounds by about 12.9% and 9.0%, respectively, for a network with 13 BSs and 25 MSs. Simulation results also show that minimizing the total BS power consumption results in sparse network topologies and reduced operational overhead in CoMP transmission and that some of the BSs are switched off when possible.

关键词： Coordinated multipoint transmission downlink beamforming low-complexity heuristic algorithms mixed integer conic programming network optimization

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ROBUST CODEBOOK-BASED DOWNLINK BEAMFORMING USING mixed integer conic programming

ROBUST CODEBOOK-BASED DOWNLINK BEAMFORMING USING MIXED INTEG...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Cheng, Yong Pesavento, Marius Tech Univ Darmstadt Commun Syst Grp D-64283 Darmstadt Germany

ISBN: (纸本)9781479903566

This paper considers robust codebook-based downlink beatnfortning (i.e., single-layer precoding), where the beamformer of each user is chosen from a fixed beamformer codebook defined, e.g., in LTE and LTE-A. Admission control and power allocation are embedded in the precoding vector selection procedure. The objective is to maximize the system utility, defined as the revenue gained from admitting users minus the cost for the transmitted power of the base station. We adopt the quality-of-service constrained approach and the robustness against channel covariance estimation errors is realized with worst-case design. The robust codebook-based beamforming problem, which is a hi-level mixed integer program, is converted into a more tractable mixed integer second-order cone program. Techniques are proposed to customize the convex continuous relaxation based branch-and-cut algorithm to compute the optimal solutions. A low-complexity inflation procedure is also developed to compute the near-optimal solutions for practical applications. Numerical examples show that the gap between the average number of admitted users achieved by the fast inflation procedure and that of the optimal solutions is less than 11.6% for all considered simulation settings. Further, the inflation procedure yields optimal solutions in 88% of the Monte Carlo runs under specific parameter settings.

关键词： Codebook-based Precoding Robustness mixed integer conic programming Fast Near-Optimal Algorithm

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DYNAMIC RATE ADAPTATION AND MULTIUSER DOWNLINK BEAMFORMING USING mixed integer conic programming

DYNAMIC RATE ADAPTATION AND MULTIUSER DOWNLINK BEAMFORMING U...

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20th European Signal Processing Conference (EUSIPCO)

作者： Cheng, Yong Philipp, Anne Pesavento, Marius Tech Univ Darmstadt Commun Syst Grp Darmstadt Germany Tech Univ Darmstadt Dept Mat Darmstadt Germany

ISBN: (纸本)9781467310680

This paper considers jointly optimized rate adaptation and beamforming (JRAB) to achieve maximum weighted sum-rate in a multiuser downlink network. In our approach the rate adaptation consists in assigning modulation and coding schemes (MCSs) for the users which are modeled by multiple-choice constraints. The challenge of the problem lies in its combinatorial nature of the MCS selection process. We address the JRAB problem within the mixed integer second order cone programming (MI-SOCP) framework. We propose a convenient MI-SOCP reformulation that is specifically suitable to reduce the run-time in branch-and-bound (BB) methods. Further, a preprocessing step and a novel branching prioritizing principle (BPP) are introduced to speed up the BB type solutions. To facilitate applications in large systems, a fast heuristic algorithm is developed. We show via simulations that the improved MI-SOCP formulation and the BPP can significantly reduce the run-time for solving the JRAB problem with BB. Numeric results also show that the heuristic algorithm yields weighted sum-rates that are larger than that computed by the state-of-the-art MI-SOCP solver IBM ILOG CPLEX under the given run-time limitations.

关键词： Dynamic rate adaptation Adaptive modulation and coding Multiuser downlink beamforming Joint optimization mixed integer conic programming

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ROBUST CODEBOOK-BASED DOWNLINK BEAMFORMING USING mixed integer conic programming

ROBUST CODEBOOK-BASED DOWNLINK BEAMFORMING USING MIXED INTEG...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Yong Cheng Marius Pesavento Communication Systems Group Technische Universit?t Darmstadt 64283 Darmstadt Germany

ISBN: (纸本)9781479903573

This paper considers robust codebook-based downlink beamforming (i.e., single-layer precoding), where the beamformer of each user is chosen from a fixed beamformer codebook defined, e.g., in LTE and LTE-A. Admission control and power allocation are embedded in the precoding vector selection procedure. The objective is to maximize the system utility, defined as the revenue gained from admitting users minus the cost for the transmitted power of the base station. We adopt the quality-of-service constrained approach and the robustness against channel covariance estimation errors is realized with worst-case design. The robust codebook-based beamforming problem, which is a bi-level mixed integer program, is converted into a more tractable mixed integer second-order cone program. Techniques are proposed to customize the convex continuous relaxation based branch-and-cut algorithm to compute the optimal solutions. A low-complexity inflation procedure is also developed to compute the near-optimal solutions for practical applications. Numerical examples show that the gap between the average number of admitted users achieved by the fast inflation procedure and that of the optimal solutions is less than 11.6% for all considered simulation settings. Further, the inflation procedure yields optimal solutions in 88% of the Monte Carlo runs under specific parameter settings.

关键词： Codebook-based Precoding Robustness mixed integer conic programming Fast Near-Optimal Algorithm Robustness optimal solution parameter setting Economic Inflation programming Transmitter power Admission control prediction coding mixed integer Local thermodynamic equilibrium BASE STATION power splitting Consumers Beamforming REVENUE

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An extended model of coordination of an all-terrain vehicle and a multivisit drone

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2024年第2期31卷 780-806页

作者： Amorosi, Lavinia Puerto, Justo Valverde, Carlos Sapienza Univ Rome Dept Stat Sci I-00185 Rome Italy Univ Seville Dept Stat Sci & Operat Res Seville 41012 Spain Univ Seville IMUS Seville 41012 Spain

In this paper, a model that combines the movement of a multivisit drone with a limited endurance and a base vehicle that can move freely in the continuous space is considered. The mothership is used to charge the battery of the drone, whereas the drone performs the task of visiting multiple targets of distinct shapes: points and polygonal chains. For polygonal chains, it is required to traverse a given fraction of its lengths that represent surveillance/inspection activities. The goal of the problem is to minimize the overall weighted distance traveled by both vehicles. A mixed integer second-order cone program is developed and strengthened using valid inequalities and giving good bounds for the Big-M constants that appear in the model. A refined matheuristic that provides reasonable solutions in short computing time is also established. The quality of the solutions provided by both approaches is compared and analyzed on an extensive battery of instances with different number and shapes of targets, which shows the usefulness of our approach and its applicability in different situations.

关键词： routing networks logistics drones mixed integer conic programming

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Transmission Grid Resiliency Investment Optimization Model With SOCP Recovery Planning

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第1期37卷 26-37页

作者： Garifi, Kaitlyn Johnson, Emma S. Arguello, Bryan Pierre, Brian J. Sandia Natl Labs Albuquerque NM 87123 USA

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model.

关键词： Investment Resilience Generators Load modeling Meteorology Switches Reactive power Power system resilience optimal transmission switching investment decisions mixed integer conic programming power systems power system planning power system optimization

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On sublinear inequalities for mixed integer conic programs

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MATHEMATICAL programming 2016年第1-2期159卷 585-605页

作者： Kilinc-Karzan, Fatma Steffy, Daniel E. Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Oakland Univ Dept Math & Stat Rochester MI 48309 USA

This paper studies -sublinear inequalities, a class of inequalities with strong relations to -minimal inequalities for disjunctive conic sets. We establish a stronger result on the sufficiency of -sublinear inequalities. That is, we show that when is the nonnegative orthant or the second-order cone, -sublinear inequalities together with the original conic constraint are always sufficient for the closed convex hull description of the associated disjunctive conic set. When is the nonnegative orthant, -sublinear inequalities are tightly connected to functions that generate cuts-so called cut-generating functions. In particular, we introduce the concept of relaxed cut-generating functions and show that each -sublinear inequality is generated by one of these. We then relate the relaxed cut-generating functions to the usual ones studied in the literature. Recently, under a structural assumption, Cornujols, Wolsey and YA +/- ldA +/- z established the sufficiency of cut-generating functions in terms of generating all nontrivial valid inequalities of disjunctive sets where the underlying cone is nonnegative orthant. We provide an alternate and straightforward proof of this result under the same assumption as a consequence of the sufficiency of -sublinear inequalities and their connection with relaxed cut-generating functions.

关键词： Valid inequalities Sublinear inequalities Cut-generating functions mixed integer conic programming

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On Minimal Valid Inequalities for mixed integer conic Programs

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MATHEMATICS OF OPERATIONS RESEARCH 2016年第2期41卷 477-510页

作者： Kilinc-Karzan, Fatma Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

We study disjunctive conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone, or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that, under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient to describe the convex hull. We focus on the properties of K-minimal inequalities by establishing algebraic necessary conditions for an inequality to be K-minimal. This characterization leads to a broader algebraically defined class of K-sublinear inequalities. We demonstrate a close connection between K-sublinear inequalities and the support functions of convex sets with a particular structure. This connection results in practical ways of verifying K-sublinearity and/or K-minimality of inequalities. Our study generalizes some of the results from the mixed integer linear case. It is well known that the minimal inequalities for mixed integer linear programs are generated by sublinear (positively homogeneous, subadditive, and convex) functions that are also piecewise linear. Our analysis easily recovers this result. However, in the case of general regular cones other than the nonnegative orthant, our study reveals that such a cut-generating function view, which treats the data associated with each individual variable independently, is far from sufficient.

关键词： minimal inequalities mixed integer conic programming disjunctive programming cutting planes

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The Hampered k-Median Problem with Neighbourhoods

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COMPUTERS & OPERATIONS RESEARCH 2024年 170卷

作者： Puerto, Justo Valverde, Carlos Univ Seville Inst Math IMUS Seville 41012 Spain Univ Seville Dept Stat & Operat Res Seville 41012 Spain

This paper deals with facility location problems in a continuous space with neighbours and barriers. Each one of these two elements, neighbours and barriers, makes the problems harder than their standard counterparts. Combining all together results in a new challenging problem that, as far as we know, has not been addressed before, but has applications for inspection and surveillance activities and the delivery industry assuming uniformly distributed demand in some regions. Specifically, we analyse the k-Median problem with neighbours and polygonal barriers in two different situations. None of these problems can be seen as a simple incremental contribution since in both cases the tools required to analyse and solve them go beyond any standard overlapping of techniques used in the separated problems. As a first building block, we deal with the problem assuming that the neighbourhoods are not visible from one another and therefore there are no rectilinear paths that join two of them without crossing barriers. Under this hypothesis, we derive a valid mixed-integer linear formulation. Removing that hypothesis leads to a more general and realistic problem, but at the price of making it more challenging. Adapting the elements of the first formulation, we also develop another valid mixed-integer bilinear formulation. Both formulations rely on tools borrowed from computational geometry that allow to handle polygonal barriers and neighbours that are second-order cone (SOC) representable, which we preprocess and strengthen with valid inequalities. These mathematical programming formulations are also instrumental to derive an adapted matheuristic algorithm that provides good quality solutions for both problems in short computing time. The paper also reports extensive computational experience, counting 2400 experiments, showing that our exact and heuristic approaches are useful: the exact approach can solve optimally instances with up to 50 neighbourhoods and different number o

关键词： Facility location Continuous location Barriers mixed integer conic programming

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