Mixed Integer Quadratic Programming Research Articles

Secure software placement and configuration

Finding the best way to place the components of an application on a set of heterogeneous servers is a challenging task, especially if some components are associated with security requirements. To address security requirements, several security controls may be available, some of them software-based (e.g., encryption), others hardware-based (e.g., trusted execution environments). Security controls may incur widely varying performance overhead. There is a non-trivial interplay between application placement (which component to place on which server) and the configuration of security controls (which security control to activate for which component). On the one hand, placing a component on a secure server may make it unnecessary to use software-based security controls for the component. On the other hand, the overhead of using a specific security control may increase the resource requirements of a component so that it does not fit onto its designated server. Therefore, this paper addresses the joint problem of application placement and configuration of security controls. We formalize the problem and use mixed integer quadratic programming to solve it. A case study is used to demonstrate that the proposed approach can automatically determine the placement and configuration of complex applications.

Impact of the Weather on the Combined Economic and Emission Optimization Problem of MG

The high integration of renewable energy resources and utilizing of storage devices with possible exchange power with the utility grid make the optimization problem of microgrid (MG) significantly difficult comparing with the conventional systems. This paper quantifies the impact of weather conditions on the combined economic and emission optimal operation of the MG. The optimization problem is formulated as mixed integer quadratic program (MIQP), where the unit commitment (UC) is taken into consideration in the optimization problem. In addition, realistic constraints are taken into account to make the problem close to the real scenario. The proposed optimization approach is applied to the low voltage MG, which includes distributed generators (DGs), renewable energy sources (wind, solar) and storage battery. The results reveal that the abundant of wind and solar energies leads to reduce the operation and emission cost.

Cruise Control for a Two-Wheeled Mobile Vehicle Using Its Mixed Logical Dynamical System Model

This paper proposes a cruise control for a two-wheeled mobile vehicle on a two-dimensional plane. The cruise control is executed using model predictive control (MPC), such that input and state constraints can be addressed explicitly. For real-time execution of MPC, we model the dynamics of the vehicle as a mixed logical dynamical system rather than an underlying nonlinear model. The cruise control is then reduced to a mixed integer quadratic programming problem, for which efficient solvers using the convexities are available. Simulations and experiments demonstrate the effectiveness of the proposed cruise control through a computation time comparison with the nonlinear MPC method.

An efficient hybrid metaheuristic algorithm for cardinality constrained portfolio optimization

Abstract Portfolio optimization with cardinality constraints turns out to be a mixed-integer quadratic programming problem which is proven to be NP-Complete that limits the efficiency of exact solution approaches, often because of the long-running times. Therefore, particular attention has been given to approximate approaches such as metaheuristics which do not guarantee optimality, yet may expeditiously provide near-optimal solutions. The purpose of this study is to present an efficient hybrid metaheuristic algorithm that combines critical components from continuous ant colony optimization, artificial bee colony optimization and genetic algorithms for solving cardinality constrained portfolio optimization problem. Computational results on seven publicly available benchmark problems confirm the effectiveness of the hybrid integration mechanism. Moreover, comparisons against other methods’ results in the literature reveal that the proposed solution approach is competitive with state-of-the-art algorithms.

A Numeric-Symbolic Solution of GNSS Phase Ambiguity

Solution of the Global Navigation Satellite Systems (GNSS) phase ambiguity is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. In this paper, three alter-native algorithms are suggested. Two of them are based on local and global linearization via McCormic Envelopes, respectively. These algorithms can be effective in case of simple configuration and relatively modest number of satellites. The third method is a locally nonlinear, iterative algorithm handling the problem as {-1, 0, 1} programming and also lets compute the next best integer solution easily. However, it should keep in mind that the algorithm is a heuristic one, which does not guarantee to find the global integer optimum always exactly. The procedure is very powerful utilizing the ability of the numeric-symbolic abilities of a computer algebraic system, like Wolfram Mathematica and it is properly fast for minimum 4 satellites with normal configuration, which means the Geometric Dilution of Precision (GDOP) should be between 1 and 8. Wolfram Alpha and Wolfram Clouds Apps give possibility to run the suggested code even via cell phones. All of these algorithms are illustrated with numerical examples. The result of the third one was successfully compared with the LAMBDA method, in case of ten satellites sending signals on two carrier frequencies (L1 and L2) with weighting matrix used to weight the GNSS observation and computed as the inverse of the corresponding covariance matrix.

Timetabling for Strategic Passenger Railway Planning

In research and practice, public transportation planning is executed in a series of steps, which are often divided into the strategic, the tactical, and the operational planning phase. Timetables are normally designed in the tactical phase, taking into account a given line plan, safety restrictions arising from infrastructural constraints, as well as regularity requirements and bounds on transfer times. In this paper, however, we propose a timetabling approach that is aimed at decision making in the strategic phase of public transportation planning and to determine an outline of a timetable that is good from the passengers’ perspective. Instead of including explicit synchronization constraints between train runs (as most timetabling models do), we include the adaption time (waiting time at the origin station) in the objective function to ensure regular connections between passengers’ origins and destinations. We model the problem as a mixed integer quadratic program and linearise it. Furthermore we propose a heuristic to generate starting solutions. We illustrate the type of solutions found by our approach on two case studies based on the Dutch railway network and analyse trade-offs that are made to balance dwell times and regularity of trains.

Power Scheduling in More Electric Aircraft Based on an Optimal Adaptive Control Strategy

In this article, an optimal control problem (OCP) for the power management system is proposed for the more electric aircraft (MEA) with consideration of the dynamics in the generators and the energy storage systems. Electrical power components included in the electrical power system (EPS) of MEA such as the generator, the bus, the rectifier, and the battery system are modeled in this OCP. Based on this formulation, a three-stage optimization architecture is introduced to obtain the optimal power references and the optimal control policies. In the first stage, an optimization problem for the power scheduling and allocation is solved as a mixed integer quadratic programming problem and the optimal power allocation schemes (power references) are obtained. In the second stage, an OCP to minimize the fluctuations in power generation systems is proposed and solved via an off-policy integral reinforcement learning approach. In the third stage, the voltage restoration is applied to maintain the main-bus voltage in the onboard high voltage dc system. Extensive case studies are carried out to illustrate the effectiveness of our proposed methodology. Simulations show that the optimal power references are obtained based on various requirements, and the optimal power control policy is achieved based on off-policy iterations.

A Pragmatic Approach to Massive MIMO for Broadband Communication Satellites

In this paper, we analyze the performance of Massive Multiple Input Multiple Output (M-MIMO) techniques aiming at increasing the throughput of broadband satellites. In particular, we investigate a “pragmatic” approach to the design of the M-MIMO to ease its implementation both at system and satellite payload level. We compare the performance of optimized classical Minimum Mean Square Error (MMSE), Zero Forcing (ZF), Matched Filter (MF) schemes with the proposed “pragmatic” M-MIMO one dubbed fixed Multi-Beam (MB). To further boost the M-MIMO performance, a novel radio resource management approach based on Mixed Integer Quadratic Programming (MIQDP-RRM) is proposed. The adoption of MIQDP-RRM is shown to greatly enhance the M-MIMO throughput performance. It is shown that the MB scheme closely approximate the MF, ZF and MMSE performance with a much simpler active antenna-based payload architecture and without requiring any user channel estimation. The MB MIQDP-RRM M-MIMO pragmatic solution allows to achieve higher satellite broadband throughput compared to a conventional four colors frequency reuse scheme (CFR) with affordable complexity for both space and ground segments. At the same time we show that by non-conventional CFR multi-beam array design, the performance gap compared to MB MIQDP-RRM M-MIMO can be significantly reduced.

FPGA Implementation Framework for Explicit Hybrid Model Predictive Control

Hybrid systems can be controlled by a Hybrid Model Predictive Control (HMPC) with an accurate prediction model and proper formulation. In the real-time evolution of HMPC, an online optimization (mostly, Mixed Integer Quadratic Programming (MIQP)) problem needs to be solved at each sample time. Online implementation of MIQP solver on resource-limited embedded platforms poses challenges, which limits its use for the slow dynamic systems. The online burden of MIQP solver can be moved offline by multi-parametric programming. In this paper, we present an implementation of explicit HMPC on Field Programmable Gate Array (FPGA) for the control of Mixed Logical Dynamical (MLD) systems. We show the step-by-step procedure of FPGA implementation of HMPC considering the model of the inverted pendulum. In the implementation, we used MATLAB-based Hybrid Toolbox to construct hybrid MPC and subsequently generate a low-level C/C++ code of the HMPC. Further, the generated C/C++ code is optimized for memory, speed, and resource utilization by the customized approach of applying pipelining and directives using Xilinx Vivado. The customized explicit HMPC is then implemented on a Xilinx ZYNQ-7000 SoC ZC706 FPGA. The implemented approach is compared with the linear (online and explicit) MPC with a linearized model of the system. The detailed analysis of controller computational complexity in terms of memory, resource utilization, clock, and power consumption is presented. The performance of implemented HMPC is verified through Hardware-in-the-Loop (HIL) co-simulations.

Exact Augmented Lagrangian Duality for Mixed Integer Quadratic Programming

Mixed integer quadratic programming (MIQP) is the problem of minimizing a convex quadratic function over mixed integer points in a rational polyhedron. This paper focuses on the augmented Lagrangian dual (ALD) for MIQP. ALD augments the usual Lagrangian dual with a weighted nonlinear penalty on the dualized constraints. We first prove that ALD will reach a zero duality gap asymptotically as the weight on the penalty goes to infinity under some mild conditions on the penalty function. We next show that a finite penalty weight is enough for a zero gap when we use any norm as the penalty function. Finally, we prove a polynomially bound on the weight on the penalty term to obtain a zero gap.

Nonlinear Model Predictive Control applied to Concentrated Solar Power Plants

This papers presents a nonlinear model predictive controller (NMPC) for temperature control in solar collector fields. The proposed NMPC uses feedback linearization for handling the systems nonlinearities in a mixed integer quadratic programming (MIQP) formulation that makes the constraints convex in the new coordinates, making the controller solution an optimal one. Several simulations are shown with real data and a validated model of solar field to illustrate the advantages of the proposed strategy over other general-purpose NMPC methods, showing great improvement in constraint satisfaction.

Semi-active vibration control of structural systems based on linear approximation of switched linear system

For vibration control of structural system, semi-active control is expected to show better performance than other control methods in terms of energy efficiency. However, because of the energy dissipation characteristics of the semi-active control devices, the mathematical model of the semi-active control system becomes a hybrid model. Optimal control of hybrid models can be solved by mixed integer quadratic programming. However, this method is computationally expensive because the optimization problem must be solved for every sampling instant. One such computationally inexpensive method is clipped-optimal control, but its performance is not guaranteed because it does not consider the constraints of energy dissipation of the semi-active device. The clipped-optimal control can be expressed as a switching system of three systems under the influence of energy dissipation constraints. In a 1-DOF (degree of freedom) system, the switching conditions of the three systems can be expressed as angles on a phase plane. The 1-DOF vibration system draws an ellipse in the forced vibration and a spiral in an initial response on the phase plane. In the case of a vibration system that draws a circle-like trajectory on the phase plane, unlike other switching systems, the selection of these three systems is performed at a substantially constant rate. In this study, we propose a semi-active control method using a single linear system composed of the above three systems. The linear systems are referred to as the averaged systems in the study. We propose a method to systematically design the clipped-optimal control, which has been conventionally designed by trial and error, with the averaged system. Simulation studies show the effectiveness of the proposed semi-active control approach.

Active Damping of Parallel Robots Driven by Elastic Cables using On-Off Actuators through Model Predictive Control Allocation

This work studies the vibration rejection on elastic cable-driven parallel robots (CDPRs). Additional cold-gas thrusters are embedded on the robot in order to improve the rejection bandwidth. Such Unilateral Force Generators (UFGs) work as on-off actuators. Under the framework of optimal control, a Model Predictive Control (MPC) is designed to compute the control law and allocate the control signals to the available actuators by assigning their binary on-off states, thus forming a Mixed Integer Quadratic Programming (MIQP)-based MPC controller. Simulations highlight the benefits of the proposed predictive approach that yields a better rejection, fuel efficiency, and a reduced switching between ON and OFF states with respect to previous approaches.

Input Design for Active Dectection of Integrity Attacks using Set-based Approach

This paper presents the design of an input sequence in order to actively guarantee detectability of integrity attacks. The design of the input sequence is formulated as an optimization problem where the performance degradation imposed in the protected system is minimized while guaranteeing attack detectability by separating the reachable sets of the system in healthy and attacked operation. By considering uncertainties bounded by zonotopes, the design of an optimal open-loop input sequence such that guarantee the separability of the reachable zonotopic sets can be computed by solving a Mixed Integer Quadratic Program (MIQP). Following this approach, attack detection can be guaranteed by: I) forcing a distinct behavior of the system outputs; II) ensuring that residuals under attack will exit the healthy residual set. Furthermore, the present work also considers the imposition of residuals detectability for the specific replay attack scenario affecting an state estimate control system. The effectiveness of the proposals is validated in simulation by means of a numerical example.

A Multi-Vehicle, Multi-Factory Assignment Problem: A Case of Coca-Cola Bottling Company at Ahinsan and Spintex-Ghana

Determining the type of vehicles to transport goods between multiple factories and numerous distributors with different demands is one of the major logistic decisions that have to be made by industry players to reduce the cost of operations. A Mixed-Integer Quadratic Programming (MIQP) model was used to optimally distribute goods to 105 distributors from two factories across Ghana. The formulated model and analysis show that the existence of multiple vehicles in a fleet purposely for long hauling of goods also renders an optimal minimum cost as compared to a single-vehicle fleet. This optimum minimum cost accounts for 0.2066 of the total cost incurred by the two factories. This resulted in a 25% reduction in transportation cost. Again, a single-vehicle fleet with loading capacity within the mean value of all individual demands gave a minimum cost next to the optimal minimum.

Event-Triggered Switched Pinning Control for Merging or Splitting Vehicle Platoons

Abstract This paper proposes a switched pinning control algorithm with an event-triggering mechanism. The target vehicle platoons are expressed by the multi-agent systems in which pinning agents receive target velocities from external devices. We construct a model predictive control (MPC) algorithm that switches pinning agents via mixed-integer quadratic programming (MIQP). The frequency of the switching, i.e., the solving of the MIQP problems is determined according to the convergence rate of vehicles to the target velocities. This event-triggering mechanism can reduce the calculation cost of the MPC in the steady. Moreover, our algorithm regroups platoons to the arbitrary ones by controlling the adjacent vector that expresses the adjacency between vehicles. As a result, our algorithm allows the external devices to form arbitrary platoons and control the velocity of each platoon while considering the calculation cost.

Risk-Based Coordination of Maintenance Scheduling and Unit Commitment in Power Systems

The line random failure caused by multiple uncertainties has become a non-negligible factor which influences the safe operation of power systems. In this paper, a risk-based coordination model of maintenance scheduling and unit commitment is established and the objective is to minimize the total operation cost consisting of the maintenance cost, generation cost and risk cost. A random generation method is proposed to obtain line failure scenarios based on arbitrary failure rate functions. In the base case, security constraints must be satisfied while the potential overflow caused by line outages is calculated in contingency scenarios. In order to handle this mixed integer quadratic programming, a solving strategy based on three-layer iterations is applied. In the exterior iterative layer, Lagrangian relaxation technology is used to coordinate the maintenance scheduling and the risk-based unit commitment until the maintenance schedule is available for the optimized unit commitment plan. In other two iterative layers, Benders decomposition method is adopted to the further problem decomposition. In the middle layer, iterations between the unit commitment sub-problem and the risk-based dispatch sub-problem are used to guarantee the optimality of risk-based unit commitment. In interior iterations, the feasibility of unit commitment plan is checked by an optimal load shedding model. Case studies are performed on a 6-bus test system and a 118-bus test system. Results show that the total operation cost decreases by coordination while the system operating risk can be effectively controlled.

Optimal Freewheeling Control of a Heavy-Duty Vehicle Using Mixed Integer Quadratic Programming

Improving the powertrain control of heavy-duty vehicles can be an efficient way to reduce the fuel consumption and thereby reduce both the operating cost and the environmental impact. One way of doing so is by using information about the upcoming driving conditions, known as look-ahead information, in order to coast in gear or to use freewheeling. Controllers using such techniques today mainly exist for vehicles in highway driving. This paper therefore targets how such control can be applied to vehicles with more variations in their velocity. The driving mission of such a vehicle is here formulated as an optimal control problem. The control variables are the tractive force, the braking force, and a Boolean variable representing closed or open powertrain. The problem is solved by a model predictive controller, which at each iteration solves a mixed integer quadratic program. The fuel consumption is compared for four different control policies: a benchmark following the reference of the driving cycle, look-ahead control without freewheeling, freewheeling with the engine idling, and freewheeling with the engine turned off. Simulations on a driving cycle with a varying velocity profile show the potential of saving 11%, 19%, and 23% respectively for the control policies compared with the benchmark, in all cases without increasing the trip time.

An Optimal Generation Scheduling Approach Based on Linear Relaxation and Mixed Integer Programming

This paper proposes an optimal generation scheduling approach based on linear relaxation and mixed integer programming, which is used to solve the generation dispatch problem. The quadratic transmission loss constraint of each transmission line is converted into linear constraints by using the linear relaxation and mixed integer programming technique. Consequently, the original optimal generation scheduling problem is formulated as a quadratic programming or mixed integer quadratic programming problem that can be solved by commercial optimization solver. In order to improve the efficiency of algorithm, this paper further analyses the generation scheduling model and deletes the redundant variables and constraints. Three test systems, including IEEE 30-node system, IEEE 118-node system, and Polish 2746-node system, are employed to examine the effectiveness of the proposed method. The comparative results obtained by the proposed method, quadratically constrained quadratic programming method (QCQP), and solving constraint integer programs solver (SCIP) verify the effectiveness of the proposed method in solving the optimal generation scheduling problem.

Piecewise Linear Function Fitting via Mixed-Integer Linear Programming

Piecewise linear (PWL) functions are used in a variety of applications. Computing such continuous PWL functions, however, is a challenging task. Software packages and the literature on PWL function fitting are dominated by heuristic methods. This is true for both fitting discrete data points and continuous univariate functions. The only exact methods rely on nonconvex model formulations. Exact methods compute continuous PWL function for a fixed number of breakpoints minimizing some distance function between the original function and the PWL function. An optimal PWL function can only be computed if the breakpoints are allowed to be placed freely and are not fixed to a set of candidate breakpoints. In this paper, we propose the first convex model for optimal continuous univariate PWL function fitting. Dependent on the metrics chosen, the resulting formulations are either mixed-integer linear programming or mixed-integer quadratic programming problems. These models yield optimal continuous PWL functions for a set of discrete data. On the basis of these convex formulations, we further develop an exact algorithm to fit continuous univariate functions. Computational results for benchmark instances from the literature demonstrate the superiority of the proposed convex models compared with state-of-the-art nonconvex models.