Integer Quadratic Programming Problem Research Articles

Two stage beamforming and combining scheme for FDD massive MIMO systems with multi‐antenna users

AbstractThis paper proposes a two‐stage beamforming and combining scheme in frequency division duplex (FDD) massive multiple‐input multiple‐output (MIMO) systems with multi‐antenna users. Specifically, the proposed scheme is a two‐stage scheme, where the pre‐beamforming matrix and pre‐combining matrix are designed using the channel covariance matrix (CCM) in the first stage. The problem of the pre‐beamforming matrix and pre‐combining matrix design are formulated as an 0–1 quadratic integer programming problem. To solve this problem, it is further transformed into an 0–1 mixed linear integer programming problem. In the second stage, the sparse code multiple access and multi‐user precoding and combining are adopted to mitigate the inter‐user interference. Different from the previous transmission scheme using CCM, the proposed scheme consider the multi‐antenna user system, and uses the CCM to design both the pre‐beamforming and pre‐combining matrices to sparsify the effective channel matrix, such that the overhead of pilot and feedback can be reduced. Moreover, the sparse code multiple access can help to better reduce the inter‐user interference. Simulation results validate the good performance of the proposed scheme.

A mathematical programming approach to export pathway planning of distributed hydrogen production in offshore wind farm

Hydrogen production is a vital development trend to improve the economics and penetration rate of offshore wind farms (OWFs), and distributed hydrogen production (DHP) is a preferred solution for deep and far sea OWFs without expensive submarine cables and offshore substations. The export pathway of OWF-DHP consists of collection pipelines, transmission pipelines, and offshore compressor stations. In this paper, mathematical programming is introduced to explore the export pathway planning problem of OWF-DHP. Firstly, the area of OWF is discretized into multiple grids with the center of the grids being the candidate locations of the offshore compressor station. Then, a binary integer quadratic programming problem is established to optimize both the offshore compressor station location and pipeline construction with different topologies. Further, the mathematical model is solved by the branch and cut algorithm integrated with the proposed dimension reduction methods. Finally, the effectiveness of the proposed export pathway planning approach is verified by the actual data of Baltic Eagle OWF in Germany, which would support the construction of the OWF-DHP project.

Hybrid model predictive control for vehicle trajectory tracking with integrated attitude adjustment

This paper presents a vehicle trajectory tracking method that integrates attitude adjustment. The method utilizes the asymmetric adjustment of the damping of the adjustable damping shock absorber to lift the left and right vehicle body and carry out the attitude adjustment of the vehicle. Additionally, it actively tilts toward the inside of the curve during turning. In order to address the nonlinear constraints of damping asymmetry regulation and the mixed logic relationship between suspension asymmetry damping switching and left and right body lifting during body attitude regulation, a mixed logic dynamic system (MLD) for vehicle attitude adjustment is established. Subsequently, the vehicle trajectory tracking controller is designed using the hybrid model predictive control theory (HMPC), which integrates active steering control and attitude adjustment. The optimal control problem of hybrid systems is transformed into a hybrid integer quadratic programming problem and solved through finite time domain rolling optimization. The effectiveness of the proposed integrated controller is confirmed through Simulink simulation. Compared with pure tracking control and roll tracking control with zero roll angle as the control target, this controller demonstrates its ability to effectively track the reference trajectory and enhance the vehicle’s dynamic performance.

Optimised operation of integrated community energy system considering integrated energy pricing strategy: A two-layer Stackelberg game approach

Aiming at the problems of new energy absorption and inter-subject interest conflict in the integrated community energy system, this study proposed an integrated energy pricing strategy that considered the interconversion of various energy sources and built a two-layer optimisation model of the electric-gas-heat‑hydrogen interconnection integrated community energy system. The upper-layer operator model maximises the revenue by setting energy price and selling energy to users. The lower-layer users model minimises the energy cost by actively adjusting energy usage strategy according to energy price. The two sides rationally pursue the maximisation of their respective interests, and the process of bargaining can be described by Stackelberg game. The model is also considered for combining the characteristics of elastic load and vehicle-to-grid on the demand side and operates jointly with the bus battery swapping station and two-stage power-to-gas for optimizing system operation. Through theoretical derivation, it is proved that there is a unique Stackelberg equilibrium solution for the proposed game model. Further, the two-layer optimisation model is transformed into a mixed integer quadratic programming problem by applying the Karush-Kuhn-Tucher optimal condition, linear relaxation technique, and duality theorem. Finally, the global optimal energy price is obtained by solving the converted model. The optimisation results in different scenarios show that the proposed model and method not only protect the interests of the operator and users but also improve the wind power absorption capacity of the community and reduce the load fluctuation.

Multi-View Randomized Kernel Classification via Nonconvex Optimization

Multi kernel learning (MKL) is a representative supervised multi-view learning method widely applied in multi-modal and multi-view applications. MKL aims to classify data by integrating complementary information from predefined kernels. Although existing MKL methods achieve promising performance, they fail to consider the tradeoff between diversity and classification accuracy of kernels, preventing further improvement of classification performance. In this paper, we tackle this problem by generating a number of high-quality base learning kernels and selecting a kernel subset with maximum pairwise diversity and minimum generalization errors. We first formulate this idea as a nonconvex quadratic integer programming problem. Then we transform this nonconvex problem into a convex optimization problem and prove it is equivalent to a semidefinite relaxation problem, which a semidefinite-based branch-and-bound algorithm can quickly solve. Experimental results on the real-world datasets demonstrate the superiority of the proposed method. The results also show that our method works for the support vector machine (SVM) classifier and other state-of-the-art kernel classifiers.

Optimization of a quadratic programming problem over an integer efficient set

Multi-objective programming problem often contains numerous efficient solutions, which confuses the decision-maker. To assist in selecting the most desirable solution, optimizing a function over the efficient set becomes crucial. In this paper, we present a novel method for optimizing a general quadratic function over the efficient set of a multi-objective integer linear programming problem. To solve this problem, a ranking approach and efficiency test is utilized. The proposed methodology obtains a globally optimal solution by systematically scanning ranked solutions of an integer quadratic programming problem until the efficiency condition is satisfied. For generating ranked solutions, we construct a related integer linear programming problem. Then, ranked solutions of the integer linear programming problem are used for enumerating ranked solutions of the integer quadratic programming problem. The convergence of our algorithm is established theoretically, and its steps are illustrated using a numerical example. Aparticular case of the proposed method for optimizing a linear function over the efficient set of a multi-objective integer linear programming problem is also discussed. Further, extensive computational results demonstrate the effectiveness of our method for solving problems with large number of constraints, variables, and objective functions. Moreover, comparative analysis shows that the developed algorithm came out to be computationally more efficient as compared to the existing state-of-the-art algorithms.

Cooperative Beamforming for RIS-Aided Cell-Free Massive MIMO Networks

The combination of cell-free massive multiple-input multiple-output (CF-mMIMO) and reconfigurable intelligent surface (RIS) is envisioned as a promising paradigm to improve network capacity and enhance coverage capability. However, to reap full benefits of RIS-aided CF-mMIMO, the main challenge is to efficiently design cooperative beamforming (CBF) at base stations (BSs), RISs, and users. Firstly, we investigate the fractional programing to convert the weighted sum-rate (WSR) maximization problem into a tractable optimization problem. Then, the alternating optimization framework is employed to decompose the transformed problem into a sequence of subproblems, i.e., hybrid BF (HBF) at BSs, passive BF at RISs, and combining at users. In particular, the alternating direction method of multipliers algorithm is utilized to solve the HBF subproblem at BSs. Concretely, the analog BF design with unit-modulus constraints is solved by the manifold optimization (MO) while we obtain a closed-form solution to the digital BF design that is essentially a convex least-square problem. Additionally, the passive BF at RISs and the analog combining at users are designed by primal-dual subgradient and MO methods. Moreover, considering heavy communication costs in conventional CF-mMIMO systems, we propose a partially-connected CF-mMIMO (P-CF-mMIMO) framework to decrease the number of connections among BSs and users. To better compromise WSR performance and network costs, we formulate the BS selection problem in the P-CF-mMIMO system as a binary integer quadratic programming (BIQP) problem, and develop a relaxed linear approximation algorithm to handle this BIQP problem. Finally, numerical results demonstrate superiorities of our proposed algorithms over baseline counterparts.

How to Share: Balancing Layer and Chain Sharing in Industrial Microservice Deployment

With the rapid development of smart manufacturing, edge computing-oriented microservice platforms are emerging as an important part of production control. In the containerized deployment of microservices, layer sharing can reduce the huge bandwidth consumption caused by image pulling, and chain sharing can reduce communication overhead caused by communication between microservices. The two sharing methods use the characteristics of each microservice to share resources during deployment. However, due to the limited resources of edge servers, it is difficult to meet the optimization goals of the two methods at the same time. Therefore, it is of critical importance to realize the improvement of service response efficiency by balancing the two sharing methods. This paper studies the optimal microservice deployment strategy that can balance layer sharing and chain sharing of microservices. We build a problem that minimizes microservice image pull delay and communication overhead and transform the problem into a linearly constrained integer quadratic programming problem through model reconstruction. A deployment strategy is obtained through the successive convex approximation (SCA) method. Experimental results show that the proposed deployment strategy can balance the two resource sharing methods. When the two sharing methods are equally considered, the average image pull delay can be reduced to 65% of the baseline, and the average communication overhead can be reduced to 30% of the baseline.

An Optimization Framework for Data Collection in Software Defined Vehicular Networks.

A Software Defined Vehicular Network (SDVN) is a new paradigm that enhances programmability and flexibility in Vehicular Adhoc Networks (VANETs). There exist different architectures for SDVNs based on the degree of control of the control plane. However, in vehicular communication literature, we find that there is no proper mechanism to collect data. Therefore, we propose a novel data collection methodology for the hybrid SDVN architecture by modeling it as an Integer Quadratic Programming (IQP) problem. The IQP model optimally selects broadcasting nodes and agent (unicasting) nodes from a given vehicular network instance with the objective of minimizing the number of agents, communication delay, communication cost, total payload, and total overhead. Due to the dynamic network topology, finding a new solution to the optimization is frequently required in order to avoid node isolation and redundant data transmission. Therefore, we propose a systematic way to collect data and make optimization decisions by inspecting the heterogeneous normalized network link entropy. The proposed optimization model for data collection for the hybrid SDVN architecture yields a 75.5% lower communication cost and 32.7% lower end-to-end latency in large vehicular networks compared to the data collection in the centralized SDVN architecture while collecting 99.9% of the data available in the vehicular network under optimized settings.

Minimal Detectable and Isolable Faults of Active Fault Diagnosis

This article aims to compute guaranteed minimal detectable and isolable faults of set-based active fault diagnosis methods for discrete linear time-invariant systems. First, guaranteed detectable and isolable faults of set-based active fault diagnosis methods are defined in this article. Second, an augmented vector is defined to integrate the effect of both inputs and faults such that the couplings of inputs and faults can be handled effectively. Third, guaranteed minimal detectable and isolable faults are computed by solving a mixed integer quadratic fractional programming problem under a proposed theoretic framework. At the end of this article, an example is used to illustrate the effectiveness of the proposed solution.

An algorithm to solve multi-objective integer quadratic programming problem

An algorithm to solve multi-objective integer quadratic programming problem

An approximation algorithm for indefinite mixed integer quadratic programming

In this paper, we give an algorithm that finds an \(\epsilon \)-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected unless P = NP. In order to design this algorithm we introduce the novel concepts of spherical form MIQP and of aligned vectors, and we provide a number of results of independent interest. In particular, we give a strongly polynomial algorithm to find a symmetric decomposition of a matrix, and show a related result on simultaneous diagonalization of matrices.

A novel preview control for MLD models and its neural network approximation for real‐time implementation: Application to semi‐active vibration control of a vehicle suspension

Advances in image processing technology have made it possible to measure the surface shape of the road ahead while driving. A new semi-active suspension control method considering the forward road surface shape is proposed. A vehicle model equipped with a semi-active suspension can be expressed as an mixed logical dynamical model. When the shape of the road ahead can be measured, the information on future disturbances is available before the vehicle undergoes. In this paper, the finite time optimization problem for the mixed logical dynamical model is formulated to consider the future disturbances as a mixed integer quadratic programming problem in the same way as the conventional control problem without future disturbance. However, the mixed integer quadratic programming problem is hard to obtain the control action within the control cycle period required in the real-time vibration control with general computers for vehicles. In this paper, the reduction of the computational load is achieved by constructing an approximation function of the designed controller. A neural network is adopted for the approximation. The performance evaluation of the proposed method is evaluated by simulations. In the simulation study, the proposed method achieves better ride comfort with the equivalent suspension stroke compared to the traditional methods.

Optimal Communication Network Design of Microgrids Considering Cyber-Attacks and Time-Delays

Distributed secondary control stands out for its flexibility and expandability in microgrids (MGs) control, in where communication network plays a fundamental and critical role. The communication topology and link-weights have significant impact on the attack-resilience and dynamic performance of MGs, which should be appropriately designed. However, the joint optimization problem of communication topology and link-weights in the existing literature of consensus-based secondary voltage control of MGs is usually neglected. To bridge this gap, we propose a novel two-stage optimization approach for the communication network design, which jointly optimizes the topological structure to enhance the structural survivability and link weights to improve the dynamic performance (including the speed of convergence and robustness to time-delay). The first stage problem is formulated into a mixed-integer semi-define programming (MISDP) model based on convex relaxation technique, which is then converted equivalently into an integer quadratic programming (IQP) problem and then a MISDP feasibility problem to facilitate the solution. The second stage problem is formulated into a bi-objective SDP model to compromise between the convergence performance and robustness to time-delay. Simulations based on a microgrid with 10 distributed generation (DG) units under different scenarios are implemented to verify the effectiveness of the proposed method.

Allocating synthetic population to a finer spatial scale: An integer quadratic programming formulation

Agent-Based Models (ABMs) are being increasingly used to evaluate urban systems, urban policies and environmental impacts. One prerequisite for using the ABM framework consists of generating a synthetic population representative of the actual population, featuring the appropriate attributes with respect to model objectives. A precise spatial positioning of the synthetic population agents is often key to ensuring ABM modeling quality. This paper considers the problem of allocating synthetic population agents to a finer spatial scale. Such an allocation process is performed from a higher-level statistical area where a synthetic population can be generated, that is, a container statistical area (CSA), to several nested non-overlapping elementary statistical areas (ESAs), where only marginals are available. This allocation step relies not only on common attributes between CSA and ESA, but also on additional discriminatory attributes, that is, attributes of interest, estimated from external data sources. The case study examined herein is based on French census and fiscal data. Common attributes include eight socio-demographic variables, totaling 17 modalities. An additional attribute of interest, that is, income, has also been added. The allocation problem at hand is modeled as an integer quadratic programming problem. An exact algorithm is first applied to solve the problem; the applicability of this algorithm proves to be limited to small-size synthetic populations. A heuristic is proposed to handle the allocation of larger-size synthetic populations. Tests carried out on the case study show that this heuristic yields near-optimal solutions; it is also computationally efficient and may fulfill the needs of a majority of users.

Global optimization on non-convex two-way interaction truncated linear multivariate adaptive regression splines using mixed integer quadratic programming

Multivariate adaptive regression splines (MARS) has been adopted as a popular surrogate function to model the unknown relationships between input and output variables in complex systems. Searching optimal solutions on the complicated surrogate response surface of MARS serves as important tasks in various applications. In this paper, we present an efficient and effective approach to find a global optimal value of MARS models that incorporate two-way interaction terms which are products of truncated linear univariate functions (TITL-MARS). Specifically, with a MARS model consisting of linear and quadratic structures, we can reformulate the optimization problem on TITL-MARS into a mixed integer quadratic programming problem (TITL-MARS-OPT), which can be further solved in a more principled way. To illustrate the effectiveness of our proposed approach TITL-MARS-OPT, we come up with a genetic algorithm and a gradient descent algorithm to solve the original version of TITL-MARS, and we compared the performance of the proposed approach with the benchmark algorithms. Numerical experiments are conducted on a spectrum of examples with different levels of complexity, including 6 existing models and a real world application in the wind farm optimization. Our proposed approach can find a global optimal successfully and efficiently while the comparison algorithms fail to find a global optimal solution. In the end, Python code for TITL-MARS and TITL-MARS-OPT is made available on GitHub ( https://github.com/JuXinglong/TITL-MARS-OPT).

Passenger-to-Car Assignment Optimization Model for High-Speed Railway with Risk of COVID-19 Transmission Consideration

Narrow and closed spaces like high-speed train cabins are at great risk for airborne infectious disease transmission. With the threat of COVID-19 as well as other potential contagious diseases, it is necessary to protect passengers from infection. Except for the traditional preventions such as increasing ventilation or wearing masks, this paper proposes a novel measurement that optimizes passenger-to-car assignment schemes to reduce the infection risk for high-speed railway passengers. First, we estimated the probability of an infected person boarding the train at any station. Once infectors occur, the non-steady-state Wells–Riley equation is used to model the airborne transmission intercar cabin. The expected number of susceptible passengers infected on the train can be calculated, which is the so-called overall infection risk. The model to minimize overall infection risk, as a pure integer quadratic programming problem, is solved by LINGO software and tested on several scenarios compared with the classical sequential and discrete assignment strategies used in China. The results show that the proposed model can reduce 67.6% and 56.8% of the infection risk in the base case compared to the sequential and discrete assignment, respectively. In other scenarios, the reduction lies mostly between 10% and 90%. The optimized assignment scheme suggests that the cotravel itinerary among passengers from high-risk and low-risk areas should be reduced, as well as passengers with long- and short-distance trips. Sensitivity analysis shows that our model works better when the incidence is higher at downstream or low-flow stations. Increasing the number of cars and car service capacity can also improve the optimization effect. Moreover, the model is applicable to other epidemics since it is insensitive to the Wells–Riley equation parameters. The results can provide a guideline for railway operators during the post-COVID-19 and other epidemic periods.

Optimizing UI layouts for deformable face-rig manipulation

Complex deformable face-rigs have many independent parameters that control the shape of the object. A human face has upwards of 50 parameters (FACS Action Units), making conventional UI controls hard to find and operate. Animators address this problem by tediously hand-crafting in-situ layouts of UI controls that serve as visual deformation proxies, and facilitate rapid shape exploration. We propose the automatic creation of such in-situ UI control layouts. We distill the design choices made by animators into mathematical objectives that we optimize as the solution to an integer quadratic programming problem. Our evaluation is three-fold: we show the impact of our design principles on the resulting layouts; we show automated UI layouts for complex and diverse face rigs, comparable to animator handcrafted layouts; and we conduct a user study showing our UI layout to be an effective approach to face-rig manipulation, preferable to a baseline slider interface.

A heuristic algorithm for medical staff's scheduling problems with multiskills and vacation control.

The main issue related to the duty schedule is to allocate medical staff to each medical department by considering personnel skills and personal vocation preferences. However, how to effectively use staff's multiskill characteristics and how to execute vocation control have not been well investigated. This article aims to develop duty scheduling and vacation permission decisions to minimize the sum of customers' waiting costs, the overtime cost of medical staff, the cost of failing to meet medical staff' vacation requirements, and the cost of mutual support between departments. This study formulated the problem as a multiperiod mixed integer nonlinear programming model and developed a hybrid heuristic based on evolutionary mechanism of genetic algorithm and linear programming to efficiently solve the proposed model. Five types of problems were solved through Lingo optimization and the proposed approach. For small-scale problems, both methods can find the optimal solutions. For a slightly larger problem, the solutions found by the proposed approach are superior those of Lingo. This research discusses the complex decision-making problem of on-duty arrangement and vacation control of medical staff in a multidepartmental medical center. This research formulates the medical staff's scheduling and vacation control problems as constrained mixed integer quadratic programming problems. Computational results indicate that the proposed approach can efficiently produce compromise solutions that outperform the solutions of the Lingo optimization software.

Station-grid Co-planning of Integrated Energy System with Consideration of Multi-energy storage and Reliability Cost

In order to improve the reliability of integrated energy system, the station-grid co-planning model and its solution method are proposed. The planning model considers the constraints of distribution network, gas distribution network, heat distribution network and energy station, and aims at minimizing the total planning cost within the planning period including investment cost, maintenance cost and reliability cost. It realizes the optimal planning for the types and locations of energy supply sources, distribution pipelines, energy stations and energy storage devices, such as electricity storage devices, gas storage devices, heat storage devices and cooling storage devices. The model is a mixed integer quadratic programming problem, which is solved by Gurobi. The case study uses the modified electricity-gas-heat integrated energy system to analyse the system planning scheme and planning cost under two scenarios. The results show that the proposed model can reasonably plan the integrated energy system and further improve the reliability of the integrated energy system.