Integer Quadratic Programming Research Articles

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.

Omnichannel product selection and shelf space planning optimization

As the retail industry is evolving toward an omnichannel paradigm, we study a product selection and shelf space planning problem faced by omnichannel retailers. We aim to maximize aggregated profits across channels by determining the optimal product offerings for the offline and online channels while optimizing the allocation of limited shelf space to these products in brick-and-mortar stores. Furthermore, the showroom effect of physical stores on online sales is also taken into account. We propose a corresponding model that jointly optimizes these decisions. To solve the nonlinear nonconvex model of practical scale, we first reformulate it into a mixed integer quadratic programming by exploring the structural properties. Next, we use the reformulation linearization technique to further improve the computational speed. Our numerical studies validate the efficiency of the proposed solution approach. In addition, we derive some managerial insights, including that retailers should adopt joint optimization and consider how the involved effects and parameters may influence their profits and decisions.

Optimal household appliances scheduling for smart energy management considering inclining block rate tariff and net-metering system

Smart grids that integrate household renewable energy sources and share information with households can help create and maintain a smarter data-driven environment. Within this environment, flexible home energy management policies that minimize household energy costs can be adopted. This paper considers a smart home with a renewable energy source that favors satisfying its energy needs at minimum cost. This is achievable by smartly scheduling the use of its domestic appliances to match a given energy grid tariff. Focusing on the case of Egypt in which an inclining block rate (IBR) tariff is imposed, this paper fills a gap in the literature regarding the load scheduling models aiming to minimize energy cost at the household level whenever such a tariff exists. A new mixed integer quadratic programming (MIQP) model is formulated for this scheduling problem, considering the adopted net metering system with installed domestic photovoltaic (PV) systems in Egypt. The model generates the optimal household load schedule and the optimal amounts of energy to exchange with the grid while considering all the system and consumer utility constraints. To assess the applicability of the proposed model, a survey is conducted to identify the diversity and characteristics of using the electrical appliances by the Egyptian households. Based on the collected survey results, the effectiveness of the proposed MIQP model is investigated. Results confirm the effectiveness of the proposed model to minimize energy cost for different categories of the Egyptian households.

A Unified Framework Integrating Trajectory Planning and Motion Optimization Based on Spatio-Temporal Safety Corridor for Multiple AGVs

Planning safe and smooth trajectories for multiple autonomous ground vehicles (MAGVs) in a complex dynamic unstructured environment is a fundamental and challenging task. In this paper, a novel unified framework integrating trajectory planning and motion optimization (TPMO) is proposed based on spatio-temporal safety corridor (STSC), which guarantees collision avoidance and trajectory smoothness. The proposed TPMO framework consists of two parts. The first part is to establish the STSC for each AGV based on the mixed integer quadratic programming (MIQP) algorithm. The proposed STSC method ensures collision avoidance in the environment of static and dynamic obstacles, and provides a longitudinal and lateral coupled trajectory (LLCT) for trajectory planning. The second part is to design a motion optimization methodology, which considers the constraints of AGV geometry as well as longitudinal and lateral coupled motion characteristics. Moreover, our formulation provides a theoretical guarantee that the entire trajectory is optimal under collision avoidance. Finally, the proposed TPMO framework is applied to solve the optimal cooperative trajectory and motion planning problem of MAGVs in a near-natural simulation and real vehicle environments, validating the proposed framework's effectiveness and practicality.

Research on Indoor Digital Design and Experience Based on Perception and Behavioral Association

Abstract This study examines interior digital design and experience based on perceptual-behavioral associations, focusing on how users’ perceptual cognition affects the internal design experience. This study collects data on users’ physiological and psychological responses when observing interior design by combining eye movement and electroencephalography techniques. Morphological analysis was used to deconstruct and reorganize the interior design elements, while the Mixed Integer Quadratic Programming (MIQP) method was used to design the interior space layout. The experimental results show that subjects’ average perceptual imagery ratings of interior schemes in the internal design perception and behavioral experiments differed significantly, and the EEG data and eye movement data exhibited specific behavioral characteristics. For example, there were statistically significant differences in perceptual imagery ratings and physiological data across interior design schemes within a particular time window. Combining eye-movement and EEG data can capture users’ perceptual perceptions and behavioral responses.

A Hierarchical Multi-Vehicle Coordinated Motion Planning Method Based on Interactive Spatio-Temporal Corridors

Multi-vehicle coordinated motion planning has always been challenged to safely and efficiently resolve conflicts under non-holonomic dynamic constraints. Constructing spatial-temporal corridors for multi-vehicle can decouple the high-dimensional conflicts and further reduce the difficulty of obtaining feasible trajectories. Therefore, this paper proposes a novel hierarchical multi-vehicle coordinated motion planning method based on interactive spatio-temporal corridors (ISTCs). In the first layer, based on the initial guidance trajectories, Mixed Integer Quadratic Programming is designed to construct ISTCs capable of resolving conflicts in generic multi-vehicle scenarios. And then in the second layer, Non-Linear Programming is settled to generate in-corridor trajectories that satisfy the vehicle dynamics. By introducing ISTCs, the multi-vehicle coordinated motion planning problem is able to be decoupled into single-vehicle trajectory optimization problems, which greatly decentralizes the computational pressure and has great potential for real-world applications. Besides, the proposed method searches for feasible solutions in the 3-D <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(x,y,t)$</tex-math></inline-formula> configuration space, preserving more possibilities than the traditional velocity-path decoupling method. Simulated experiments in unsignalized intersection and challenging dense scenarios have been conducted to verify the feasibility and adaptability of the proposed framework.

Optimal Solution for the Integrated Model of the Problems in Capacitated Vehicle Routing and Vehicle Scheduling at the Multi-door Depot

To have an efficient Supply Chain (SC), the coordination and integration of the activities in the SC are mandatory. Routing vehicles is an optimization problem in the SC. When the routed vehicles return to the depot and the doors at the depot are busy, the returned vehicles must wait to unload the accumulated shipments. Therefore, properly scheduling these vehicles to those doors at the depot to minimize the waiting time is an optimization problem in the SC. Therefore, in this study, routing vehicles to collect the shipments from suppliers and scheduling vehicles to doors at the depot, based on a first-come-first-serve basis, are simultaneously solved. Hence, the objective of this integrated vehicle routing and scheduling problem (VR&amp;SP) is to minimize the total cost which contains the following components: vehicle travelling cost between suppliers, loading cost at the suppliers, vehicle waiting cost, unloading cost at the depot and vehicle operations cost. A Mixed Integer Quadratic Programming (MIQP) model is developed to solve the integrated VR&amp;SP. The Branch and Bound algorithm method is employed to obtain the exact optimal solution to this MIQP using LINGO optimization software. The compatibility of the developed MIQP model is verified by the randomly generated small-scale instances of VR&amp;SP. Therefore, it can be concluded that, this model solves the vehicle routing to suppliers and vehicle scheduling to doors at the depot simultaneously. Since VR&amp;SP is a NP-hard problem, heuristics or meta-heuristic methods are recommended to solve the large-scale instances of VR&amp;SP. Moreover, it can be recommended for further studies to amend this model by incorporating additional constraints to make it more applicable to real-world scenarios.

Optimal design of hydrogen-based storage with a hybrid renewable energy system considering economic and environmental uncertainties

Hydrogen and electricity derived from renewable sources present feasible alternative energy options for the decarbonisation of the transportation and power sectors. This study presents the utilisation of hydrogen generated from solar and wind energy resources as a clean fuel for mobility and backup storage for stationary applications under economic and environmental uncertainties. This is achieved by developing a detailed techno-economic model of an integrated system consisting of a hydrogen refuelling station and an electric power generation system using Mixed Integer Quadratic Constrained Programming (MIQCP), which is further relaxed to Mixed Integer Linear Programming (MILP). The model is implemented in the Advanced Interactive Multidimensional Modelling Software (AIMMS) and considering the inherent uncertainties in the wind resource, solar resource, costs and discount rate, the total cost of the three configurations (Hybrid PV-Wind, Standalone PV, and Standalone wind energy system) was minimised using robust optimisation technique, and the corresponding optimal sizes of the components, levelised cost of energy (LCOE), excess energy, greenhouse emission avoided, and carbon tax were evaluated. The levelised cost of the deterministic optimisation solution for all the configuration ranges between 0.0702 $/kWh to 0.0786 $/kWh, while the levelised cost of the robust optimisation solution ranges between 0.07188 $/kWh to 0.1125 $/kWh. The proposed integration has the advantages of affordable hydrogen and electricity prices, minimisation of carbon emissions and grid export of excess energy.

Trade-off between optimal design and operation in district cooling networks

Especially in densely populated areas, district cooling represents an opportunity to reduce energy consumption and emissions. Nevertheless, this technology is characterised by large capital costs which impede its diffusion. As a consequence, optimization tools can significantly help to unleash their potential. In this paper, a methodology is proposed to combinedly optimize the design and operation of a district cooling system based on a Mixed Integer Quadratic Programming. The model is compared to the design only optimization, based on a properly tailored heuristic approach. The models, when applied to a case study characterized by seasonal demand, provide similar solutions, which differ by 0.5 % in terms of objective value for a standard scenario. The simultaneous design and operation optimization does not provide sensible savings with respect to optimizing solely the design. A sensitivity analysis is performed to prove the robustness of the results. The results showed that the simultaneous operation and design optimization would be limited to 1 % of total costs in the case of seasonal cooling demand. On the other hand, if the cooling demand persists throughout the year, as in tropical climates, the combined optimization provides significant benefits, since these savings reach 4.7 % of total costs.

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.

Risk-based distributionally robust optimal dispatch for multiple cascading failures in regional integrated energy system using surrogate modeling

Regional integrated energy system (RIES) with the close coupling of multiple energies faces various cascading failure risks in its operation, and formulating the risk-based optimal dispatch scheme is important to ensure the secure and economic operation of the RIES. Considering that the occurrence probability of each subsequent failure path caused by the initial failure in the cascading failure chain varies with the change of dispatch scheme, the cooling/heating and gas pipeline dynamics and the uncertainty of renewable energy, a risk-based distributionally robust optimal dispatch model for multiple cascading failures in a RIES is proposed. A kernel ambiguity set is constructed by using the maximum mean discrepancy between the real and reference probability distributions and the kernel mean embedding technology, which can obtain the more accurate worst-case probability distribution. Moreover, a surrogate modeling method based on piecewise convex quadratic functions is proposed to learn the mapping between the cascading failure risks and the decision variables, and the original large-scale mixed integer nonlinear programming model is transformed into a small-scale mixed integer quadratic constrained programming model for efficient solution. Finally, case study on an actual RIES demonstrates the effectiveness and advantages of the proposed method. Compared to optimal dispatch without considering the cascading failure risks, the proposed method can reduce the total failure risk cost by nearly 60%.

Techno-economic investigation of hybrid peaker plant and hydrogen refuelling station

The power and transport sectors are responsible for significant emissions of greenhouse gases. Therefore, it is imperative that substantial efforts are directed towards the decarbonisation of these industries. This study establishes a combined-solar-wind system's economic and technical practicality for producing hydrogen for an onsite hydrogen refuelling station (HRS) and electricity to meet peak demand. To minimise the levelised cost of electricity and maximise the system's reliability at different commercial locations in South Africa, the dual-objective optimisation sizing is carried out using Mixed Integer Quadratic Constrained Programming (MICQP) model and was executed with an Advanced Multi-dimensional Modelling System (AIMMS) [61], [62]. The levelised costs of electricity and hydrogen at Johannesburg, Pretoria and Cape Town for 2 MW grid export benchmark are 74.2 $/MWh/5.85 $/kg, 76.3 $/MWh/5.97 $/kg and 50 $/MWh/4.45 $/kg respectively. The CO₂ equivalent emissions (tonnes) are 54,000, 55,800, 59,000 and the corresponding carbon taxes ($) avoided for the locations are 432,100, 446,200, and 472,000 for Johannesburg, Pretoria and Cape Town respectively. The results of the framework show that it can be adopted as a viable and fossil-free replacement for conventional peaking generators.

Flexible yard space allocation plan for new type of automated container terminal equipped with unilateral-cantilever rail-mounted gantry cranes

In this paper, new automated container terminals equipped with Unilateral-cantilever Rail-Mounted Gantry Cranes (URMGC) are considered as the research object. In the scenario, the automated guided vehicles can go deep among the container blocks arranged perpendicularly to the shoreline, which completely changes the yard’s operation mode and affects its operational efficiency. In addition, considering the shortage of storage space in the yard, a flexible space allocation strategy for these yards is studied, and a mixed integer quadratic programming model is established to minimize the horizontal transportation cost of containers. An improved particle swarm optimization algorithm is designed to compensate for the increased complexity of the proposed model. To accelerate the solution speed, the quantity and priority rules are developed to generate reasonable initial solutions, and two velocity updating strategies are adopted to accelerate convergence. Numerical experiments are conducted to validate effectiveness and efficiency of the proposed method, and comparisons with fixed space allocation strategy are presented. The results show that the strategy and solution adopted in this paper can reduce the driving distance of AGVs in such terminal configurations effectively and potentially increase the handling capacity of the yard.

Smart distribution grid management during a worst-case scenario of renewable energy outage

Nowadays, due to the high penetration of renewable energy sources such as wind generation and PV in the distribution network and the possibility of their outage, the optimal operation of the distribution grid has faced challenges. In this paper, a bi-level model based on mixed integer quadratic programming (MIQP) is proposed for the optimal operation of smart distribution networks under the worst case of the outage of renewable energy resources. At the upper-level problem, minimization of the energy losses, energy purchase, and load shedding in the demand side management program is formulated, and at the lower-level problem, the maximization of output and curtailment of renewable energy resources is modeled. At the lower level, the worst-case realization of the renewable outage is derived and at the upper level, optimal operation of the distribution network is done under the worst-case realization of renewable resources. The reformulation method based on Karush–Kuhn–Tucker (KKT) conditions is considered to solve the proposed bi-level model, which is faster and less complicated than similar algorithms. The IEEE 33-bus distribution grid is considered for the analysis of the proposed model and method, which proves the accuracy and optimal performance of the proposed model and method. The findings indicate that, with the implementation of the suggested model, the smart distribution network successfully avoided load-shedding even when various renewable resources were disconnected. Also, the proposed model in operation under normal conditions has caused a 56% reduction in losses and a 53% reduction in energy purchases compared to the outage of 6 renewable units in the distribution network.

Feature matching of remote‐sensing images based on bilateral local–global structure consistency

AbstractThe goal of feature matching is to establish accurate correspondences between feature points in different images depicting the same scene. To address the polymorphism of local structures, the authors propose a mismatch removal method using bilateral local–global structural consistency. This method incorporates the problem of mismatch removal into the framework of graph matching, constructs a global affinity matrix using local structural similarity and global affine transformation consistency, and optimizes it using a constrained integer quadratic programming method. To comprehensively describe the local structure, the signature quadratic form distance (SQFD) is used to measure the consistency of the neighbourhood structure. Specifically, the weights of edges are constructed based on the SQFD of the local structure, while the matching correctness of nodes and edges between the two graphs is described using local vector similarity. Furthermore, the consistency of the global affine transformation is evaluated by assessing the consistency of the local neighbourhood affine transformation between different corresponding point pairs. In estimating the local affine transformation, a bilateral correction is performed using a total least‐squares (TLS) algorithm to measure the similarity of nodes between the two different graphs. Experimental results demonstrate that the proposed algorithm outperforms state‐of‐the‐art methods in terms of accuracy and effectiveness.

Complex energy-reserve orders for generators with income and ramping restrictions on European electricity markets

Electricity market integration is an ongoing process in the European power sector. One of its important development areas concerns the integrated, combined trading of different power system products such as energy and control reserves. However, the complicated technical and economic characteristics of generators pose challenges for simple energy-reserve offers. Our solution approach is to unify them with complex orders. The latter have been introduced to represent special generator characteristics on the currently operating European energy-only market. The unified order type is designed to keep all the advantageous properties and functionality of its predecessors. Similarly to simple energy-reserve offers, the decision between energy and control reserve products takes opportunity costs into account. This is a necessary property of optimal capacity allocation. The non-convex fixed costs of suppliers are represented using Minimum Income Conditions and Scheduled Stop Conditions while their ramping limits are handled by Load Gradient Conditions. All three of these components belong to complex orders originally. The resulting new model can be formulated in a single convex Mixed Integer Quadratic Program, and it is fully compatible with European market rules. The viability and adequacy of the proposal are demonstrated using numerical case studies.

Risk-averse decision-making to maintain supply chain viability under propagated disruptions

In this paper, stochastic optimisation of CVaR is applied to maintain risk-averse viability and improve resilience of a supply chain under propagated disruptions. In order to establish the risk-averse boundaries on supply chain viability space, two stochastic optimisation models are developed with the two conflicting objectives: minimisation of Conditional Cost-at-Risk and maximisation of Conditional Service-at-Risk. Then, the risk-averse viable production trajectory between the two boundaries is selected using a stochastic mixed integer quadratic programming model. The proposed approach is applied to maintain the supply chain viability in the smartphone manufacturing and the results of computational experiments are provided. The findings indicate that when the decision-making is more risk-aversive, the size of the viability space between the two boundaries is greater. As a result, more room is available for selecting viable production trajectories under severe disruptions. Moreover, the larger is viability space, the higher is both worst-case and average resilience of the supply chain. Risk-neutral, single-objective decision-making may reduce the supply chain viability. A single-objective supply chain optimisation which moves production to the corresponding boundary of the viability space, should not be applied under severe disruption risks to avoid greater losses.