Mixed Integer Quadratic Programming Research Articles

FuncPipe: A Pipelined Serverless Framework for Fast and Cost-Efficient Training of Deep Learning Models

Training deep learning (DL) models in the cloud has become a norm. With the emergence of serverless computing and its benefits of true pay-as-you-go pricing and scalability, systems researchers have recently started to provide support for serverless-based training. However, the ability to train DL models on serverless platforms is hindered by the resource limitations of today's serverless infrastructure and DL models' explosive requirement for memory and bandwidth. This paper describes FuncPipe, a novel pipelined training framework specifically designed for serverless platforms that enable fast and low-cost training of DL models. FuncPipe is designed with the key insight that model partitioning can be leveraged to bridge both memory and bandwidth gaps between the capacity of serverless functions and the requirement of DL training. Conceptually simple, we have to answer several design questions, including how to partition the model, configure each serverless function, and exploit each function's uplink/downlink bandwidth. In particular, we tailor a micro-batch scheduling policy for the serverless environment, which serves as the basis for the subsequent optimization. Our Mixed-Integer Quadratic Programming formulation automatically and simultaneously configures serverless resources and partitions models to fit within the resource constraints. Lastly, we improve the bandwidth efficiency of storage-based synchronization with a novel pipelined scatter-reduce algorithm. We implement FuncPipe on two popular cloud serverless platforms and show that it achieves 7%-77% cost savings and 1.3X-2.2X speedup compared to state-of-the-art serverless-based frameworks.

분산전원 수용률 향상을 위한 전압 및 무효전력 제어 알고리즘

In this paper, a global measurement-based voltage and reactive power control algorithm using a linear equation is proposed. For linear optimization, the voltage control characteristics of the voltage controllers of the distribution system are expressed in a linear form. It was divided according to the characteristics of each control device and expressed in a linear expression, and the final voltage was expressed as the sum of each control device from the principle of superposition. The voltage equation expressed as a linear expression was formulated as a quadratic programming method (QP). The optimal solution was derived using the mixed integer quadratic programming (MIQP, Mixed-Integer Quadratic Programming), which is a mixed integer nonlinear programming (MINLP), for the objective function expressed by the quadratic programming method. The proposed algorithm was verified through simulation.

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.

Receding-Horizon Control of Constrained Switched Systems with Neural Networks as Parametric Function Approximators

This work studies receding-horizon control of discrete-time switched linear systems subject to polytopic constraints for the continuous states and inputs. The objective is to approximate the optimal receding-horizon control strategy for cases in which the online computation is intractable due to the necessity of solving mixed-integer quadratic programs in each discrete time instant. The proposed approach builds upon an approximated optimal finite-horizon control law in closed-loop form with guaranteed constraint satisfaction. The paper derives the properties of recursive feasibility and asymptotic stability for the proposed approach. A numerical example is provided for illustration and evaluation of the approach.

Entropy-Maximization-Based Customer Order Allocation of Clothing Production Enterprises in the Sharing Economy

With the rapid development of the sharing economy, more and more platform operators apply the sharing concept in manufacturing, which increases the efficiency of assets utilization. Considering the apparel industry, clothing enterprises or manufacturers may share their excess orders between each other via a manufacturing cloud platform. Under the traditional production mode, manufacturers focus on processing their individual orders. There may be a coexistence of insufficient and surplus production capabilities. Some manufacturers cannot meet their customer demands due to limited capabilities and some orders have to be rejected, while some other manufacturers may have excess capacities with insufficient demands. It results in loss of revenue, and it is not conducive to maintaining a good customer relationship. In this paper, we consider a shared system with multiple manufacturers that produce homogeneous products, and the manufacturers in the shared system can share customer orders with each other. Once any manufacturer cannot fulfill all of its orders, the unsatisfied ones will be shared with other manufacturers that have surplus capacities with the aim of improving the balance of resource utilization and risk resistance of all manufacturers on the platform. The entropy maximization theory is mainly adopted to facilitate the formulation of the objective function. We apply a Taylor expansion to reformulate the objective function and construct a mixed-integer quadratic programming (MIQP) model. We employ off-the-shelf solvers to solve small-scale problems, and also propose a two-stage constructive heuristic algorithm to solve large-scale problems. Numerical experiments are conducted to demonstrate the efficiency of the algorithm.

Data-driven robust optimization using deep neural networks

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called the uncertainty set. An ongoing challenge in the recent literature is to derive uncertainty sets from given historical data that result in solutions that are robust regarding future scenarios. In this paper we use an unsupervised deep learning method to learn and extract hidden structures and anomalies from data, leading to non-convex uncertainty sets and better robust solutions. We prove that most of the classical uncertainty classes are special cases of our derived sets and that optimizing over them is strongly NP-hard. Nevertheless, we show that the trained neural networks can be integrated into a robust optimization model by formulating the adversarial problem as a convex quadratic mixed-integer program. This allows us to derive robust solutions through an iterative scenario generation process. In our computational experiments, we compare this approach to a similar approach using kernel-based support vector clustering and to other benchmark methods. We find that uncertainty sets derived by the unsupervised deep learning method find a better description of data and lead to robust solutions that often outperform the comparison methods both with respect to objective value and feasibility.

Distributed MPC-based energy scheduling for islanded multi-microgrid considering battery degradation and cyclic life deterioration

In this paper, distributed model predictive control (MPC) based energy scheduling problem is presented for islanded multi-microgrids. The objective is to achieve supply–demand balance in an individual microgrid through energy coordination and reduce the battery degradation for its extended cycle life. In order to achieve desired objective, the battery state of charge is taken as zone control optimization problem and new slack variable is introduced as optimized variable to restrict the battery state of charge in optimal range with considering battery degradation. Furthermore, accelerated distributed augmented Lagrangian (ADAL) based distributed coordination strategy is presented, which can improve power supply reliability through coordinated cooperation among MGs for energy exchanges. The system framework is modeled as mixed-integer dynamic model which switches between different operating conditions. A mixed-integer quadratic programming approach is addressed to solve the MPC optimization problem. The effectiveness of the proposed scheme is validated through comparative performance with existing model. Finally, convergence analysis and comparative fast convergence performance of the proposed scheme is provided.

Robust energy management for industrial microgrid considering charging and discharging pressure of electric vehicles

The growing number of electric vehicles (EVs) has resulted in increasing availability of battery storage capacities. The energy storage capacity of EVs is used to provide demand flexibility for the supply side. However, the different preferences of EV users will affect the charge and discharge decision of EVs. To overcome this problem, the concept of charging and discharging pressure is proposed to restrict the charging and discharging behavior of EVs. It is mainly dominated by the electricity price. Simultaneously, the charging and discharging time anxiety and state of charge (SoC) of EVs also affect the charging and discharging mode of EVs. This paper proposes a novel industrial microgrid (IMG) structure, which is mainly composed of power demand of industrial production, renewable energy sources (RES), energy storage systems (ESS), EVs and thermal power generation units. The aim of the proposed model is to minimize the operation cost of IMG and maximize the income of EV users. For the management of demand side, the strategy of time of use (ToU) price is adopted. In addition, considering the uncertainty of RES and industrial load, a robust optimization algorithm is proposed, and the operation of IMG under different uncertain scenarios is analyzed. Finally, the robust mixed integer quadratic programming (MIQP) of IMG is studied. The detailed simulation and comparison results verify the effectiveness of the proposed energy system under different charging and discharging pressures based on EVs.

Real-time neural network based semiactive model predictive control of structural vibrations

Semiactive model predictive control (sMPC) can be very effective, but its computational cost due to the inherent mixed-integer quadratic programming (MIQP) optimization precludes its use in real-time vibration control. This study proposes training neural networks (NNs) to predict in real-time only the MIQP’s integer variables’ values, called a strategy, for a given structure state. Because the number of strategies is exponential in the number of sMPC horizon steps, the resulting NN can be massive. This study proposes to reduce the NN dimension by exploiting the homogeneity-of-order-one nature of this control problem and, using state vector statistics, to efficiently choose training samples. The single large NN is proposed to be split into several much smaller NNs, each predicting a strategy grouping, that together uniquely and efficiently predict the strategy. Given the strategy’s integer values, the MIQP optimization reduces to a quadratic programming (QP) problem, solved using a fast QP solver with proposed adaptations: exploiting optimization efficiencies and bounding sub-optimality; using several NN predictions; and reverting to a simpler (suboptimal) semiactive control algorithm upon occasional incorrect NN predictions or QP solver nonconvergence. Shear building examples demonstrate significant online computational cost reductions with control performance comparable to the conventional MIQP-based control.

An improved column generation algorithm for the disrupted flight recovery problem with discrete flight duration control and aircraft assignment constraints

The disrupted flight recovery problem is well-studied in the literature owing to its significant impact on airlines and passengers. In this work, we consider the disrupted flight recovery problem with two new realistic aspects, i.e., a new implementation for changing flight duration as a recovery option and considering the aircraft assignment constraints. Firstly, we develop a new mixed-integer quadratic programming model encapsulating a functional relationship between the reduced flight duration and the changes in fuel consumption using a piecewise function. Secondly, we propose an improved column generation approach to solve some scenarios based on actual flight data obtained from an airline. Lastly, the experimental results show that the improved column generation algorithm can obtain the optimal solution for all scenarios. Compared with not considering changing the flight duration, considering changing the flight duration can save about 24% of recovery costs on average. In addition, we analyze the effect of enforcing aircraft assignment constraints and different fuel prices on recovery costs. Based on the experimental results, we discuss how to support practitioners in choosing the appropriate combination of recovery options.

Linear approximations to improve lower bounds of a physician scheduling problem in emergency rooms

The physician assignment process consists of coverage of shifts and duties allocated to physicians in a planning period, taking into account work regulations, individual preferences, and organizational rules, which mostly conflict with each other. In this work, we propose a reformulated mixed-integer programming model based on the literature to tackle fairness in physician scheduling in Emergency Rooms (ERs). In particular, we propose two mixed-integer quadratic programming formulations that consider quadratic costs and two models with linear costs. Our approaches provide balanced schedules concerning target hours and weekends in terms of fairness. Our models also provide a high degree of demand coverage, providing decision-makers a significant advantage.

An integrated two‐dimensional merging trajectory optimization model for automated vehicles considering mixed traffic flow

Recently, automated vehicles have been recognized as a promising tool to address the problem of on-ramp merging. However, the complexity of the problem includes ignorance of the vehicle's lateral dynamics, the limitation of the fixed merging point, the mismatch problem caused by the sequential optimization scheme, and the fixed terminal states assumption. These factors make it intractable in practical driving scenarios. This paper proposed an integrated optimization model for on-ramp automated vehicles, which can guide the vehicle to complete the merging behaviour from the ramp lane to the main lane safely and efficiently. A merging path is first constructed in the two-dimensional plane with two critical parameters recommended by a neural network predictor, enabling it to incorporate both longitudinal and lateral dynamics. Then, an integrated Mixed Integer Quadratic Program (MIQP) model is built to determine the optimal velocity profiles and merging gap simultaneously while considering the safety and efficiency factors. Specifically, with the introduction of discretization and linearization techniques, linear collision avoidance constraints and smooth transition constraints can be built, which can address the challenging computational problem. The effectiveness of the proposed model is validated through the microscopic and macroscopic numerical results under different levels of mixed traffic.

Stackelberg game-based optimal scheduling of integrated energy systems considering differences in heat demand across multi-functional areas

Demand-side management is very critical in China’s energy systems because of its high fossil energy consumption and low system energy efficiency. A building shape factor is introduced in describing the architectural characteristics of different functional areas, which are combined with the characteristics of the energy consumed by users to investigate the features of heating load in different functional areas. A Stackelberg game-based optimal scheduling model is proposed for electro-thermal integrated energy systems, which seeks to maximize the revenue of integrated energy operator (IEO) and minimize the cost of users. Here, IEO and users are the Stackelberg game leader and followers, respectively. The leader uses real-time energy prices to guide loads to participate in demand response, while the followers make energy plans based on price feedback. Using the Karush–Kuhn–Tucker (KKT) condition and the big-M method, the model is transformed into a mixed-integer quadratic programming (MIQP) problem, which is solved by using MATLAB and CPLEX software. The results demonstrate that the proposal manages to balance the interests of IEO and users. Furthermore, the heating loads of public and residential areas can be managed separately based on the differences in energy consumption and building shape characteristics, thereby improving the system operational flexibility and promoting renewable energy consumption.

Maximum Flow Routing Strategy With Dynamic Link Allocation for Space Information Networks Under Transceiver Constraints

In this paper, we investigate the maximum flow routing strategy with dynamic link allocation under a constraint on the number of transceivers for space information networks (SINs). Specifically, the time-expanded graph (TEG) is exploited to characterize the dynamic topology of SINs. Furthermore, although there exist multiple feasible links for SINs, only a limited number of them can be actually established due to the constraint on the number of transceivers. Traditionally the established link is fixed within one time interval in the TEG. In order to fully exploit the resource of multiple feasible links, we divide each time interval in the TEG into multiple fine-grained time periods and design the maximum flow routing strategy by jointly optimizing both the fine-grained time period duration and the link allocation as well as the amount of data transmitted on each transmission link and the amount of data stored in each caching link. This problem can be formulated as a mixed-integer quadratic program (MIQP), which is difficult to solve. To overcome this difficulty, we transform the MIQP into an equivalent mixed-integer linear program (MILP), which can be effectively solved by existing methods. Simulation results show that the proposed dynamic link allocation strategy can significantly outperform the fixed link allocation strategy within each time interval.

Real-Time Topology Detection and State Estimation in Distribution Systems Using Micro-PMU and Smart Meter Data

Distribution network topology detection and state estimation in real-time are critical for modern distribution systems management and control. However, number of sensors in distribution networks are limited and communication links between switch devices and distribution management system are not well-established. In this regard, this paper proposes mixed-integer quadratic programming (MIQP) formulations to determine the topology of distribution network and estimate distribution system states simultaneously using micro-phasor measurement units (micro-PMUs) and smart meter data. Two approaches based on AC optimal power flow are proposed and analyzed: (i) polar power-voltage (PPV) formulation, and (ii) rectangular current-voltage (RIV) formulation. The proposed models include convex objective function while constraints are linearized using first-order approximation of Taylor series and Big M method. The proposed models can identify multiple simultaneous switching actions at each time instant and different topology configurations including radial and meshed networks. Only measurement data at each time interval is needed to identify topology and states of the system correctly. The proposed models are tested on a modified IEEE-33 bus system with realistic load data from Pecan Street Inc. database. The results confirm that both models can identify system topology and states with remarkable accuracy in real-time, while RIV model outperforms PPV model.

Coordinating transportation and pricing policies for perishable products

We study the joint pricing and transportation problem in a perishable product supply chain where products with different levels of quality are substitutable depending on the pricing policy and the customers’ quality sensitivity. We propose two frameworks to study this problem under sequential and integrated systems. Pricing and transportation decisions are made separately and then coordinated through an iterative process in the sequential model, but jointly optimized in the integrated system. The integration of transportation and pricing leads to a challenging mixed-integer quadratic programming (MIQP) formulation which is intractable for the current state-of-the-art commercial solvers. We exploit the special structure of this formulation and develop a Benders type decomposition method with a transportation master problem and a collection of pricing subproblems. To evaluate the proposed models and algorithms, we perform numerical experiments on an illustrative case study. We show that the performance of the sequential model is noticeably inferior to the integrated optimization model on two key metrics: profit and product waste. We observe, counter-intuitively, that the presence of customers with lower quality sensitivity who tolerate imperfect products increases the waste to sales ratio. Moreover, due to the interrelationship between pricing and transportation policies, the waste to sales ratio is not monotone in the cost of the freshness keeping efforts. Finally, we show the practical efficiency of our proposed decomposition-based algorithm in solving the MIQP compared to the state-of-the-art solver.

Two-stage resilience-constrained planning of coupled multi-energy microgrids in the presence of battery energy storages

In recent years, severe weather-related catastrophes have caused irreparable damages to the body of power systems, which has attracted the attention of planners to increase the resilience of power systems. In line with the goals of this issue, this paper introduces a two-stage programming on the basis of resilience oriented model to design solar panels, micro-turbines, and mobile batteries within the multi energy carrier microgrid to increase the resilience of the system against high-impact events. The propounded framework is formulated as mixed-integer quadratic programming that takes investment decisions at the first stage while optimizing operation variables at the second stage in order to reinforce the resilience of the system. An integrated power and gas model is used to increase the perception of readers about the mutual interactions between electricity and heat energy. Therefore, the availability of fuel and the price of the micro turbine are explicitly formulated and evaluated. One-line diagram of 14-bus coupled micro energy grids is used to investigate the efficiency and proficiency of the proposed model. Comparative studies numerically show that the suggested method helps the microgrid operator in identifying optimal solutions to reinforce the resilience of power system against severe events.

Experimental tests on the performance of an economic model predictive control system in a lightweight building

• Economic MPC was tested in a lightweight laboratory. • Effect of HVAC system models accuracy was discussed. • MPC improved PV self-consumption and operating costs compared to thermostat. • Oversimplified models led to higher thermal discomfort and increased consumption. European policies are fostering the electrification of energy use, including space heating and cooling systems, in order to decarbonise the building stock. The significant penetration of electrical loads and domestic photovoltaic (PV) plants has therefore become an important topic for researchers and engineers working in the building sector. In this context, this paper presents a recently constructed laboratory for testing efficient management strategies in all-electric houses. The article describes the laboratory and the Model Predictive Control (MPC) strategy developed to minimize economic costs for space heating while ensuring thermal comfort in the indoor environment with a simulated rooftop PV system. The proposed controller leverages prior knowledge about the physical and geometric properties of the building and the optimization problem is formulated using mixed-integer quadratic programming. This article reports the results of calibration and optimization performed in open loop, as well as two closed loop tests where the MPC controls the HVAC system using receding horizon. The predictive controller was able to substantially increase PV self-consumption in both tests compared to a conventional thermostat, thus cutting electricity costs for heat pump by 10–17%. Such improvement was obtained at the price of a higher thermal comfort violations, mainly due to oversimplified HVAC system models. In light of these findings, the article analyses the effect of such simplifications and suggests possible alternative modelling approaches.

An ℓ0ℓ2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

We introduce the $\ell_0\ell_2$-norm regularization and hierarchy constraints into linear regression for the construction of cluster expansion to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The $\ell_2$-norm regularization is used to suppress intrinsic data noise, while $\ell_0$-norm is used to penalize the number of non-zero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged, and effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of $\ell_0\ell_2$-norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation and convergence speed, reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional $\ell_1$-norm regularized cluster expansion model.

Real-time power optimization for application server clusters based on Mixed-Integer Programming

In the environment of peer competition and energy conservation, optimizing the deployment of application server clusters in real time according to actual workload conditions to reduce operating costs and energy consumption is an important issue that must be urgently addressed. In this paper, we propose a real-time power optimization strategy for application server clusters, and the optimization measures include CPU dynamic voltage/frequency scaling and server dynamic switching. First, the feasibility of defining variables for server types is proved, and appropriate variables are defined to describe the cluster power optimization as a mixed-integer programming (MIP) problem. Then, two solution methods are proposed: the exact method based on the Gurobi optimizer and the approximate method based on primary–secondary optimization and differential evolution with two mutations (PSODE). The former turns the MIP problem into a standard mixed-integer quadratic programming form by introducing intermediate variables and solves it using the Gurobi optimizer. The latter rewrites the MIP problem as a primary–secondary optimization problem and proposes a differential evolutionary-based solution algorithm for the primary optimization problem. The evolutionary process consists of two mutation operations, inter- and intraindividual mutations, which both use a heuristic policy to accelerate the evolution convergence. The test results reveal that the Gurobi-based method can quickly determine the global optimal deployment when the cluster size is small. The PSODE-based method can quickly determine the global optimal deployment or high-quality suboptimal deployment when applied to large-scale clusters.