Mixed-integer Programming Problem Research Articles

Distributed reinforcement learning-based optimization of resource scheduling for telematics

As a reliable computational model in telematics, Mobile Edge Computing (MEC) is utilized to lighten the load on individual autonomous vehicles. It enables computationally expensive and latency-sensitive jobs to be offloaded from cars with limited processing power to servers at edge nodes. This paper presents the joint optimization problem as a mixed nonlinear integer programming problem. The scheduling of vehicle tasks and the distribution of communication resources are then rationalized using a resource allocation algorithm based on Deep Deterministic Policy Gradient (DDPG) reinforcement learning to arrive at a suboptimal solution based on the resource allocation policies of single-intelligent DDPG and multi-intelligent DDPG. The numerical simulation demonstrates the superior service experience of the proposed joint optimization strategy of distributed task offloading and resource allocation based on multi-intelligent DDPG over other association and channel selection strategies and joint resource allocation based on single-intelligent DDPG.

Assessment of reliability measures and cost optimization of a solar seed sowing machine

PurposeIn this research work, the general form of reliability measures, which include availability, mean time to failure (MTTF), and sensitivity analysis, are investigated with their graphical representation, which would help designers and engineers improve the reliability of the system. Along with reliability assessment, a mathematical model is developed and solved to achieve the minimum cost of the system as well as maximum reliability.Design/methodology/approachIn the proposed work, a general model of a solar seed sowing machine is considered for reliability evaluation using the Markov model process. The proposed system is a series-parallel arrangement of components where three components, namely the solar panel, batteries and direct current (DC) motor, are connected in series while all the operators are connected in parallel. The implemented Markov model approach assesses several parameters of reliability, which opens the scope for improvement in reliability and other measures like mean time to failure (MTTF) and sensitivity of the proposed system. So that the machine can deliver the desired output on the field. Also, the particle swarm optimization (PSO) algorithm is applied to optimize the cost of the system with the desired level of reliability.FindingsImplementation of PSO provides the optimal cost for the proposed system with a predetermined level of reliability, which shows the relationship between reliability and cost of the system. Also, the Markov process approach provides the availability function, reliability function, reliability at different time values, MTTF and sensitivity of the proposed system.Originality/valueThis work evaluates the crucial characteristics of reliability for the proposed solar seed sowing machine using the Markov model which is a stochastic model. The assessment of reliability measures such as MTTF, availability and sensitivity plays a vital role in measuring and improving the performance of the machine in the actual environment. Examining the data obtained in this research is of great importance for the manufactures and system designers. Also, the powerful optimization technique PSO is implemented to solve a non-linear mixed-integer programming problem that provides the optimal cost for the system with desired reliability.

Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality

This work introduces a framework to address the computational complexity inherent in Mixed Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics that identify and exploit common structures across MIP instances. We train deep learning models to estimate complicating binary variables for target MIP problem instances. The resulting reduced MIP models are solved using standard off-the-shelf solvers. We present an algorithm for generating synthetic data enhancing the robustness and generalizability of our models across diverse MIP instances. We compare the effectiveness of (a) feed-forward neural networks (ANN) and (b) convolutional neural networks (CNN). To enhance the framework's performance, we employ Bayesian optimization for hyperparameter tuning, aiming to maximize the occurrence of global optimum solutions. We apply this framework to a flow-based facility location allocation MIP formulation that describes long-term investment planning and medium-term tactical scheduling in a personalized medicine supply chain.

Network-level pavement maintenance and rehabilitation planning considering uncertainties using chance-constrained programming

ABSTRACT In practice, given limited funds, to consider multiple strategic goals/objectives that different stakeholders concern, pavement network-level maintenance and rehabilitation (M&R) planning becomes a multi-objective optimisation (MOO) based project selection and budget allocation problem. In an attempt to solve this problem, most agencies established MOO models under the deterministic situation without appropriate consideration of uncertainties. However, ignoring performance uncertainties often leads to unreasonable decisions. To provide more convincing and reliable pavement M&R decisions, this paper proposes a Chance-Constrained Programming (CCP) based MOO method to incorporate performance uncertainties in network-level single period pavement M&R planning. First, a general deterministic MOO model with budget and network performance constraints is established. Then, three commonly-used statistical forms of network-level performance measures are introduced. To incorporate uncertainties, the probability distribution of each form of performance measure is derived. Based on the CCP method, the MOO model is transformed to an equivalent deterministic formulation as a mixed non-linear integer programming (MNLIP) problem. To demonstrate the proposed method, a case study using real data is conducted. The results show that the proposed method can effectively help decision-makers to appropriately incorporate performance uncertainties in conducting network-level pavement M&R planning.

A spiral modeling based on manta ray foraging optimization for wireless networks resource allocation

SummaryThe wireless network resource allocation is a NP‐hard combinatorial optimization problem. This paper proposes a new optimization method using the manta ray foraging optimization (MRFO) based on spiral modeling to solve the wireless network resource problem. In order to reduce the computational complexity and ensure the optimal performance of the allocation scheme, a MRFO algorithm based on spiral modeling and mutation strategy is proposed. In the first stage, spiral modeling is introduced to narrow the exploration area, while the mutation strategy of the genetic algorithm enhances the ability of the algorithm to jump out of the local optimal. In the second stage, a binary MRFO algorithm for using different transfer functions is proposed to solve the mixed integer programming problem. The experimental results show that IMRFO and BIMRFO have high comprehensive performance advantages, achieve better effects than the other optimization algorithms, which lead to faster convergence, faster accuracy, and lower complexity.

Establishing a hierarchical local market structure using multi-cut Benders decomposition

Local electricity markets (LEMs) such as peer-to-peer (P2P) and community-based markets allow prosumers and consumers to exchange electricity products and services locally. In order to coordinate electricity trading and flexibility services, this paper proposes a hierarchical prosumer-centric market framework with a hybrid LEM and a local flexibility market (LFM). Multi-cut Benders decomposition (MCBD) is employed to decompose the integrated hybrid LEM into a centralized P2P market and multiple community-based markets. The aggregators coordinate energy sources and demands of households in low voltage (LV) distribution networks (DN) as virtual power plants (VPPs) and engage in trading through a P2P market over the medium voltage (MV) DN. In addition, a modified MCBD (M-MCBD) approach is proposed to accelerate the convergence process. The LFM is operated by the distribution system operator (DSO) and is formulated as a mixed-integer nonlinear programming (MINLP) problem which is further relaxed to a mixed-integer second-order cone programming (MI-SOCP) problem. The case study demonstrates that aggregators were able to collaborate on trading within the hybrid LEM to minimize the costs incurred by prosumers within the network. Furthermore, the proposed M-MCBD method improves the scalability of the MCBD by enhancing its convergence speed and accuracy, as demonstrated by testing on problems of varying scales.

Mobility-aware and energy-efficient offloading for mobile edge computing in cellular networks

Mobile edge computing (MEC) is a promising paradigm that helps mobile terminals save energy and increase battery life by offloading tasks to MEC servers. To obtain full benefit from MEC, the joint optimization of offloading decision-making and resource allocation, while considering user mobility, is crucial and challenging. The objective of this paper was to propose mobility-aware and energy-efficient offloading schemes for MEC in cellular networks. The proposed schemes helped to make offloading decisions, allocate transit power, and schedule transmissions among multiple moving users. An optimal scheme was proposed, in terms of minimizing total energy consumed by all users, which was based on Mixed-Integer Programming (MIP). Considering the high computational complexity of solving MIP problems, a practical heuristic scheme was also proposed. Simulation results showed the effectiveness in reducing energy consumption of both the proposed optimal and heuristic schemes and demonstrated the importance of mobility awareness as well.

On the fair scheduling of truck drivers in delivery companies: balancing fairness and profit

AbstractFairness is crucial in transportation systems to ensure that all drivers are treated equally and have the same opportunities. Fair payment policies, equal access to work opportunities, and fair scheduling are some of the policies delivery companies implement to ensure fairness between drivers. In this paper, we study a fair scheduling mixed-integer programming problem where we consider a bi-objective function that aims to maximize profit and improve fairness between drivers by minimizing the maximum deviation from the average driving time. To solve this problem, we employ the weighted comprehensive criterion method and propose an iterative population-based heuristic. The results show that the relative gap between the heuristic and exact approach is acceptable. We also report the fairness price which is the relative difference between total profit with and without incorporating fairness. We find out that improving fairness between drivers does not always lead to a significant reduction in total profit. When the reduction in total profit is important, we recommend formulating the scheduling problem differently where instead of minimizing the maximum deviation from the average driving time, drivers are rewarded when their driving times are longer than the average. We explore incorporating the cost of rewarding these drivers in the objective function.

Optimization of trucks and drones in tandem delivery network with drone trajectory planning

Drones are widely recognized as an efficient method for delivering small and lightweight parcels, such as medicines, to customers who are difficult to reach by logistic vehicles. Various studies and projects have been conducted to integrate drones into the traditional logistic service. In this approach, drones stay on trucks, take off from trucks at specific locations to make deliveries to customers, and return to the trucks to replenish and recharge. However, drone trajectories could overlap when multiple drones are used for delivery, which can lead to the risk of collisions. Consequently, the need to address the trajectory planning of drones becomes essential. This work introduces a novel truck-drone routing problem. The novelty presented by this problem lies in the integration of drone trajectory planning problems into the truck-drone routing to generate collision-free routes for drones. This concept has not been previously explored in the existing body of literature. The problem is formulated as a mixed-integer programming problem, and a matheuristic is proposed to solve it. Computational experiments show that the proposed matheuristic outperforms the commercial solver and genetic algorithm in terms of solution quality and search efficiency. Results demonstrate that the integrated truck-drone delivery mode has a lower operating cost than the mere truck mode, and including trajectory planning can prevent potential collisions.

Carbon-Aware Operation of Resilient Vertical Farms in Active Distribution Networks

Emerging utilization of Electric Vehicles (EVs) in Distribution Networks (DNs) decreases the power quality in the DN. The main quest of this research is to find out Can EVs and Photovoltaic (PV) systems support the DN and mitigate the voltage magnitude violations due to utilizing high penetration level EV? This article proposes a novel volt/VAR optimization (VVO) model by leveraging the reactive power support of EVs and PVs as Distributed Energy Resources (DERs) for the DN. The proposed VVO model contains the second-order conic relaxed form of the AC power flow equations. Thus, the presented VVO problem is a Mixed-Integer Second-Order Cone Programming (MISOCP) problem. To obtain the ability to support the DN, Smart Inverters (SIs) are utilized to connect EVs and PV systems to the DN. Thus, to add the PV and EV systems to the convexified form of the VVO problem, the P-Q characteristics and the model of SIs working at different operating points are presented based on experimental results. The proposed model of SIs allows the participation of DERs in the reactive power compensation to mitigate voltage issues of DN due to utilizing high penetration level EVs. Besides, the proposed model of SIs enables DERs to increase their dispatchability. The performance of the proposed model is examined in the case studies using the IEEE 33-bus system and the 123-bus system. It is illustrated in the case studies that the solar dispatchability increases by 12% when the proposed volt/VAR model is utilized for IEEE 33-bus system. Besides, it is illustrated in the case studies that the voltage profile of buses remains in the desired operating range when the proposed model is leveraged, even if the penetration level of EVs increased to 40%.

Look-Ahead Rolling Economic Dispatch Approach for Wind-Thermal-Bundled Power System Considering Dynamic Ramping and Flexible Load Transfer Strategy

With a wind-thermal-bundled power system (WTBPS) under high wind penetration levels, the sharp power fluctuations of tie-lines for interconnected grids trigger a significant challenge of security-constrained power system operation. Smoothing power fluctuations with economic dispatch is widely concerned against this challenge. In this paper, an appropriate look-ahead economic dispatch framework for WTBPS considering the variable ramp rate of retrofitted coal-fired units and the flexible load transfer strategy (LTS) in high voltage distribution networks (HVDNs) is proposed. To cope with this issue, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) we derive a new family of tightened ramping constraints of retrofitted coal-fired units in the linear and second-order conic (SOC) forms, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) Using graph characterization of typical HVDNs, the simplified voltage-constrained LTS via topological structures can be developed. This proposed look-ahead economic dispatch model is cast as a mixed-integer second-order cone programming (MISOCP) problem, which can be reformulated by Multi-cut Generalized Benders Decomposition (MGBD). This MGBD enables multiple sub-problems can be solved in parallel and accelerates the solving process. Finally, simulation results of a large-scale practical system validate the computational accuracy and efficiency of the proposed approach.

Achieving Emission-Reduction Goals: Multi-Period Power-System Expansion Under Short-Term Operational Uncertainty

Stochastic adaptive robust optimization is capable of handling short-term uncertainties in demand and variable renewable-energy sources that affect investment in generation and transmission capacity. We build on this setting by considering a multi-year investment horizon for finding the optimal plan for generation and transmission capacity expansion while reducing greenhouse gas emissions. In addition, we incorporate multiple hours in power-system operations to capture hydropower operations and flexibility requirements for utilizing variable renewable-energy sources such as wind and solar power. To improve the computational performance of existing exact methods for this problem, we employ Benders decomposition and solve a mixed-integer quadratic programming problem to avoid computationally expensive big-M linearizations. The results for a realistic case study for the Nordic and Baltic region indicate which investments in transmission, wind power, and flexible generation capacity are required for reducing greenhouse gas emissions. Through out-of-sample experiments, we show that the stochastic adaptive robust model leads to lower expected costs than a stochastic programming model under increasingly stringent environmental considerations.

A General Framework for Providing Interval Representations of Pareto Optimal Outcomes for Large-Scale Bi- and Tri-Criteria MIP Problems

The Multi-Objective Mixed-Integer Programming (MOMIP) problem is one of the most challenging. To derive its Pareto optimal solutions one can use the well-known Chebyshev scalarization and Mixed-Integer Programming (MIP) solvers. However, for a large-scale instance of the MOMIP problem, its scalarization may not be solved to optimality, even by state-of-the-art optimization packages, within the time limit imposed on optimization. If a MIP solver cannot derive the optimal solution within the assumed time limit, it provides the optimality gap, which gauges the quality of the approximate solution. However, for the MOMIP case, no information is provided on the lower and upper bounds of the components of the Pareto optimal outcome. For the MOMIP problem with two and three objective functions, an algorithm is proposed to provide the so-called interval representation of the Pareto optimal outcome designated by the weighting vector when there is a time limit on solving the Chebyshev scalarization. Such interval representations can be used to navigate on the Pareto front. The results of several numerical experiments on selected large-scale instances of the multi-objective multidimensional 0–1 knapsack problem illustrate the proposed approach. The limitations and possible enhancements of the proposed method are also discussed.

Optimization of film-type optical fiber wiring design using mixed-integer programming problem

Optimization of film-type optical fiber wiring design using mixed-integer programming problem

Smart and efficient EV charging navigation scheme in vehicular edge computing networks

With the increasing number of electric fast charging stations (FCSs) deployed along roadsides of both urban roads and highways, the long-distance travel of electric vehicles (EVs) becomes possible. The EV charging navigation scheme is significant for the quality of user experience. However, the variable conditions of both power grid and traffic networks make it a serious challenge. In this paper, we propose an efficient EV charging navigation scheme while considering both the electric and computation resource sharing. With the support of vehicular edge computing networks in intelligent transportation systems (ITSs), EVs perform both the flexible power load and edge computing nodes. When the traffic network in the established route starts to become congested, EVs can select to enter the nearest FCS. In addition to being supplemented by electric resources, EVs also benefit by sharing their own computing resource with FCSs. We formulate the EV charging navigation as a mixed integer programming problem, the EV moving route planning, FCS selection, and staying time in FCSs are optimized, to balance the relationships among the traveling time, traveling cost and reward. To address the influence caused by the randomness of traffic conditions and charging prices, a two-stage charging navigation algorithm combined with A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^{*}$$\\end{document} algorithm and deep reinforcement learning (DRL) is proposed, with a novel designed reward function. Eventually, numerous experimental results show the effectiveness of the proposed schemes.

Optimal energy management of grid-connected PV for HVAC cooling with ice thermal storage system

Studies have shown that reducing cooling energy costs and increasing operational efficiency may be achieved by utilizing ice thermal energy storage (ITES) technology while maintaining the thermal requirements in space cooling facilities. Optimal control of the ITES system and integration of renewable energy (RE) sources such as PV and geothermal, depending on the availability of resources and application, can further improve the operation of HVAC's cooling systems and mitigate the increased energy cost required for ice formation and overall cooling energy.This study presented optimal switching control of the ice-build chiller for ITES charging and PV power source. Inputs to the model, simulations, and validations were implemented using the available data, which include the historical exogenous meteorological data, temperatures at the inlet and exit of the plant components, manufacturer's information, and readings from the plant's SCADA chosen for the case study.The main aim of the study was to develop an optimal control model that minimizes the energy consumption and cost in the Ice built chiller and other devices, such as pump fans in the HVAC system, by optimal charge and discharge of the ITES and supplementary utilization of the greener energy source PV source under the time of use (ToU) tariff and desired cooling load demand. The case study for a healthcare building was considered in implementing the model.Simulations were implemented in the MATLAB optimization toolbox with the Solving Constrained Integer Programs (SCIP) solver, which was chosen to address mixed integer programming (MIP) problems. It incorporates algorithms like a branch and cut conflict analysis and pre-solving techniques to handle intricate optimization problems involving continuous and discrete decision variables.The optimal switching control model yields approximately 33 % of energy cost savings during the summer months that involve using the HVAC with ITES compared to the current system control (baseline). Additionally, the ITES temperature remained below 0 °C to maintain thermal requirements as an operation constraint. The inclusion of PV and battery options as a source of power to the pumps accounted for 10–15 % of the overall energy usage of the system. Optimal control of the system to utilize the stored energy during peak pricing and high demand periods eliminated the extreme dependence on grid energy in some instances. Despite the additional capital required for the controller, solar PV, and batteries installation, the study projects a return on investment within two years, with a 20-year lifetime energy cost savings estimate of 35 % if inflation and annual electricity price increases are estimated at 5 % and 10 %, respectively.

Random Caching Design for Multi-User Multi-Antenna HetNets With Interference Nulling

The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.

3D deployment of UAV-mounted base stations for heterogeneous access requirements

Recently, unmanned aerial vehicles (UAVs) have been reported a lot as aerial base stations (BSs) to assist wireless communication in Internet of Things (IoT). However, most results for UAV deployment require uniform access requirements and obstacle-free environment. This paper considers multi-UAV-mounted BSs deployment problem in obstacle-laden environment to achieve on-demand coverage for ground user equipments (UEs), with the goal of minimizing the number of required UAVs for full coverage of all UEs by optimizing the three-dimensional (3D) positions of UAVs as well as UE clustering. On one hand, the considered problem is challenging as the constraints on the non-uniform Quality of Service (QoS) requirements, the service ability of each UAV, the beamwidth of the directional antenna equipped by each UAV and obstacle avoidance are jointly taken into account. On the other hand, these practical considerations contribute to broadening the scope of applications. We formulate the problem as a mixed-integer programming problem and develop a three-step placement algorithm to achieve the goal. First, the maximum allowed service radius of each UE is derived based on the Karush-Kuhn-Tucker (KKT) condition to satisfy required signal-to-interference-plus-ratio (SINR) threshold. Second, a greed-prior chaotic search enabled adaptive artificial bee colony (GP-CA2BC) algorithm is proposed to group the UEs such that the minimum number of required UAVs can be obtained. Third, the 3D position of each UAV is optimized to further enhance the QoS. Finally, some simulation results are presented to demonstrate the superiority of the proposed scheme in decreasing the number of required UAVs as well as improving the QoS compared with the existing works.

An Energy-Efficient Multimode Transmission Scheme for Underwater Sensor Network

Underwater sensor network plays a critical role in the ocean data collection owing to its capability of providing reliable and wide communication coverage. How to assure lifetime performance of the network with limited energy supply has always been a key research issue. In this paper, we propose an underwater acoustic sensor network model which supports data delivery from each underwater sensor node (USN) to sea surface sink node (SN) in either direct or relay-assisted transmission mode, i.e., transmission mode between each USN and the SN can be dynamically selected according to network’s current state. To optimize its lifetime performance, we model the mode selection and resource allocation issue jointly into a non-convex and mixed integer programming problem. In order to efficiently solve it, we further divide the original problem into two subproblems: resource allocation subproblem and joint mode and relay selection subproblem. We prove that the reformulated non-convex resource allocation problem can be equivalent to a convex optimization problem, and its optimal solution can be found by using Lagrange dual decomposition method. For the second subproblem, some critical conditions are analyzed to determine optimal relays with the criterion of balancing energy consumption between USNs and a matching approach is designed to obtain the mode and relay selection results based on USNs’ priorities. Simulation results validate that the proposed transmission scheme is effective and superior to the traditional time division multiple access scheme.

RIS Subarray Optimization With Reinforcement Learning for Green Symbiotic Communications in Internet of Things

Symbiotic communications have been deemed as a critical technology for Internet of things (IoT) communications owing to its high spectrum and energy efficiency. Reconfigurable intelligent surface (RIS), which can tune wireless transmission channels by manipulating incident waves through the corresponding electromagnetic elements, is a promising enabler of various symbiotic communications scenarios in IoT. However, when the full electromagnetic elements of RIS are activated, system capacity will be improved and energy efficiency will be reduced inevitably, also with undesirable power consumption. To address this issue, an intelligent dynamic subarray RIS framework based on deep reinforcement learning (DRL) has been proposed. The key idea is to divide RIS electromagnetic elements into several groups and optimize power amplifier factor, independent phase shifts to improve the system energy efficiency under the premise of user’s basic requirements. In particular, we formulate a hybrid optimization problem of RIS subarray partition and beamforming to maximize system energy efficiency. It can be proved that this hybrid optimization is a mixed non-convex integer programming problem. To solve this issue, we proposed a comprehensive DRL framework including two parts, i.e., (1) a Markov decision process (MDP) to model the subarray partition design, amplitude and phase shifts of RIS, and (2) an active RIS subarray optimization scheme based on deep deterministic policy gradient. Numerical results have demonstrated that, compared with the conventional fully-connected RIS, the system energy efficiency can be significantly improved.