Mixed Integer Linear Programming Technique Research Articles

Multi-objective models for crop rotation planning problems

CONTEXTAgriculture is a vital component of the global economy and modern societies. It has undergone significant consolidation and transformation in response to the food supply crisis, highlighting the important relationship between humans and the environment. However, concerns remain about food security, particularly with the projected population growth of over 9.5 billion by 2050. The computerization of agri-food supply chains has emerged as a significant response to these challenges. OBJECTIVE(1) Develop a multi-objective model that explores both net return and crop diversity. (2) Solve the problem using techniques that guarantee optimality. (3) Evaluate the gain in crop diversity versus the net return of the optimized configuration. METHODSThe study presents four Multi-objective Mixed-Integer Linear Programming models with integer and binary decision variables for Crop Rotation Planning Problems. The objectives are to maximize net income and increase crop diversity and land utilization. RESULTS AND CONCLUSIONSThe study exclusively employs linear programming techniques to solve the models resulting in an optimal solution. A comparative analysis with existing models in the literature, which primarily focused on maximizing net income, yielded a noteworthy result. The proposed models demonstrate an average increase of 60% in crop diversity, with net return losses of less than 5%. SIGNIFICANCEIn conclusion, this research provides valuable information for crop rotation planning and highlights the importance of agricultural farm management and precision agriculture in addressing current challenges. The innovative nature of this research is exemplified by the use of mixed-integer linear programming techniques to solve a multi-objective problem with integer and binary variables. The obtained results demonstrate increased crop diversity and minimal economic losses, which have significant implications for several areas of agricultural science, policy, and practice.

Designing a Dispatch Engine for Hybrid Renewable Power Stations Using a Mixed-Integer Linear Programming Technique

Designing a Dispatch Engine for Hybrid Renewable Power Stations Using a Mixed-Integer Linear Programming Technique

Vertical Takeoff and Landing for Distribution of Parcels to Hospitals: A Case Study about Industry 5.0 Application in Israel’s Healthcare Arena

To gain a sustained competitive advantage, organizations such as UPS, Fedex, Amazon, etc., began to seek for industry 5.0 innovative autonomous delivery options for the last mile. Autonomous unmanned aerial vehicles are a promising alternative for the logistics industry. The fact that drones are propelled by green renewable energy source fits the companies’ need to become sustainable, replacing their fuel truck fleets, especially for traveling to remote rural locations to deliver small packages, but a major obstacle is the necessity for charging stations which is well documented in the literature. Therefore, the current research embarks on devising a novel yet practical piece of technology adopting the simplicity approach of direct flights to destinations. The analysis showcases the application for a network of warehouses and hospitals in Israel while controlling costs. Given the products in the case study are medical, direct flight has the potential to save lives when every moment counts. Hydrogen cell technology allows long-range flying without refueling, and it is both vibration-free which is essential for sensitive medical equipment and environmentally friendly in terms of air pollution and silence in urban areas. Importantly, hydrogen cells are lighter, with higher energy density than batteries, which makes them ideal for drone usage to reduce weight, maintain a longer life, and enable faster charging, all of which minimize downtime. Also, hydrogen sourcing is low-cost and unlimited compared to lithium-ion material which needs to be mined. The case study investigates an Israeli entrepreneurial company, Gadfin, which builds a vertical takeoff-and-landing-type of drone with folded wings that enable higher speed for the delivery of refrigerated medical cargo, blood, organs for transplant, and more to hospitals in partnership with the Israeli medical logistic conglomerate, SAREL. An analysis of shipping optimization (concerning the number and type of drone) is conducted using a mixed-integer linear programming technique based on various types of constraints such as traveling distance, parcel weight, the amount of flight controllers and daily number of flights allowed in order to not overcrowd the airspace. Importantly, the discussion assesses the ecosystem’s variety of risks and commensurate safety mechanisms for advancing a newly shaped landscape of drones in an Israeli tight airspace to establish a network of national routes for drone traffic. The conclusion of this research cautions limitations to overcome as the utilization of drones expand and offers future research avenues.

Modeling favorable locations for biogas plants that generate electricity from dairy and beef cattle manure through mixed integer linear programming

Mixed integer linear programming (MILP) is known as a type of programming that can combine continuous variables, integer variables, and (0-1) variables in the same algorithm and generate fitting results for the data. Using this technique, it is possible to model and solve complex problems in many different fields such as economics, biology, engineering, etc. In the present study, a regional planning model was developed using MILP technique for the conversion of manure from dairy and beef cattle into biogas and electrical energy. For this regional planning study, considering the locations of future facilities, data on dairy and beef cattle in the Isparta province of Türkiye were used. According to the model written and solution outputs, to utilize all manure obtained from dairy and beef cattles in Isparta, 5 biogas plants with a total manure processing capacity of approximately 522,000 tons should be built in different districts. It is possible to produce a total of approximately 21,000,000 m3 of biogas and 38,500 MW of electricity per year in these biogas plants. This electrical energy obtained can meet 3.83% of the annual electricity consumption of Isparta province.

Smart home energy management and active power loss analysis of a residential community

As the demand for energy continues its upward trajectory, judiciously managing the global energy resources has become increasingly imperative. One effective strategy to accomplish this efficiency is by strategically scheduling intelligent household appliances, a process that considers dynamic pricing schemes and the availability of renewable energy sources. This paper presents a comprehensive study that delves into optimizing smart home appliance utilization, considering electric vehicles and a modest rooftop photovoltaic installation. The study seeks to ascertain their potential impact on both energy consumption and cost mitigation. The proposed scheduling approach is centered on the optimal scheduling of smart appliances, harnessing the power of real-time pricing schemes to curtail the overall energy expenditure. The scheduling conundrum is meticulously modelled using General Algebraic Modeling System software and subsequently tackled by the CPLEX solver, leveraging mixed-integer linear programming techniques. Results reveal a remarkable achievement, with the potential for up to an 80.6 % reduction in the overall cost compared to the base case under various scenarios considering different approaches. To validate the integrity of the study, outcomes are juxtaposed with those of the base paper, and the superiority of the proposed method is evident from the results. Furthermore, the paper considers the ramifications of optimized scheduling on the voltage profile and overall system losses nearly 7 % less compared to the base case within the context of the IEEE 33-bus system. Thus, the presented work successfully analyzes the effect of household energy scheduling on the community level and scales up to a microgrid level.

Support vector machines within a bivariate mixed-integer linear programming framework

Support vector machines (SVMs) are a powerful machine learning paradigm, performing supervised learning for classification and regression analysis. A number of SVM models in the literature have made use of advances in mixed-integer linear programming (MILP) techniques in order to perform this task efficiently. In this work, we present three new models for SVMs that make use of piecewise linear (PWL) functions. This allows effective separation of data points where a simple linear SVM model may not be sufficient. The models we present make use of binary variables to assign data points to SVM segments, and hence fit within a recently presented framework for machine learning MILP models. Alongside presenting an inbuilt feature selection operator, we show that the models can benefit from robust inbuilt outlier detection. Experimental results show when each of the presented models is effective, and we present guidelines on which of the models are preferable in different scenarios.

Efficient continuous piecewise linear regression for linearising univariate non-linear functions

Due to their flexibility and ability to incorporate non-linear relationships, Mixed-Integer Non-Linear Programming (MINLP) approaches for optimization are commonly presented as a solution tool for real-world problems. Within this context, piecewise linear (PWL) approximations of non-linear continuous functions are useful, as opposed to non-linear machine learning-based approaches, since they enable the application of Mixed-Integer Linear Programming techniques in the MINLP framework, as well as retaining important features of the approximated non-linear functions, such as convexity. In this work, we extend upon fast algorithmic approaches for modeling discrete data using PWL regression by tuning them to allow the modeling of continuous functions. We show that if the input function is convex, then the convexity of the resulting PWL function is guaranteed. An analysis of the runtime of the presented algorithm shows which function characteristics affect the efficiency of the model, and which classes of functions can be modeled very quickly. Experimental results show that the presented approach is significantly faster than five existing approaches for modeling non-linear functions from the literature, at least 11 times faster on the tested functions, and up to a maximum speedup of more than 328,000. The presented approach also solves six benchmark problems for the first time.

Energy-Optimized Truck Door Assignment Problem (TDA): Scalability and Capacity Analysis

The Energy-Optimized Truck Door Assignment Problem (TDA) addresses the optimization of truck assignments to doors in cross-docking facilities with the aim of minimizing energy consumption and operational costs. In this paper, we propose a scalable optimization model for the TDA and evaluate its capacity to handle varying numbers of trucks and doors. The model integrates mixed-integer linear programming (MILP) techniques to formulate the assignment problem, considering constraints such as truck arrival times, door capacities, and energy-efficient routing strategies. Through a comprehensive analysis, we assess the scalability and effectiveness of the TDA model in optimizing truck door assignments and promoting energy-efficient logistics operations. Results indicate promising performance and highlight opportunities for further research in sustainable logistics management.

Optimal design of PV-based grid-connected hydrogen production systems

A cost-optimal design of power-to-hydrogen (PtH) systems is crucial to produce hydrogen at the lowest specific cost. New challenges arise when it comes to ensuring a reliable and cost-effective hydrogen supply in the presence of variable renewable energy sources. In this context, the aim of this analysis is to investigate the optimal design of PV-based grid-connected hydrogen production systems under different scenarios. To this end, an optimisation framework based on the mixed integer linear programming (MILP) technique is developed. Results are presented by employing a set of techno-economic and environmental indicators to provide general guidance on how to optimally size PtH systems, going beyond the analysis of a specific case study. The analysis is applied to Italy and particular attention is paid to exploring the impact of the price of grid electricity.The results indicate that the price of grid electricity strongly affects the optimal design of PtH systems. Specifically, in scenarios with high electricity prices, it is economically convenient to significantly oversize the PV plant and the electrolyser. The optimal PV ratio, representing the ratio between the PV size and the electrolyser size, increases from 1.6 to 2.7 as the electricity price rises from 50 to 300 €/MWh. Additionally, when electricity prices exceed approximately 120 €/MWh, the optimal electrolyser size (in terms of hydrogen production under rated conditions) becomes almost three times larger than the average hydrogen demand. By comparing grid-connected and off-grid scenarios, the importance of the electrical grid is also highlighted: even when poorly used, it plays a crucial role in limiting the size of the hydrogen storage. The levelised cost of hydrogen for the optimal PtH configuration falls within the range of 3.5–7 €/kg (depending on the price of grid electricity) and increases to 8.2 €/kg when the system operates off-grid. Finally, the hydrogen carbon footprint, quantified as kgCO2,e/kgH2, is also explored. Considering the current price and carbon intensity of grid electricity, the cost-optimal PtH configuration already involves the production of renewable hydrogen (<3 kgCO2,e/kgH2).

An overview of AC and DC microgrid energy management systems

&lt;abstract&gt; &lt;p&gt;In 2022, the global electricity consumption was 4,027 billion kWh, steadily increasing over the previous fifty years. Microgrids are required to integrate distributed energy sources (DES) into the utility power grid. They support renewable and nonrenewable distributed generation technologies and provide alternating current (AC) and direct current (DC) power through separate power connections. This paper presents a unified energy management system (EMS) paradigm with protection and control mechanisms, reactive power compensation, and frequency regulation for AC/DC microgrids. Microgrids link local loads to geographically dispersed power sources, allowing them to operate with or without the utility grid. Between 2021 and 2028, the expansion of the world's leading manufacturers will be driven by their commitment to technological advancements, infrastructure improvements, and a stable and secure global power supply. This article discusses iterative, linear, mixed integer linear, stochastic, and predictive microgrid EMS programming techniques. Iterative algorithms minimize the footprints of standalone systems, whereas linear programming optimizes energy management in freestanding hybrid systems with photovoltaic (PV). Mixed-integers linear programming (MILP) is useful for energy management modeling. Management of microgrid energy employs stochastic and robust optimization. Control and predictive modeling (MPC) generates energy management plans for microgrids. Future microgrids may use several AC/DC voltage standards to reduce power conversion stages and improve efficiency. Research into EMS interaction may be intriguing.&lt;/p&gt; &lt;/abstract&gt;

Design Methodology for Wireless Backhaul/Fronthaul Using Free Space Optics and Fibers

The recent increase in data rates for Free space optics (FSO) transmission technology, means they could be used for designing the backhaul/fronthaul for 5G and beyond cellular networks. The flexibility and cost-effectiveness provided by FSO are the primary reasons for the mobile operators to investigate the potential of the technology as a mobile backhaul/fronthaul. Unfortunately, the reliability of FSO links is weather dependent, especially if the link covers considerable distance. Optical fibers, on the other hand, are expensive but more reliable. Hence, optimally designing a hybrid network consisting of both fiber and FSO connections can bring in the cost-effectiveness of FSO as well as the robustness of fibers. In such a design, the more important links are connected using fibers while the links with higher tolerance towards failure are designed using FSO. Therefore, in this paper, we propose a hybrid FSO/fiber backhaul/fronthauling methodology for connecting wireless base stations (BSs) to the network core. We first formulate a mixed integer non-linear program (MINLP) for determining the number of splitter/FSO distribution points required in the network that optimally provide connectivity to the BSs. The MINLP is designed to identify the locations of the splitters/FSO distribution points as well. Thereafter, we solve the MINLP with the help of particle swarm optimisation (PSO) and mixed integer linear programming (MILP) techniques. We also derive a heuristic for solving the MILP. Finally, we propose another method for determining the number of splitters required in a relatively shorter time: K-means cluster based method. The results verify that the hybrid network is cost-effective while conforming to the data rate and reliability requirements of the links. The proposal allows evaluation of a seamless design solution of the hybrid network with practical time-complexity.

An optimization‐based CCUS source‐sink matching model for dynamic planning of CCUS clusters

AbstractCarbon capture, utilization and storage (CCUS) is a critical technology option in achieving large‐scale CO2 mitigation for power and industrial sectors. A full‐chain CCUS cluster could be formed based on numerous scattered capture sources and one or more storage sites connected by a pipeline network. Reasonable source‐sink matching planning for a full‐chain CCUS cluster could substantially reduce the system overhead. However, most of the previous studies could hardly address the dynamic source‐sink matching planning problem of a full‐chain CCUS cluster with multiple types of emission sources and sinks during multiple periods. Therefore, the objective of this study is to investigate an optimized source‐sink matching scheme within a CCUS cluster through developing an optimization‐based CCUS source‐sink matching model. The proposed model is based on multistage mixed integer linear programming techniques with the objective of least‐cost strategy; thus, it can deal with dynamics of capacity expansion associated with CCUS activities. The developed method is then applied to a CCUS cluster facing long‐term dynamic planning issues. The modeling results suggest that the optimization‐based CCUS source‐sink matching model is applicable in reflecting dynamics of time, scale and location of CO2 capture, transportation and storage within a CCUS cluster. The obtained solutions can provide decision bases for formulating an optimal planning scheme of a full‐chain CCUS cluster under evolving reduction targets or constraints. © 2022 Society of Chemical Industry and John Wiley &amp; Sons, Ltd.

Size optimization and power allocation of a hybrid energy storage system for frequency service

Aiming at the scenario where the energy storage system participates in the grid enhanced frequency response auxiliary service, this research initially constructs a frequency response model to provide power requirements for the energy storage system (ESS). A two-layer optimization approach is proposed to solve the size optimization problem. A mixed-integer linear programming technique is researched on the bottom layer to optimize the power allocation of the hybrid energy storage system (HESS). On the top layer, a size optimization framework is proposed for optimising the configuration of the energy storage system. The size optimization results show that compared with the battery energy storage system (BESS), the capacity of the HESS was reduced by 64%, the battery aging cost was reduced by 52%, and the total cost was reduced by 35%. The results also show that the proposed optimal HESS design could fully leverage the advantages of the battery and the supercapacitor (SC). In addition, the proposed method is investigated in a long-term frequency service case. With the optimal setup and adaptive power distribution approach, both energy storage units operate within the specified power and capacity range at the same time the battery is protected from high-frequency power fluctuations.

Continuous Piecewise Linear Approximation of Plant-Based Hydro Production Function for Generation Scheduling Problems

An essential challenge in generation scheduling (GS) problems of hydrothermal power systems is the inclusion of adequate modeling of the hydroelectric production function (HPF). The HPF is a nonlinear and nonconvex function that depends on the head and turbined outflow. Although the hydropower plants have multiple generating units (GUs), due to a series of complexities, the most attractive modeling practice is to represent one HPF per plant, i.e., a single function is built for representing the plant generation instead of the generation of each GU. Furthermore, due to the computation time constraints and representation of nonlinearities, the HPF must be given by a piecewise linear (PWL) model. This paper presented some continuous PWL models to include the HPF per plant in GS problems of hydrothermal systems. Depending on the type of application, the framework allows a choice between the concave PWL for HPF modeled with one or two variables and the nonconvex (more accurate) PWL for HPF dependent only on the turbined outflow. Basically, in both PWL models, offline, mixed-integer linear (or quadratic) programming techniques are used with an optimized pre-selection of the original HPF dataset obtained through the Ramer-Douglas-Peucker algorithm. As a highlight, the framework allows the control of the number of hyperplanes and, consequently, the number of variables and constraints of the PWL model. To this end, we offer two possibilities: (i) minimizing the error for a fixed number of hyperplanes, or (ii) minimizing the number of hyperplanes for a given error. We assessed the performance of the proposed framework using data from two large hydropower plants of the Brazilian system. The first has 3568 MW distributed in 50 Bulb-type GUs and operates as a run-of-river hydro plant. In turn, the second, which can vary the reservoir volume by up to 1000 hm3, possesses 1140 MW distributed in three Francis-type units. The results showed a variation from 0.040% to 1.583% in terms of mean absolute error and 0.306% to 6.356% regarding the maximum absolute error even with few approximations.

A single-layer approach for joint optimization of traffic signals and cooperative vehicle trajectories at isolated intersections

A joint control approach that simultaneously optimizes traffic signals and trajectories of cooperative (automated) vehicle platooning at urban intersections is presented in this paper. In the proposed approach, the signal phase lengths and the accelerations of the controlled platoons are optimized to maximize comfort and minimize travel delay within the signal cycle, subject to motion constraints on speeds, accelerations and safe following gaps. The red phases are initially considered as logic constraints, and then recast as several linear constraints to enable efficient solutions. The proposed approach is solved by mixed integer linear programming (MILP) techniques after linearization of the objective function. The generated outputs of the MILP problem are the optimal signal timings and the optimal accelerations of all vehicles. This joint control approach is flexible in incorporating multiple platoons and traffic movements under different traffic demand levels and it does not require prespecified terminal conditions on position and speed at the signal cycle tail. The performance of the proposed control approach is verified by simulation at a standard four-arm intersection under the balanced and unbalanced vehicle arrival rates from different arms, taking the released traffic movement numbers, turning proportions, signal cycle lengths and the controlled vehicle numbers into account. The simulation results demonstrate the platoon performance of the joint controller (such as split, merge, acceleration and deceleration maneuvers) under the optimal signals. Based on the simulation results, the optimal patterns of trajectories and signals are explored, which provide insights into the optimal traffic control actions at intersections in a cooperative vehicle environment. Furthermore, the computational performance of the proposed control approach is analyzed, and the benefits of the proposed approach on the average travel delay, throughput, fuel consumption, and emission are proved by comparing with the two-layer approaches using the car following model, the signal optimization models, and the state-of-the-art approach.

Size Optimization and Power Allocation Optimization of a Hybrid Energy Storage System for Grid Enhanced Frequency Response Service

Aiming at the scenario where the energy storage system participates in the grid enhanced frequency response auxiliary service, this paper first establishes a frequency response model to provide power requirements for the ESS. A two-layer optimization approach is proposed to solve the size optimization problem. On the bottom layer, a mixed-integer linear programming technique is investigated to optimally allocate the power of the HESS. On the top layer, a size optimization framework is proposed to optimize the configuration of the ESS. The size optimization results show that comparing with the BESS, the capacity of the HESS was reduced by 64%, the battery aging cost was reduced by 52.5%, and the total cost was reduced by 35.1%. Based on the feature of the optimal power allocation result, a novel adaptive online power allocation method is proposed. Simulation results show that the adaptive power allocation method can fully utilize the advantages of batteries and supercapacitors. Finally, the case of a HESS participating in long-term enhanced frequency response is studied. Based on the optimal configuration and adaptive power allocation method, each energy storage unit works within the set power and capacity range, and the fluctuation of the battery power is significantly reduced.

Assessment and multi-objective optimization of an off-grid solar based energy system for a Conex

In this study, an off-grid PV system is optimized to supply a Conex electricity demand in the top ten earthquake-prone cities using mixed-integer linear programming techniques. The stand-alone photovoltaic system is designed by a photovoltaic array, a cooling/heating system, battery banks, an inverter, and a charge controller. For determining the optimum size and specifications of the system components such as PV panel, HVAC coefficient of performance, by considering two objectives of the study, a mixed-integer linear programming method is used. These conflicting objectives are the probability of lack of power and total cost of the system. The weighted factor method is utilized, and final optimized systems are achieved using MATLAB 2019b. Using the weighted factor method, several optimum solutions, in which the importance of objectives are different from each other, are obtained for each case concerning objectives. The suggested model is optimized for ten earthquake-prone cities globally, while it can be utilized for any location. The Pareto frontiers are presented to show the trade-offs between two objective functions. The average cost of off-grid PV system supplied electrical power is from about 1000$ for lima (subtropical desert climate) to 4000$ for Tokyo and Osaka (humid subtropical). Analysis of obtained results demonstrates that the system is suitable for all of the considered cities. It can supply the load demand of an off-grid Conex with a loss of power supply probability as low as 1%.

Performance safety enforcement in stochastic event graphs against boost and slow attacks

This paper studies a performance safety enforcing problem in stochastic event graphs, a subclass of stochastic Petri net models. We assume that an intruder can attack part of the transitions to increase/decrease their firing rate such that the performance of the system violates a given safety interval. The difficulty in solving this problem is that the capability of the intruder, i.e., the number of transitions that can be simultaneously attacked, is limited. The control aim is to find a protecting policy such that the performance of the protected plant is guaranteed to be in a given safety interval. We show that this problem can be formulated as a two-player game between the intruder and the operator of the plant. By using mixed integer linear programming technique, we develop a heuristic method to compute a protecting policy that is locally optimal.

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands.

Time-Sensitive Mobile User Association and SFC Placement in MEC-Enabled 5G Networks

The ongoing roll-out of 5G networks paves the way for many fascinating applications such as virtual reality (VR), augmented reality (AR), and autonomous driving. Moreover, 5G enables billions of devices to transfer an unprecedented amount of data at the same time. This transformation calls for novel technologies like multi-access edge computing (MEC) to satisfy the stringent latency and bitrate requirements of the mentioned applications. The main challenge pertaining to MEC is that the edge MEC nodes are usually characterized by scarce computational resources compared to the core or cloud, arising the challenge of efficiently utilizing the edge resources while ensuring that the service requirements are satisfied. When considered with the users' mobility, this poses another challenge, which lies in minimization of the service interruption for the users whose service requests are represented as service function chains (SFCs) composed of virtualized network functions (VNFs) instantiated on the MEC nodes or on the cloud. In this paper, we study the problem of joint user association, SFC placement, and resource allocation, employing mixed-integer linear programming (MILP) techniques. The objective functions of this MILP-based problem formulation are to minimize (i) the service provisioning cost, (ii) the transport network utilization, and (iii) the service interruption. Moreover, a heuristic algorithm is proposed to tackle the scalability issue of the MILP-based algorithms. Finally, comprehensive experiments are performed to draw a comparison between these approaches.