Integer Linear Programming Techniques Research Articles

INTEGER LINEAR PROGRAMMING MODEL FOR AGGREGATE PRODUCTION PLANNING, APPLICATION OF LEARNING CURVES, AND HYPOTHESIS TESTING

ABSTRACT: Efficient production management and business administration are essential to maintain competitiveness in a business environment in constant change and complexity; the optimization of production systems becomes imperative to minimize costs and maximize operational efficiency. In this context, the implementation of advanced integer linear programming techniques emerges as a solution for aggregate production planning, based on the establishment of a uniform flow of processes to contribute to improving the efficiency of the system and reducing associated cost overruns. This article presents the analysis of the use of integer linear programming for aggregate production planning, applied to the production process of concrete blocks and concrete for structural masonry in the company Blocks del Sinú SAS in the department of Córdoba - Colombia. An optimization model is proposed that satisfies the forecasted demand through adjustments to the levels of production, labor, inventories, contracting and raw materials. The results show that with the standardization of the production process and work methods to minimize the costs of the production plan and meet the demand requirements in accordance with the company's capacity, demand will strictly occur within the planning horizon. , which implies that there will be no shortage of raw materials. Keywords: Aggregate planning, integer linear programming, production.

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).

Strong SDP based bounds on the cutwidth of a graph

Given a linear ordering of the vertices of a graph, the cutwidth of a vertex v with respect to this ordering is the number of edges from any vertex before v (including v) to any vertex after v in this ordering. The cutwidth of an ordering is the maximum cutwidth of any vertex with respect to this ordering. We are interested in finding the cutwidth of a graph, that is, the minimum cutwidth over all orderings, which is an NP-hard problem. In order to approximate the cutwidth of a given graph, we present a semidefinite relaxation. We identify several classes of valid inequalities and equalities that we use to strengthen the semidefinite relaxation. These classes are on the one hand the well-known 3-dicycle equations and the triangle inequalities and on the other hand we obtain inequalities from the squared linear ordering polytope and via lifting the linear ordering polytope. The solution of the semidefinite program serves to obtain a lower bound and also to construct a feasible solution and thereby having an upper bound on the cutwidth.In order to evaluate the quality of our bounds, we perform numerical experiments on graphs of different sizes and densities. It turns out that we produce high quality bounds for graphs of medium size independent of their density in reasonable time. Compared to that, obtaining bounds for dense instances of the same quality is out of reach for solvers using integer linear programming techniques.

Optimal profitable allocation of associated natural gas resource on a countrywide basis to mitigate flaring

The flaring of large volumes of the natural gas that is produced as a by-product of crude oil, has puzzled the energy-hungry world for long. In recent years, it has also drawn the angst of the environmental and global-warming advocacy groups. The issues behind gas flaring are complex, as they involve a dynamic interplay of geosciences, engineering, economics, finance and natural resource policy-making.The purpose of this research is to analyze the associated gas problem quantitatively from a country-wide perspective. Unlike prior studies, this work focusses on the upstream side where the crucial strategic decisions are made upfront. To this end, a mathematical model is proposed for seeking the optimal integrated management strategy for the said national resource. The model is based on the Mixed Integer Linear Programming (MILP) technique and consists of scores of techno-economic decision variables and constraint equations along with a profit maximization objective.The model is general in nature but is applied herein to Nigeria as a case study. Several simulation runs are made to provide results for explanatory and prediction purposes. Model results indicate, for example, that a minimum gas price of $4.4/Mscf and minimum spend of $22B are jointly required to achieve zero-flaring, yielding a $10B profit. This is achievable via a strategy of reinjecting all associated gas produced from medium and large-sized fields, but gathering and selling all gas from small fields. Capital availability, rather than nationwide government-decreed flaring control, is shown to be the dominant determinant of profitable flaring mitigation. The model has proven to be a valuable tool for establishing the inter-relations between the key problem parameters under various pricing and resource base scenarios, and for prognosticating the trajectory of the gas industry in various jurisdictions.

An optimal fog-cloud offloading framework for big data optimization in heterogeneous IoT networks

Executing complex and time-sensitive operations has become difficult due to the increased acceptance of Internet of Things (IoT) devices and IoT-generated big data, which can result in problems with power consumption and lag time. The fog computing layer is a distributed computing option that can handle some of these issues. However, fog computing devices’ limited computing and power capabilities make it difficult to complete operations under time constraints while minimizing service latency and fog resource energy consumption in delay-sensitive IoT-Fog applications. This paper suggests a dynamic integer linear programming technique for facilitating optimal task offloading that distributes resources from the fog computing layer to IoT devices while considering the constraints on timely task execution and resource availability. The offloading challenge is modeled as an integer linear programming (ILP) problem to ease the burden on finite fog resources and speed up the completion of time-sensitive operations. Given the large dimensionality of tasks in a dynamic environment, a task prioritization method is adopted to minimize tasks’ latency and the energy consumption of fog nodes. The findings demonstrate that the suggested approach performs better than benchmark approaches regarding energy utilization and service latency. Overall, the proposed technique offers an efficient and practical response to the issues raised by IoT devices and fog computing while enhancing system efficiency regarding power consumption and latency.

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.

Comparison of Grid Reactive Voltage Regulation with Reconfiguration Network for Electric Vehicle Penetration

Renewable energy sources and EV growth brings new challenges for grid stabilization. Smart grid techniques are required to reconfigure and compensate for load fluctuation and stabilize power losses and voltage fluctuation. Numerical tools are available to equip the smart grid to deal with such challenges. Distribution Feeder reconfiguration and reactive voltage injection to the disturbed grid are some of the techniques employed for the purpose. However, either reconfiguration or injection alone is used commonly for this purpose. In this study, both techniques are applied to EV penetration as load and compared. A balanced IEEE 33 Radial network is used in this study and selected branches with high power losses are targeted for the reactive voltage injection and Minimum Spanning tree techniques (MST). EV charging loads are usually modelled with time base distribution which requires times base power flow analysis for reactive power injection. A comparison between coordinated, reconfiguration, and reactive voltage injection shows differences in power losses, voltage distortion, and cost saving. The analysis is carried out with an integer linear programming technique for coordinated charging, a minimum spanning tree for network reconfiguration, and genetic optimization for reactive power injection. Besides, all power flow analyses are carried out with the Backward/Forward sweep method. The information would help lowering power losses, grid stabilization, and charging station infrastructure planning.

Path Planning of Multi-Type Robot Systems with Time Windows Based on Timed Colored Petri Nets

Mobile robots are extensively used to complete repetitive operations in industrial areas such as intelligent transportation, logistics, and manufacturing systems. This paper addresses the path planning problem of multi-type robot systems with time windows based on timed colored Petri nets. The tasks to be completed are divided into three different types: common, exclusive and collaborative. An analytical approach to plan a group of different types of mobile robots is developed to ensure that some specific robots will visit task regions within given time windows. First, a multi-type robot system and its environment are modeled by a timed colored Petri net. Then, some methods are developed to convert the task requirements that contain logic constraints and time windows into linear constraints. Based on integer linear programming techniques, a planning approach is proposed to minimize the total cost (i.e., total travel distance) of the system. Finally, simulation studies are investigated to show the effectiveness of the developed approach.

Appointment Scheduling Problem under Fairness Policy in Healthcare Services: Fuzzy Ant Lion Optimizer

This study addresses the application of the Integer Linear Programming technique for the patient Appointment Scheduling Problem (ASP). In this research, we propose a Mixed-Integer Linear Programming (MILP) model to formulate the problem and treat patients admitted to hospitals and stay in a queue based on their general health status (urgent or regular patients). Moreover, the ASP has two main objectives that often provide early patient admissions. The first objective is based on fairness policy as an essential factor in the healthcare service to help minimize patient waiting time. The second one is to maximize the efficiency of healthcare services in line with patients’ satisfaction. Moreover, we have addressed the Fuzzy Ant Lion Optimization (FALO) strategy and Non-dominated Sorting Genetic Algorithm II (NSGA-II) are utilized to compare and solve the resulting multi-objective ASP. As the application of the model, fairness policy is analyzed in scenario 1 using FALO, and in scenario 2, NSGA-II is applied. The performances of the solution algorithms are then tested using datasets of a big regional hospital in Shanghai. The outcomes indicate potential advantages of implementing the presented approach. In particular, the suggested FALO increases the fairness and patients’ satisfaction by more than 80% while reducing the waiting times by 50% within the basic appointment scheduling system.

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.

Power-aware test scheduling framework for IEEE 1687 multi-power domain networks using formal techniques

The IEEE 1687 Std. (IJTAG) introduces an efficient access methodology based on reconfigurable scan networks to address the ever-increasing complexity of the latest system-on-chips. By invoking this new methodology, the overall test time can considerably be reduced by shortening the scan chains' length without sacrificing the test quality. IJTAG allows for designing highly complex test networks compromising the latest test structure that enables to achieve the high test quality, as required by today's customers' applications. Besides the time overhead induced by the required network (re-)configuration, the access sequence of the instruments itself greatly affects the overall test time. Furthermore, the power characteristics of the complex test facilities have to be taken into account to avoid effects like IR drop during the later test application that is even more critical in highly multi-power domain networks. Consequently, the IJTAG methodology strictly requires an effective test scheduler that considers the individual instruments' constraints and is compatible with recent multi-power domain chip designs. This work proposes two novel power-aware test scheduling approaches based on pseudo-Boolean optimization and integer linear programming techniques that are both seamlessly integrated into a fully-automated test scheduling framework for IJTAG test networks even with multiple power domains. The first proposed optimization scheme allows for determining a local optimal test schedule, applicable to networks with more than one thousand instruments since the required run-time is manageable. Furthermore, the second optimization scheme determines a global optimal test scheduler, which is most suitable for mid-sized networks in which it is clearly outperforming any other existing technique.

A Parallelizable Integer Linear Programming Approach for Tiling Finite Regions of the Plane with Polyominoes

The general problem of tiling finite regions of the plane with polyominoes is NP-complete, and so the associated computational geometry problem rapidly becomes intractable for large instances. Thus, the need to reduce algorithm complexity for tiling is important and continues as a fruitful area of research. Traditional approaches to tiling with polyominoes use backtracking, which is a refinement of the ‘brute-force’ solution procedure for exhaustively finding all solutions to a combinatorial search problem. In this work, we combine checkerboard colouring techniques with a recently introduced integer linear programming (ILP) technique for tiling with polyominoes. The colouring arguments often split large tiling problems into smaller subproblems, each represented as a separate ILP problem. Problems that are amenable to this approach are embarrassingly parallel, and our work provides proof of concept of a parallelizable algorithm. The main goal is to analyze when this approach yields a potential parallel speedup. The novel colouring technique shows excellent promise in yielding a parallel speedup for finding large tiling solutions with ILP, particularly when we seek a single (optimal) solution. We also classify the tiling problems that result from applying our colouring technique according to different criteria and compute representative examples using a combination of MATLAB and CPLEX, a commercial optimization package that can solve ILP problems. The collections of MATLAB programs PARIOMINOES (v3.0.0) and POLYOMINOES (v2.1.4) used to construct the ILP problems are freely available for download.

Drainage area maximization in unconventional hydrocarbon fields with integer linear programming techniques

Drainage area maximization in unconventional hydrocarbon fields with integer linear programming techniques

Power System State Estimation using Non-Iterative Weighted Least Square method based on Wide Area Measurements with maximum redundancy

The power system state estimation (PSSE) accuracy is crucial for monitoring and surveillance in an energy management system (EMS). Wide-area measurement systems (WAMS) are a pivotal technology to enhance the accuracy of PSSE. Further, with the advent of phasor measurement units (PMUs), state estimation got revolutionized by its performance. To attain better estimation accuracy, the main considerations for a power system are; observability and redundancy. In order to achieve full observability with maximum redundancy, the problem of optimal PMU placement (OPP) in power systems is investigated. This paper proposes a Modified- Integer Linear Programming (M-ILP) technique to achieve full observability with minimal PMU placement and maximum redundancy. Furthermore, A Non-iterative Weighted Least Square (NI-WLS) approach has been developed to improve the accuracy of power system state estimation by leveraging hybrid measurements consisting of traditional SCADA data and phasor measurements. The efficacy and precision of the proposed algorithms have been demonstrated through extensive simulations on a wide range of test systems, including standard IEEE- 14, 30, 57, 118 systems and real-time Indian Northern Region Power Grid-246 (NRPG-246) bus system. Moreover, the proposed methods show significant improvement in the accuracy and stability of the state estimate solution.

Delay-Optimal Task Offloading for UAV-Enabled Edge-Cloud Computing Systems

The emergence of delay-sensitive and computationally-intensive mobile applications and services pose a significant challenge for Unmanned Aerial Vehicles (UAVs) devices due to the scarcity in their resources such as computational power and battery lifetime. Mobile cloud computing has been introduced as a promising solution to overcome these limitations through task offloading. However, high-latency and security issues are considered the main challenges of this paradigm. Subsequently, the edge-cloud computing paradigm has been introduced and widely used to help to mitigate these issues. Nevertheless, the current task offloading models permit UAVs to execute their intensive tasks at the connected edge server, which leads to excessive loads due to the large number of UAVs and thereby increases the delay. Therefore, in this paper, we propose a delay-optimal task offloading approach for multi-tier edge-cloud computing in a multi-user environment. The problem is formulated as an optimization model using Integer Linear Programming (ILP) techniques to minimize the total service time of UAVs. Simulation results demonstrate that the proposed approach not only saves the service time by 33.5% and 55% for edge and cloud execution policies respectively, but also scales well for a large number of UAVs.

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.

A robust model for aggregated bidding of energy storages and wind resources in the joint energy and reserve markets

The high reliability and flexibility of Battery Energy Storage (BES) resources in comparison with other renewable technologies promote the development of this technology in smart grids. The fast response of BES to load variations could help the power system operators to maintain the balance of generation and consumption in real-time, and improve the flexibility of the smart grid, effectively. In this work, a new model is presented that determines the aggregated scheduling of BES and Wind Power Resource (WPR) in the joint energy and reserve markets. To evaluate the performance of BES in different markets, the proposed model is divided into day-ahead and real-time planning horizons. According to market prices, ramp rates, marginal costs, and technical constraints of units, the optimal participation levels in different markets are determined. The deployed power in real-time and wind power are considered as the uncertain parameters and the Robust Optimization (RO) framework is proposed to manage the related financial risk based on the worst-case realizations of uncertain parameters. The robust strategy is formulated based on the Mixed Integer Linear Programming (MILP) technique, which can be solved via the branch-and-bound method. Finally, the performance and effectiveness of the model are analyzed via different case studies. Simulation results show that the day-ahead and real-time markets are the best options for buying and selling the energy of BESs, and participation in the reserve market and regulation service increases their profit, significantly. Furthermore, the expected profit greatly depends on the risk preferences of decision-makers, and reducing the variation interval of wind generation by 40 % leads to an increase of 74.65 % in revenues.

Blocking analysis of suspension-based protocols for parallel real-time tasks under global fixed-priority scheduling

With the wide use of multiprocessor architecture, parallel tasks have been receiving growing attention in both industry and academia. In real-time systems, the scheduling and synchronization that ensure predictable task execution and resource access are of utmost importance. Although the scheduling of (independent) parallel tasks is widely studied in recent years, few works have been done for the synchronization with intra-task parallelism. In particular, the performance of the classical priority inheritance mechanism is still unfathomed for parallel tasks. In this paper, we extend the Priority Inheritance Protocol (PIP) and the Flexible Multiprocessor Locking Protocol (FMLP) for real-time parallel tasks (i.e., called P-PIP and P-FMLP respectively) under the global fixed-priority scheduling, and present the blocking analysis for both protocols with the state-of-the-art linear optimization technique. Empirical evaluations show that the P-PIP outperformed the P-FMLP with increasing shared resource contentions. • This paper first studies the synchronization of parallel tasks under global scheduling. • This paper proposes a unified analysis framework under the global scheduling. • A Mixed Integer Linear Programming technique is used to reduce analytical pessimism.

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.