Integer Linear Programming Problem Research Articles

Integrated real-time signal control and routing optimization: A two-stage rolling horizon framework with decentralized solution

This paper presents an integrated framework for optimizing signal control and vehicle routing. An important feature of the proposed framework is the ability to simultaneously determine signal states and individual vehicle routes in real time. The general objective is to minimize the network travel time, which can be represented as a trade-off between the total route length of all vehicles and traffic conditions at signalized intersections. A two-stage rolling horizon framework is proposed to explicitly describe the relationship between individual vehicle routes and predicted traffic flow dynamics at signalized intersections. The first stage involves a signal optimization problem, while the second stage optimizes a joint signal control and vehicle routing problem. Both stages are formulated as mixed integer linear programming problems. The optimization procedure is decentralized, and the effects of vehicle routing on control performance is considered by incorporating the route length cost into the objective function. Simulation experiments validate the advantages of the proposed framework over advanced signal control strategies and dynamic user-optimal routing strategies in various scenarios. The effectiveness in improving network capacity, alleviating spillback, and decreasing congestion dissipation time under over-saturation conditions is discussed. The results of vehicle routing suggest that the total travel time can be reduced at a low rerouting cost. Sensitivity analyses demonstrate the network control performance under different compliance rates and model coefficients. Moreover, the computational feasibility of the framework is verified.

Two stage beamforming and combining scheme for FDD massive MIMO systems with multi‐antenna users

AbstractThis paper proposes a two‐stage beamforming and combining scheme in frequency division duplex (FDD) massive multiple‐input multiple‐output (MIMO) systems with multi‐antenna users. Specifically, the proposed scheme is a two‐stage scheme, where the pre‐beamforming matrix and pre‐combining matrix are designed using the channel covariance matrix (CCM) in the first stage. The problem of the pre‐beamforming matrix and pre‐combining matrix design are formulated as an 0–1 quadratic integer programming problem. To solve this problem, it is further transformed into an 0–1 mixed linear integer programming problem. In the second stage, the sparse code multiple access and multi‐user precoding and combining are adopted to mitigate the inter‐user interference. Different from the previous transmission scheme using CCM, the proposed scheme consider the multi‐antenna user system, and uses the CCM to design both the pre‐beamforming and pre‐combining matrices to sparsify the effective channel matrix, such that the overhead of pilot and feedback can be reduced. Moreover, the sparse code multiple access can help to better reduce the inter‐user interference. Simulation results validate the good performance of the proposed scheme.

Planning a Hybrid Battery Energy Storage System for Supplying Electric Vehicle Charging Station Microgrids

This paper presents a capacity planning framework for a microgrid based on renewable energy sources and supported by a hybrid battery energy storage system which is composed of three different battery types, including lithium-ion (Li-ion), lead acid (LA), and second-life Li-ion batteries for supplying electric vehicle (EV) charging stations. The objective of this framework is to determine the optimal size for the wind generation systems, PV generation systems, and hybrid battery energy storage systems (HBESS) with the least cost. The framework is formulated as a mixed integer linear programming (MILP) problem, which incorporates constraints for battery ageing and the amount of unmet load for each year. The system uncertainties are managed by conducting the studies for various scenarios, generated and reduced by generative adversarial networks (GAN) and the k-means clustering algorithm for wind speed, global horizontal irradiation, and EV charging load. The studies are conducted for three levels of unmet load, and the outputs are compared for these reliability levels. The results indicate that the cost of hybrid energy storage is lower than individual battery technologies (21% compared to Li-ion, 4.6% compared to LA, and 6% compared to second-life Li-ion batteries). Additionally, by using HBESS, the capacity fade of LA batteries is decreased (for the unmet load levels of 0, 1%, 5%, 4.2%, 6.1%, and 9.7%, respectively), and the replacement of the system is deferred proportional to the degradation reduction.

Optimizing the number, locations, and chlorine dosages of booster chlorination stations in water distribution networks

ABSTRACT Safe and reliable drinking water is essential for sustaining life. Chlorination is widely used for disinfection in water distribution networks (WDNs). A higher dose of chlorine is required in an overhead service reservoir to maintain minimum residual chlorine at the farthest end in WDNs. However, delivering high dosages of chlorine from storage tanks can pose public health issues, especially for the residents living near overhead service reservoirs due to the formation of trihalomethanes, haloacetic acids, and chlorophenols. In addition, a higher dosage will lead to increased chlorine consumption and will accelerate pipe corrosion. Booster chlorination (BC) stations with smaller dosages are a solution to this problem. However, identifying the optimal number, locations, and dosage of each BC station in a cost-effective manner is challenging. This study proposes a methodology for determining the optimal number, locations, and chlorine dosages of BC stations in WDNs using a mixed integer linear programming problem. The methodology is illustrated through a simplified WDN in Holeta town, Ethiopia. The results indicate that if one adds two BC stations beyond the three dosage stations at the source, it will lead to a 49% reduction in chlorine use and a 27% decrease in the life cycle cost.

Measure this, not that: Optimizing the cost and model-based information content of measurements

Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) problem to optimize the selection of measurements. The solver MindtPy is modified to support calculating the D-optimality objective and its gradient via an external package, SciPy, using the grey-box module in Pyomo. The new approach is demonstrated in two case studies: estimating highly correlated kinetics from a batch reactor and estimating transport parameters in a large-scale rotary packed bed for CO2 capture. Both case studies show how examining the Pareto-optimal trade-offs between information content measured by A- and D-optimality versus measurement budget offers practical guidance for selecting measurements for scientific experiments.

Wasserstein generative adversarial networks-based photovoltaic uncertainty in a smart home energy management system including battery storage devices

Rooftop photovoltaic (PV) power generation uncertainty is one of the prominent challenges in smart homes. Home Energy Management (HEM) systems are essential for appliance and Energy Storage System (ESS) scheduling in these homes, enabling efficient usage of the installed PV panels' power. In this context, effective solar power scenario generation is crucial for HEM load and ESS scheduling with the objective of electricity bill cost reduction. This paper proposes a two-step approach, where a machine learning technique, Wasserstein Generative Adversarial Networks (WGANs), is used for PV scenario generation. Then, the generated scenarios are used as input for the HEM system scheduler to achieve the goal of cost minimization. The generated solar energy scenarios are considered in a single household case study to test the presented method's effectiveness. The WGAN scenarios are evaluated using different metrics and are compared with the scenarios generated by Monte Carlo simulation. The results prove that WGANs generate realistic solar scenarios, which are then used as input to a Mixed Integer Linear Programming (MILP) problem aiming for electricity bill minimization. A 41.5% bill reduction is achieved in the presented case study after scheduling both the load and ESS, with PV fluctuations taken into account, compared to the case where no scheduling, PV, or ESS are considered.

The United Kingdom electricity market mechanism: A tool for a battery energy storage system optimal dispatching

In this paper, the role of a Battery Energy Storage System (BESS) in the United Kingdom (UK) electricity market is investigated. Such device is selected since research works related to the topic demonstrate that BESSs help facing challenges caused by renewable energy sources increasing penetration in the power systems’ field. Indeed, in the next future, BESSs will assume a relevant role thanks to their fast response time. In the present paper, an optimization model is implemented to encode the UK market rules and output the optimal set of offers on day-ahead and intraday markets, dynamic frequency response services and imbalance settlement. The market rules are formalised in a mathematical model considering market temporal sequencing and BESS technical limitations. The tool also models the state of energy management, necessary since BESSs are energy limited assets. Objective function and constraints are linearized to define a Mixed Integer Linear Programming problem to reduce the computational burden and to integrate the model in the Energy Management System previously developed at University of Genoa. Specific tests are performed including and excluding ancillary services to evaluate the related advantages. The obtained outcomes reveal that ancillary services are the most convenient options within all the implemented scenarios.

Модель оптимізації портфеля купівлі-продажу електричної енергії компанією-постачальником

The study examined the market dynamics of an electricity supply company and proposed an optimization model aimed at enhancing its profitability in the wholesale market. This model is formulated as a mixed integer linear programming problem. By solving this optimization problem, the most advantageous contractual terms for purchasing and selling electricity from those available on the market are determined. This allows the company to efficiently manage its electricity portfolio and meet its consumption schedule as per existing supply contracts with consumers. The IBM ILOG CPLEX Optimization Studio software was employed to develop and solve the optimization problems related to the company's portfolio. The computational experiments conducted provide insights into the effectiveness of the proposed model and its practical applicability. These results demonstrate the model's adequacy and its potential for real-world implementation.

Integrated optimization of charging infrastructure, fleet size and vehicle operation in shared autonomous electric vehicle system considering vehicle-to-grid

Shared autonomous electric vehicles (SAEVs) are predicted to become a significant solution to reduce global emissions and energy consumption resulting from urban transportation. The centralized operation of SAEVs not only allows large-scale travel demand response but also can provide essential ancillary services to the smart grid through the concept of vehicle-to-grid (V2G). With V2G technology, unused electric vehicles can work as a distributed energy storage facility for the electricity grid to smoothen the intermittent demand. Designing and operating a V2G-enabled SAEV system is challenging. This problem involves complicated planning and operational decisions, as well as time-varying electric tariffs. In this work, a flow-based Integer Linear Programming (ILP) model is formulated for determining the optimal configurations (charging infrastructure and fleet size) and daily operation strategies (serving passengers, relocation, charging/discharging). The developed mathematical model allows for maximizing the total profit, comprising investment cost, revenue from serving passengers, and V2G profit through charging/discharging schedules. A two-stage Benders decomposition-based algorithm is proposed to address the sophisticated ILP problem. Via testing instances in the Manhattan network based on real-world and synthetic data, we have demonstrated the feasibility of our approaches and studied the benefits of integrating V2G in the SAEV system.

A Set Covering Approach to Design Maximally Permissive Supervisors for Flexible Manufacturing Systems

The supervisory control of Petri nets aims to enforce the undesired behavior as unreachable by designing a set of control places. This work presents a set cover approach to design maximally permissive supervisors. For each first-met bad marking, an integer linear programming problem is developed to obtain a control place to prohibit it. An objective function is formulated to make the maximal number of first-met bad markings forbidden. Then, we develop a set covering approach to minimize the number of selected control places. The proposed approach can guarantee the maximal permissiveness of the obtained supervisor and provide a trade-off between structural complexity and computational cost. Several examples are considered to validate the proposed method.

Polynomial-time server allocation algorithm in delay-sensitive internet-of-things monitoring services

This paper proposes a polynomial-time algorithm for a server allocation problem in delay-sensitive Internet-of-Things (IoT) monitoring services. The server allocation problem determines the appropriate servers to which the database and application are allocated to minimize the maximum delay between the latest update of reference data and the start of application processing for monitoring data. The server allocation problem was previously handled by expressing it as an integer linear programming (ILP) problem. Nevertheless, it fails to meet the computational time complexity needed to solve the problem, and it does not offer a more efficient technique than the ILP approach. The proposed algorithm consists of two components. The first step entails choosing utilization servers for both the database and the application. Next, the second phase entails matching each usage server and its corresponding IoT device. We prove that the proposed algorithm obtains an optimal solution in polynomial time. We compare computation times between the ILP approach and the proposed algorithm. Numerical results show that the proposed algorithm obtains the optimal solution faster than the ILP approach.

Peer-to-peer multi-period energy market with flexible scheduling on a scalable and cost-effective blockchain

Peer-to-Peer (P2P) electricity trading is an emerging means for allowing communities to share local energy production and demand response through direct trading. It is projected to play an important role in the future energy market by increasing the incentive to own and operate distributed energy resources (DERs) and participate in demand response (DR). A common approach to implementing P2P trading is with blockchain, however, existing solutions feature limitations. Typically, concerns involve either scalability and high transaction costs or projects implementing a permissioned blockchain that does not provide the trust and decentralization desired. In addition, the majority of market designs are simplified and do not capture the distinct complexity of electricity markets. They do not consider the inter-temporal constraints of appliances and DERs that need to run for multiple periods. Complex market designs that address these issues have not been implemented in blockchain based systems due to the computational limitations of such systems. To improve these two aspects, this paper proposes a market formulation that supports products running multiple periods with flexible scheduling, modeled as a mixed integer linear programming problem that optimizes social welfare. The trading platform is then implemented as a side chain of Polkadot, a network of blockchains designed to be secure, scalable, and economically feasible to foster an ecosystem of application-specific sidechains. This design is demonstrated to improve social welfare and achieve scalability by benchmarking the number of transactions that can be included per second, based upon typical assumptions of the market size. The result is a decentralized and performant system that allows for complex market designs to be implemented in a blockchain environment. This approach simplifies the process for participants, allowing them to bid DER or DR devices, directly and easily, even when this requires constraints across periods.

Further results on the hop domination number of a graph

A hop dominating set S in a connected graph G is called a minimal hop dominating set if no proper subset of S is a hop dominating set of G. The upper hop domination number γ+h (G) of G is the maximum cardinality of a minimal hop dominating set of G. Some general properties satisfied by this concept are studied. It is shown that for every two positive integers a and b where 2 ≤ a ≤ b, there exists a connected graph G such that γh(G) = a and γ+ h (G) = b. It is proved that minimal hop dominating set is NP-complete. It is proved that γh(G) and γ(G) are in general incomparable. It is shown that for every pair of positive integers a and b with a ≥ 2 and b ≥ 1, there exists a connected graph G such that γh(G) = a and γ(G) = b. We present an algorithm to compute minimal hop dominating set of G. Finally, we formulate an Integer linear programming problem to compute the hop domination number of G.

Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization

This paper considers sensitivity analysis of the cost coefficients in multiobjective integer linear programming problems. We define the sensitivity region as the set of simultaneous changes to the coefficients for which the efficient set and its structure remain the same. In particular, we require that the component-wise relation between efficient solutions is preserved and that inefficient solutions remain inefficient, and we show that this is sufficient for the efficient set to be the same upon changes. For a single coefficient, we show that a subset of the inefficient solutions can be excluded from consideration. More specifically, we prove that it suffices to inspect the inefficient solutions of a q-objective problem that are efficient in one of two related q + 1-objective problems. Finally, we show that the sensitivity region is a convex set (an interval). Our approach generalizes to simultaneous changes in multiple coefficients. For illustration, we consider mean-variance capital budgeting and determine the region for which the set of efficient portfolios remains the same, despite a misspecification or a change in the net present values of the projects. Further computational experience with multiobjective binary and integer knapsack problems demonstrates the general applicability of our technique. For instance, we obtain all sensitivity intervals for changes to single coefficients of biobjective problems with 500 binary variables in less than half an hour of CPU time by excluding a large number of inefficient solutions. In fact, the number of excluded solutions is above 100 orders of magnitude larger than the number of remaining solutions. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.01406 .

Optimization method for renewable energy investment planning in the electricity carbon coupling market environment considering economy

China is developing rapidly in renewable energy development, electricity market reform, and carbon market construction, using market mechanisms for efficient planning and investment. The electricity and carbon markets are interrelated for market entities. This context has led to a dual-level optimization model for renewable energy investment planning, considering cost recovery and new power system goals. The model includes deriving electricity carbon coupling quotations for conventional units based on dynamic carbon emission characteristics and proposing an electricity spot market mechanism influenced by carbon quota trading. The model’s upper level maximizes renewable energy investment capacity, determining its size and location, while the lower level simulates electricity spot and voluntary emission reduction market trading to guide investment decisions. The model transformed into a mixed integer linear programming problem for optimal solutions was validated numerically, examining various factors affecting optimal renewable energy investment capacity.

Supervisor Synthesis for Petri Nets With Uncontrollable and Unobservable Transitions

This paper focuses on designing event feedback supervisors to enforce control specifications on Petri nets with uncontrollable and unobservable transitions. For each observation, the supervisor is able to select some controllable transitions to disable such that the system never reaches illegal markings. Two different methods are given to design such a supervisor. The first method computes the control policy by solving some integer linear programming problems, while the second one designs supervisors by taking advantage of the structural properties of a class of Petri nets. The computational efficiencies of these two methods increase successively at the expense of their application scopes. Two examples are given to illustrate the proposed methods, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper consists in ensuring the behavior of a manufacturing system within a given legal behavior. The typical task for a designer is to design a supervisor to restrict that the system never reaches a forbidden state under limited control and observation ability. To this end, this paper proposes two different methods to design such a supervisor. The first one needs to solve integer linear programming problems, while the second one is based on the structural analysis of a special class of systems. It should be noted that although the application scope of the first method is wider, the second method has higher computational efficiency. Therefore, the suitable method can be chosen in accordance with the specific application scenario, which is significant and useful to manufacturing engineers.

Micro-grid tri-level EPEC based model for finding equilibria in the day-ahead and balancing markets

This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state.

Integrating Compressed CO2 Energy Storage in an Integrated Energy System

The integration of an energy storage system into an integrated energy system (IES) enhances renewable energy penetration while catering to diverse energy loads. In previous studies, the adoption of a battery energy storage (BES) system posed challenges related to installation capacity and capacity loss, impacting the technical and economic performance of the IES. To overcome these challenges, this study introduces a novel design incorporating a compressed CO2 energy storage (CCES) system into an IES. This integration mitigates the capacity loss issues associated with BES systems and offers advantages for configuring large-scale IESs. A mixed integer linear programming problem was formulated to optimize the configuration and operation of the IES. With an energy storage capacity of 267 MWh, the IES integrated with a CCES (IES–CCES) system incurred an investment cost of MUSD 161.9, slightly higher by MUSD 0.5 compared to the IES integrated with a BES (IES–BES) system. When not considering the capacity loss of the BES system, the annual operation cost of the IES–BES system was 0.5 MUSD lower than that of the IES–CCES system, amounting to MUSD 766.6. However, considering the capacity loss of the BES system, this study reveals that the operation cost of the IES–BES system surpassed that of the IES–CCES system beyond the sixth year. Over the 30-year lifespan of the IES, the total cost of the IES–CCES system was MUSD 4.4 lower than the minimum total cost of the IES–BES system.

Application of Stochastic Programming in Agricultural and Newsvendor Problems and It's Application in Real Life

The study of making the best decision under risk management in a variety of areas of our lives is known as Stochastic Programming. We will go through two-stage Stochastic Linear Programming approaches for a variety of real-world choice issues, as well as how to solve them. We will achieve this by constructing stochastic linear programming models based on real-world situations like the well-known Farmer's situation and News Vendors problems. The influence of pricing, Stochastic Integer Linear Programming problem, second stage Stochastic Integer Linear Programming problem, first stage Stochastic Binary Linear Programming problem, risk aversion problem, and continuous function for random variables based on two-stage SLP with the aid of Farmer's problem will all be examined. We will address the Newsvendor’s problem with Deterministic Equivalent Stochastic Linear Programming, an extension of Deterministic Stochastic Linear Programming for risk aversion with a high number of decision variables and restrictions, utilizing the two-stage Stochastic Linear Programming approach once more. Hand calculation is a challenging way to acquire the solution to the problems. As a result, we will use the programming language AMPL to design computer solutions for tackling both farmer and newsvendor difficulties. We will also utilize MATLAB to create graphs for the farmer's problem's continuous function. Dhaka Univ. J. Sci. 72(1): 30-45, 2024 (January)

Identification of labeled Petri nets from finite automata

Automata and Petri nets are two typical models of discrete event systems. The paper studies the problem of converting a finite automaton into a Petri net that satisfies the specified structural features. More specifically, we identify a labeled Petri net from a nondeterminstic finite automaton such that the reachability graph of the identified net is isomorphic to the given automaton, meaning that the Petri net models exactly the same dynamic system as the automaton. The identified net necessarily satisfies the specified structural requirements, such as the numbers of places and transitions, absence of self-loops, the exact structure of a part of the net, and so on. Since label Petri nets and nondeterminstic finite automata are generalizations of Petri nets and deterministic finite automata, respectively, the proposed approach can identify a larger spectrum of Petri nets and effectively handle the nondeterminstic cases in the given automaton. Four kinds of conditions are first extracted from the given automaton, namely deterministic enabling conditions, nondeterministic enabling conditions (i.e., multiple transitions with the same label are enabled simultaneously at a marking), transition disabling conditions, and marking inequality conditions. Then, an integer linear programming problem is formulated by characterizing these four kinds of conditions using integer linear constraints. A labeled Petri net satisfying the structural requirements is obtained by solving the integer linear programming problem. We also present two examples to show the possible applications of the proposed identification approach.