Integer Linear Programming Problem Research Articles

The Efficacy of Multi-Period Long-Term Power Transmission Network Expansion Model with Penetration of Renewable Sources

The electrical energy demand increase does evolve rapidly due to several socioeconomic factors such as industrialisation, population growth, urbanisation and, of course, the evolution of modern technologies in this 4th industrial revolution era. Such a rapid increase in energy demand introduces a huge challenge into the power system, which has paved way for network operators to seek alternative energy resources other than the conventional fossil fuel system. Hence, the penetration of renewable energy into the electricity supply mix has evolved rapidly in the past three decades. However, the grid system has to be well planned ahead to accommodate such an increase in energy demand in the long run. Transmission Network Expansion Planning (TNEP) is a well ordered and profitable expansion of power facilities that meets the expected electric energy demand with an allowable degree of reliability. This paper proposes a DC TNEP model that minimises the capital costs of additional transmission lines, network reinforcements, generator operation costs and the costs of renewable energy penetration, while satisfying the increase in demand. The problem is formulated as a mixed integer linear programming (MILP) problem. The developed model was tested in several IEEE test systems in multi-period scenarios. We also carried out a detailed derivation of the new non-negative variables in terms of the power flow magnitudes, the bus voltage phase angles and the lines’ phase angles for proper mixed integer variable decomposition techniques. Moreover, we intend to provide additional recommendations in terms of in which particular year (within a 20 year planning period) can the network operators install new line(s), new corridor(s) and/or additional generation capacity to the respective existing power networks. This is achieved by running incremental period simulations from the base year through the planning horizon. The results show the efficacy of the developed model in solving the TNEP problem with a reduced and acceptable computation time, even for large power grid system.

Joint energy management and trading among renewable integrated microgrids for combined cooling, heating, and power systems

Energy depletion and rising demand cause a demand-supply imbalance and power system instability. Centralized energy production makes the system less reliable and less efficient because of problems with transmission and line losses. Conventional microgrids use electricity to heat, cool, and power loads, wasting microturbine surplus heat. To address these issues, a joint energy management and trading model for combined cooling, heating, and power (CCHP) microgrids is proposed to minimize the system cost as well as enhance the system’s efficiency and reliability. The framework is designed in such a way that, in the first step, each CCHP microgrid will apply demand-side management to meet its load demands from its own generation. If any CCHP microgrid does not have enough self-generated energy to meet its load demands, then it can purchase energy from nearby CCHP microgrids or utility. On the other hand, each CCHP microgrid has the option to sell any extra energy to nearby CCHP microgrids or utility. Furthermore, each CCHP microgrid can use a diesel generator to meet its energy demands if the available energy from its own generation and energy purchased from other CCHP microgrids or utilities is not enough. To solve the problem of integer linear programming, the branch, and bound algorithm is used. The results show a reduction in the system’s overall cost by 33.29% whereas peak energy demand is reduced by 25.76%. Reduction in peak energy demand will minimize the line losses, and hence the system efficiency and reliability will be improved.

Joint Power Control and Task Offloading in Collaborative Edge–Cloud Computing Networks

Mobile edge computing arises as a promising technology to allow mobile devices to offload delay-sensitive and computation-intensive tasks to the nearby edge servers. However, overloaded tasks from mobile devices (MDs) lead to a large latency due to limited computing and channel resources. To mitigate this situation, a collaborative edge-cloud computing network is considered in this paper. Based on power control and task offloading, we formulate a mixed-integer nonlinear programming (MINLP) problem to minimize the weighted sum of the energy consumption and the latency. This NP-hard problem is decomposed into a real variable problem and an integer linear programming problem. By leveraging the proposed extremevalue descent (EVD) method, the optimal power strategy is obtained by solving the real variable problem. The simplex method and branch-and-bound method are adopted to find the optimal offloading strategy. Although these two sub-problems are well solved, the solutions may be unsatisfactory for the original problem. To find a high-quality solution, we use an alternating optimization (AO) method to jointly optimize the decomposed problems. Theoretical analysis demonstrates that the EVD method converges at the rate of O(1/s) and the AO method can converge to a sub-optimal solution if not the optimal solution. Simulation results show that the proposed algorithms significantly outperform other benchmark schemes.

Don’t-Care-Based Logic Optimization for Threshold Logic

In this paper, we present a don’t-care-based threshold logic gate (TLG) minimization method for threshold logic network (TLN) optimization. We first introduce a sufficient condition for the don’t cares of a TLG to exist in a TLN and propose a logic-implication-based method to identify the don’t cares. Then, we present two different methods for minimizing the TLG with the don’t cares. The first one is an integer linear programming (ILP)-based method. We model the minimization problem as an ILP problem, and propose an approach to compute the necessary constraints of the ILP formulation. The second one is a heuristic method adapted from a threshold function identification approach. In the experiments, we applied the proposed methods to two sets of TLNs generated by the up-to-date synthesis technique. The results show that, for the two sets of TLNs, the ILP-based method achieves an average of 12% and 23% area reduction without any overhead on the TLG count and logic depth. Furthermore, the heuristic method is more efficient than the ILP-based method with only a little quality loss.

Cooperative Service Placement and Request Routing in Mobile Edge Networks for Latency-Sensitive Applications

The emergence of mobile applications like self-driving cars, networked gaming, virtual reality, and augmented reality has created a demand for computation-intensive and latency critical applications. The dense deployment of base stations (BSs) makes the overlapping coverage of BS that induces the placement of services and routing the requests to the appropriate node is a challenging issue. Further, the limited resources at the edge node invite additional problems of allocating the existing limited edge resources cooperatively to fulfil the user demands. To address the problems mentioned above, we formulate the cooperative service placement and routing problem by placing the diversified latency critical services to maximize the time utility with the deadline and resource constraints. The problem is formulated as an integer linear programming problem for cooperative service placement in mobile edge networks. A greedy and randomized rounding technique is presented to solve the service caching and request routing problems decomposed from the proposed problem. Further, a heuristic algorithm based on the circular convex set is presented to solve the proposed NP-hard problem. Extensive simulation results demonstrate that the proposed cooperative service placement schemes significantly improve the delay, cache hit ratio, load on cloud, and time utility performance compared with existing mechanisms.

Chance-Constrained Dispatching of Integrated Energy Systems Considering Source–Load Uncertainty and Photovoltaic Absorption

Because of their renewable and non-polluting characteristics in power production, distributed photovoltaics have been developed, but they have also been criticized for the volatility of their output power. In this paper, an integrated energy system optimal dispatching model is proposed to improve the local absorption capacity of distributed photovoltaics. First, an integrated energy system consisting of electricity, heat, cooling, gas, and hydrogen is modeled, and a mathematical model of the system is constructed. After that, the uncertainty of distributed photovoltaic power and load demand is modeled, and a typical scenario data set is generated through Monte Carlo simulation and K-means clustering. Finally, an optimal dispatching model of the integrated energy system is constructed to minimize the daily operating cost, including energy consumption, equipment operation and maintenance, and curtailment penalty costs, as the optimization objective. In the objective, a segmented curtailment penalty cost is Introduced. Moreover, this paper presents a chance constraint to convert the optimization problem containing uncertain variables into a mixed integer linear programming problem, which can reduce the difficulty of the solution. The case shows that the proposed optimal dispatching model can improve the ability of photovoltaics to be accommodated locally. At the same time, due to the introduction of the segmented curtailment penalty cost, the system improves the absorption of distributed photovoltaic generation at peak tariff intervals and enhances the economy of system operation.

An optimized trading strategy for an energy storage systems aggregator in an ancillary service market

With increasing proportion of intermittent renewable energy sources in the electric power system, the system operator (SO) is facing a challenge of maintaining the demand-supply balance which is more dynamic and uncertain than before. To manage the balance, the SO procures different services from balancing service providers like balancing mechanism units and distributed energy resources aggregators. In this work, we propose a model for an aggregator of energy storage systems (ESS). The distributed small size ESS can be grouped and utilized by an aggregator for trading of multiple services with different specifications and bidding rules in ancillary service markets. ESS, being flexible and having quick response time, can contribute in both directions for all the services and assist in maintaining the real time demand-supply balance of the system. The trading strategy proposed in this work captures the regulations and the bidding characteristics of all the services individually. This proposed solution is a Mixed Integer Linear Programming (MILP) problem which becomes computationally complex as the size of ESS dataset of the aggregator increases. Hence, we also propose an alternate approximation method which is scalable, comparatively easy to solve and takes less computation time while giving comparable optimal schedules. These proposed methods have also been compared with an intuitive baseline method. We have demonstrated the efficacy of the proposed methods with real world data of France balancing market.

Synthesis of hybrid membrane distillation processes with optimal structures for ethanol dehydration

Conventional distillation is the most used unit operation to separate zeotropic mixtures. However, it is combined other unit operations to separate azeotropic mixtures. This work proposes a synthesis and intensification framework to obtain hybrid membrane distillation process structures. The synthesis problem was represented by a low aggregation superstructure comprised of functional modules. Then, the superstructure was reformulated as a Mixed Integer Linear Programming (MILP) problem to derive the optimal structure. The synthesis problem does not consider any pre-established process structure or connectivity; therefore, the optimal solution must be interpreted, simulated, and validated to generate a known process structure. Finally, the validated structure was post-optimized to fine-tune the detailed design of the process structure. The presented framework was applied to separating an ethanol/water mixture. The obtained solutions attained high energy and cost savings compared to the typical pressure swing and extractive distillation.

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.

A Computationally Efficient Benders Decomposition for Energy Systems Planning Problems with Detailed Operations and Time-Coupling Constraints

Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or mixed integer linear programming (MILP) problems. Despite the relative efficiency and maturity of LP and MILP solvers, large scale problems are often intractable without abstractions that impact quality of results and generalizability of findings. We consider a macro-energy systems planning problem with detailed operations and policy constraints and formulate a computationally efficient Benders decomposition separating investments from operations and decoupling operational timesteps using budgeting variables in the master model. This novel approach enables parallelization of operational subproblems and permits modeling of relevant constraints coupling decisions across time periods (e.g., policy constraints) within a decomposed framework. Runtime scales linearly with temporal resolution; tests demonstrate substantial runtime improvement for all MILP formulations and for some LP formulations depending on problem size relative to analogous monolithic models solved with state-of-the-art commercial solvers. Our algorithm is applicable to planning problems in other domains (e.g., water, transportation networks, production processes) and can solve large-scale problems otherwise intractable. We show that the increased resolution enabled by this algorithm mitigates structural uncertainty, improving recommendation accuracy. Funding: Funding for this work was provided by the Princeton Carbon Mitigation Initiative (funded by a gift from BP) and the Princeton Zero-carbon Technology Consortium (funded by gifts from GE, Google, ClearPath, and Breakthrough Energy). Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0005 .

Cyber Restoration of Power Systems: Concept and Methodology for Resilient Observability

In order to have a properly functioning cyber–physical power system, the operational data need to be properly measured, transmitted, and processed. In case of a malicious event on the cyber layer of the power system, such as the wide-area monitoring system, cyber components, such as phasor measurement units (PMUs), communication routers, and phasor data concentrators (PDCs) may be compromised, leading to an unobservable power system. This article proposes the concept of cyber restoration of power systems, and an optimal restoration scheme to recover the system observability swiftly after massive interruptions. The cyber restoration problem is formulated as a mixed integer linear programming (MILP) problem considering PMU measurability, communication network connectivity, and PDC processability conditions, as well as cyber restoration resources as constraints. Results in the IEEE 57-bus system validate that the proposed optimization method can provide solutions that recover system observability much faster than heuristic methods, demonstrating the need for systematic cyber restoration planning research and implementation.

A hybrid approach to solve a raw material collecting vehicle routing problem

PurposeThe purpose of this study is to formulate a new class of vehicle routing problem with an objective to minimise the total cost of raw material collection and derive a new approach to solve optimization problems. This study can help to select the optimum number of suppliers based on cost.Design/methodology/approachTo model the raw material vehicle routing problem, a mixed integer linear programming (MILP) problem is formulated. An interesting phenomenon added to the proposed problem is that there is no compulsion to visit all suppliers. To guarantee the demand of semiconductor industry, all visited suppliers should reach a given raw material capacity requirement. To solve the proposed model, the authors developed a novel hybrid approach that is a combination of block and edge recombination approaches. To avoid bias, the authors compare the results of the proposed methodology with other known approaches, such as genetic algorithms (GAs) and ant colony optimisation (ACO).FindingsThe findings indicate that the proposed model can be useful in industries, where multiple suppliers are used. The proposed hybrid approach provides a better sequence of suppliers compared to other heuristic techniques.Research limitations/implicationsThe data used in the proposed model is generated based on previous literature. The problem derives from the assumption that semiconductor industries use a variety of raw materials.Practical implicationsThis study provides a new model and approach that can help practitioners and policymakers select suppliers based on their logistics costs.Originality/valueThis study provides two important contributions in the context of the supply chain. First, it provides a new variant of the vehicle routing problem in consideration of raw material collection; and second, it provides a new approach to solving optimisation problems.

Determining optimal generator start-up sequence in bulk power system restoration considering uncertainties: A confidence gap decision theory based robust optimization approach

A reasonable start-up sequence of generators considering renewable energy generation integration can effectively improve the restoration efficiency of the power system concerned. The restoration strategy of generators is time-sensitive, however, the computation procedure of existing methods is not fast enough to meet the requirements of practical applications. In this paper, the generator start-up sequence optimization (GSSO) problem is addressed with the integration of wind-solar hybrid systems (WSSs) considered in bulk power systems. Specifically, a deterministic model for GSSO is formulated to maximize the total generation capability during the restoration procedure, in which fewer auxiliary variables are required to promote the computational efficiency. On this basis, in order to deal with the inherent and significant uncertainties of WSSs, a confidence gap decision theory (CGDT) based approach is proposed combining the advantages of stochastic optimization and the information gap decision theory based method while considering the worst-case realization of unknown probability distributions, so that a chance-constrained robust generator start-up solution is thereby attained. Moreover, the formulated CGDT based model is transformed into a mixed integer linear programming problem. Finally, the IEEE 39-bus power system and a modified version of an actual power system in China are employed to demonstrate the feasibility and efficiency of the proposed method.

Optimal planning and forecasting of active distribution networks using a multi-stage deep learning based technique

This paper presents a comprehensive methodology for long-term planning in distribution networks to address the challenges associated with integrating renewable energy resources (RERs) and battery energy storage systems (BESSs). The methodology incorporates active network management (ANM) schemes, coordinated voltage control (CVC), and demand side management (DSM) to optimize the sizing and siting of RERs and BESS. Deep learning-based long-term forecasting techniques are utilized to capture the hourly variations in load demand, solar irradiance, and wind speed throughout the year. The objective is to minimize overall network costs, considering investment and operational costs, while planning over a 5-year horizon with a 3% annual load growth. The model includes tie-lines as a decision variable for network expansion investments, ensuring efficient network flexibility. The linearized mathematical model is developed as a mixed integer linear programming (MILP) problem to enhance scalability. A case study is conducted on the UKGDS 16-bus system to verify the optimization model, and further validation is performed on the IEEE 69-bus system to assess scalability. The results demonstrate the effectiveness of the proposed method in achieving accurate forecasting and efficient sizing and siting decisions for RERs and BESSs, including tie-line investments, providing valuable insights for real-world distribution network scenarios.

Scalable inter-domain network virtualization

To realize inter-domain network virtualization for hybrid cloud, the following challenges must be resolved. (1) Scalability. The network virtualization system should allow tenant virtual networks to use on-demand addressing schema and span multiple domains. This requirement, combined with the expansion of the network scale, can lead to a rapid increase in flow rule consumption, posing a significant challenge for network scalability. (2) Inter-domain network flow scheduling. To allocate bandwidth for inter-domain network flows with low cost and guaranteed bandwidth is complex (NP-hard). Existing researches fail to address this problem in a flexible yet efficient manner. This paper proposes a network virtualization solution that jointly considers the two challenges. Towards the scalability challenge, we use MAC translation to encode location hierarchy and tenant information into MAC addresses, thereby enabling L2 forwarding rule aggregation on each switch. Besides, we offload the L3 virtual network rules onto the first hop software switches and tackle L3 routing through VMAC-based forwarding. We formally prove that our approach can bound the worst-case rule consumption by combining these two techniques. Towards the second challenge, we formulate the inter-domain network flow scheduling (INFOS) problem into an integer linear programming (ILP) problem and prove its NP-hardness. We also propose a heuristic algorithm that can guarantee bandwidth lower-bound while avoiding causing significant profit loss or introducing too many network updates. Evaluation shows that our approach can reduce the average flow rule consumption significantly, compared with state-of-the-art approaches. Besides, towards the same bandwidth guarantee target, we can avoid up to 94.4% of the network update operations.

Resilience improvement model of distribution network based on two-stage robust optimization

Frequent natural disasters have a serious impact on the power system. It is urgent to ensure the normal operation of the distribution network under disaster events. This paper divides the stages of improving the resilience of the distribution network into two aspects: long-term investment planning and short-term response. We combine the decision-making process with the chronological order of natural disasters, and a N-k uncertainty set is applied to describe the uncertainty of distribution network damage. We propose a line hardening and distributed generations configuration strategy for the purpose of enhancing the resilience of distribution networks and countering extreme natural disasters. The problem is expressed as a tri-level robust optimization formulation in order to minimize the load shedding under the worst line damaged scheme. The first level corresponds to the long-term investment planning and preparation of pre-disaster stage. The second level represents the stage of line damage, and the third level matches the optimal scheduling during the post-disaster period. On the basis, this mixed integer linear programming problem is transformed into a solvable form, which is calculated by a modified Column and Constraint Generation (C&CG) algorithm. Case studies show that our proposed model can reduce load shedding to 70% of the original level, and the running time of the algorithm is less than 60 s, which verifies the model can effectively enhance the resilience of the distribution network and enhance its ability to respond to natural disasters.

Optimum exploitation of an integrated energy system considering renewable sources and power-heat system and energy storage

The increasing population and energy consumption have led to a greater emphasis on managing and storing different energy sources. Researchers are now focusing on integrating renewable energy into energy systems and improving efficiency through accurate modeling and calculations. This article presents the optimal operation of an integrated energy system that incorporates wind energy as a renewable source. The study focuses on enhancing the modeling accuracy of equipment such as combined heat and power units and storage devices to align the obtained results with real-world scenarios. To effectively manage electrical and thermal loads, a load management program is implemented. Furthermore, the uncertainty of wind speed is addressed using the interval-valued grey decision Theory method. Two sensitivity analyses are conducted to further investigate the system's performance. Firstly, the impact of incorporating storage resources and load management programs on the overall operating cost is examined. The results demonstrate a significant 22.87% improvement in the objective function when both storage devices and load management programs are employed simultaneously. Secondly, a sensitivity analysis is performed to evaluate the objective function's response to changes in the uncertainty budget parameters and wind speed deviation. The findings highlight the greater impact of wind speed deviation on the objective function compared to changes in the uncertainty budget. The problem is formulated as a mixed integer linear programming problem, and the GAMS software and CPLEX solver are utilized to obtain the relevant results. The findings emphasize the potential of integrating wind energy into an integrated energy system and underscore the importance of accurate modeling, load management, and the consideration of storage resources. These insights contribute to the optimization of energy system operations and the advancement of sustainable energy practices.

Planning of UAV Flight Routes in the Problems of Group Patrolling of the Extended Territories

Currently one of the promising areas of joint use of unmanned aerial vehicles (UAVs) is group air patrolling of large territories. Here the organization of patrolling assumes the solving the planning problem of routes flight of UAV group. The paper considers the problem of optimal planning of flight routes of the same type of UAVs during group patrolling of large territories. The territorial waters or narrow border areas of any State may serve as an example of such territories. It is suggested that the patrolled area has an elongated shape and is divided into a chain of adjacent patrol zones prescribed by a separate UAV. The drone’s flight route passes through adjacent zones. The flight task performed periodically by each drone consists in moving it to a given flight zone, collecting operational data and transmitting this data to a control point (center, station). The optimization aspect of UAV flight route planning is to minimize the maximum time required to complete flight tasks. The considered problem of group patrolling reduced to the multiple traveling salesman problem — one of the classic intractable combinatorial optimization problems. A brief analysis of modern methods for solving the multiple traveling salesman problem is given. Due to the lack of effective exact methods for solving this problem, it is natural to use approximate heuristic and metaheuristic methods focused on solving NP-hard optimization problems, reducing the full search and giving a solution close to the exact one. The multiple traveling salesman problem considered in this paper is reduced to the problem of integer linear programming, for the solution of which a genetic algorithm implemented in MATLAB based on the mathematical package Global Optimization Toolbox is proposed. An illustrative example of patrolling by three UAVs of an extended territory with 11 adjacent zones is considered. Computational experiments confirm the effectiveness of the algorithmic solutions proposed in the work.

A sharing economy model for a sustainable community energy storage considering end-user comfort

A promising solution for the current and future power system challenges like the increasing penetration of demand-side distributed energy resources and the economies of scale of individual energy storage systems could be the concept of the smart Community Energy Storage (CES). This paper focuses on developing an energy cooperation framework between photovoltaic prosumers and CES. In the proposed structure, an appropriate environment is provided in the energy community to consider several smart homes that together form an energy community. They can store and generate energy by some central devices, including combined heat and power unit, thermal storage system, and electrical energy storage. Furthermore, each end-user individually owns a rooftop PV system and a heating, ventilation, and air conditioning system where the uncertainty of the PV generation unit is modeled by a scenario-based approach. The main question of this study is what benefits an energy community provides to the set of end-users. The goal of the energy community manager of the smart CES as the objective function of the scheduling problem is to minimize energy cost and end-user discomfort level, where ε-constraint method is used to solve the multi-objective CES scheduling problem. The main contribution of this paper is introducing the sharing economy concept and considering the role of occupants' thermal comfort, the impacts of time importance and end-user thermal sensitivity, and the impact of thermal comfort in the CES. The proposed model is structured as a mixed integer linear programming problem that is implemented in the GAMS software. Results show that by using CES, the energy cost decreases about 28.48% while the end-user discomfort level significantly improves.

Two-stage distributionally robust optimization for joint system design and maintenance scheduling in high-consequence systems

The failures of high-consequence systems can cause serious harm to humans, including loss of human health, life security, finance, and even social chaos. To protect high-consequence systems, both optimal system design and maintenance activities contribute to improving system reliability and social safety. The existing works generally optimize these two problems sequentially and assume that the degradation process of components is precisely known. However, sequential optimization often results in significant losses due to redundancies, and such a presumption usually cannot be guaranteed in practice, due to limited historical data or a lack of expert knowledge, referred to as epistemic uncertainty. To fill this gap, in this article, we consider an integrated optimization of system design and maintenance scheduling for multi-state high-consequence systems in which the component’s degradation is known with limited distributional information. To address this issue, we utilize the framework of distributionally robust optimization to provide a risk-averse decision to decision-makers even under the worst realizations of random parameters, and develop a two-stage integer distributionally robust model with moment-based ambiguity set to determine the system design and maintenance scheduling simultaneously. The proposed model can be converted to a tractable approximation as an integer linear stochastic programming problem. In order to solve large-scale problems, we develop a sample-based adaptive large neighborhood search algorithm to find the optimal system designs. In the numerical experiments, we present a case study on feedwater heating systems in nuclear power plants and demonstrate that an integrated optimization consideration creates significant benefits in profitability. We also present the out-of-sample performance of the distributionally robust design to avoid extreme risk.