Mixed Integer Linear Programming Optimization Research Articles

Protograph Based Low-Density Parity-Check Codes Design With Mixed Integer Linear Programming

An approach to design protograph-based low-density parity-check (LDPC) codes utilizing mixed integer linear programming (MILP) optimization is presented in this paper. The protograph (base graph) cyclic lifting for a class of quasi-cyclic LDPC codes is considered. In general, the short cycles elimination is the primary optimization goal, possibly weighted by a metric of cycles connectivity. A notion of closed walks in the base graph is shown to be a convenient way for representing sources of cycles in the lifted graph. We express the condition for non-existence of a cycle in the lifted graph corresponding to a closed walk in the base graph in the form of a set of linear inequalities. Such inequalities, collected for all closed walks shorter than a desired limit corresponding to girth, form a set of linear constraints. Meanwhile, the longer closed walks can be reflected in a linear objective function of the optimization. The proposed combination of constraints and objective function forms an input to a MILP solver. As a result, a globally optimized code graph can be obtained. The method can be utilized for binary as well as nonbinary LDPC codes. The numerical results show that the constructed codes can outperform similar codes deigned with reference heuristic search methods.

A MILP-Based Restoration Technique for Multi-Microgrid Distribution Systems

The main focus of the work presented in this paper is on the outage management of interconnected microgrids during islanded operation after being disconnected from the utility main supply. The proposed two-stage load restoration technique is formulated as a Mixed Integer Linear Programming (MILP) optimization problem with the sole objective of optimally restoring the maximum number of disconnected loads. The proposed technique is applied to a distribution system comprising of several microgrids, i.e., Multi-Microgrid (MMG) distribution system. In this proposed technique, the power transactions between individual microgrids are managed through (1) determining the schedule of local energy resources, and (2) by obtaining the control signals pertaining to local flexible loads. Flexible load control signals are prioritized through two incorporated Demand Response (DR) programs, namely emergency load shedding and preemptive load shifting. To quantify the restoration technique performance, a new index—denoted as restoration technique success index (SI)—is proposed. The effectiveness of the proposed restoration technique is verified through different test case scenarios and the obtained results are discussed.

A mixed-integer linear programming approach for energy-constrained mobile anchor path planning in wireless sensor networks localization

In sensors localization, it is not economically argumentative to equip many static nodes with GPS. The most widespread solution is to utilize from mobile location-aware nodes called mobile anchors. A substantial amount of research to propose mobile anchor trajectory to improve localization accuracy, localization latency, network coverage and traversed path has been reported. However, none of the existing static mobile anchor path planning mechanisms has emphasized on increasing mobile anchor lifetime and reliability that is necessary due to limited energy. In this paper we propose a novel mobile anchor trajectory planning scheme called Optimal Priority based Trajectory with Energy Constraint (OPTEC) in order to address these issues. The proposed scheme utilizes the Mixed Integer Linear Programming optimization (MILP) approach for optimal route planning in the presence of location uncertainty for deployed sensors. Several important evaluation metrics including localization coverage, localization success, ineffective beacon points and energy-location uncertainty product are also defined for a comprehensive comparison of static mobile anchor trajectory plans. In this paper, static sensors utilize a range-free localization algorithm. Simulation results reveal that the proposed mobile anchor trajectory planning approach can surpass other existing trajectories in terms of localization error, mobile anchor energy consumption and even sensors lifetime.

Mixed Integer Linear Programming Optimization of Multi-Node Transportation Transshipment Network

Transportation network is time bound supply mechanism and it involves multiple levels. It is beneficial for an organization to identify optimal transportation routes by exploring different options. This practice can help in minimizing the transportation costs and Optimizing the delivery time. In this study, multiple levels of transportation transshipment network are considered and by adopting Mixed Integer Linear Programming (MILP), cost of transportation network is minimized. A comparison with the existing cost indices is provided for effectiveness of the tool used. Result indicates an improvement in the cost saving and comparison with the initial results suggests cost saving by 9.41% in transporting raw materials from depot to the factory level while 8.7% cost saving is achieved in transshipment of finished goods from warehouses to distribution centers. Overall, the total cost is reduced by 18.17% which is a significant improvement and can be translated into profit margin of the production supply chain. We also generalize the findings of the study by assessing the statistical robustness of the results.

Mixed Integer Linear Programming Optimization of Multi-Node Transportation Transshipment Network

Transportation network is time bound supply mechanism and it involves multiple levels. It is beneficial for an organization to identify optimal transportation routes by exploring different options. This practice can help in minimizing the transportation costs and Optimizing the delivery time. In this study, multiple levels of transportation transshipment network are considered and by adopting Mixed Integer Linear Programming (MILP), cost of transportation network is minimized. A comparison with the existing cost indices is provided for effectiveness of the tool used. Result indicates an improvement in the cost saving and comparison with the initial results suggests cost saving by 9.41% in transporting raw materials from depot to the factory level while 8.7% cost saving is achieved in transshipment of finished goods from warehouses to distribution centers. Overall, the total cost is reduced by 18.17% which is a significant improvement and can be translated into profit margin of the production supply chain. We also generalize the findings of the study by assessing the statistical robustness of the results.

Bounds on GreenTouch GreenMeter Network Energy Efficiency

In this paper, we validate the energy efficiency improvements in core networks obtained through mixed integer linear programming (MILP) optimization models as part of the GreenMeter study carried out by the GreenTouch consortium by developing closed form expressions and bounds for the power consumption of core networks. We consider nonbypass, bypass, mixed line rates, and physical topology optimization energy efficiency schemes. In addition to validating the optimization model results by setting bounds on the power consumption, these bounds can predict network performance at operating conditions highly complex for the MILP models. The derivation of a single bound that includes all the measures proved intractable and therefore each measure is evaluated separately.

S2VC: An SDN-based framework for maximizing QoE in SVC-based HTTP adaptive streaming

HTTP adaptive streaming (HAS) is quickly becoming the dominant video delivery technique for adaptive streaming over the Internet. Still considered as its primary challenges are determining the optimal rate adaptation and improving both the quality of experience (QoE) and QoE-fairness. Most of the proposed approaches have relied on local information to find a result. However, employing techniques that provide a comprehensive and central view of the network resources can lead to more gains in performance. By leveraging software defined networking (SDN), this paper proposes an SDN-based framework, named S2VC, to maximize QoE metrics and QoE-fairness in SVC-based HTTP adaptive streaming. The proposed framework determines both the optimal adaptation and data paths for delivering the requested video files from HTTP-media servers to DASH clients. In fact, by utilizing an SDN controller and its complete view of the network, we introduce an SVC flow optimizer (SFO) application module to determine the optimal solution in a centralized and time slot fashion. In the current approach, we first formulate the problem as a mixed integer linear programming (MILP) optimization model. The MILP is designed in such a way that it applies defined policies, e.g. setting priorities for clients in obtaining video quality. Secondly, we show that this problem is NP-complete and propose an LP-relaxation model to enable S2VC framework for performing rate adaptation on a large-scale network. Finally, we conduct experiments by emulating the proposed framework in Mininet, with the usage of Floodlight as the SDN controller. In terms of improving QoE-fairness and QoE metrics, the effectiveness of the proposed framework is validated by a comparison with different approaches.

Cascade energy optimization for waste heat recovery in distributed energy systems

The efficiency of distributed energy systems can be significantly increased through waste heat recovery from industry or power generation. The technologies used for this process are typically dependent on the quality and temperature grades of waste heat. To maximize the efficiency of cascade heat utilization, it is important to optimize the choice of waste heat recovery technologies and their operation. In this paper, a detailed mixed integer linear programming optimization model is proposed for waste heat recovery in a district-scale microgrid. The model can distinguish waste heat quality for planning and operation optimization of distributed energy systems. Heat utilization technologies are formulated in this developed model and categorized in different temperature grades. The developed model is validated using four typical cases under different settings of system operation and business models. It is found that the optimization model, by distinguishing waste heat temperature, can increase energy cost savings by around 5%, compared to models that do not consider waste heat temperature grades. Additionally, the results indicate that the developed model can provide more realistic configuration and technologies dispatch.

Risk-based method to secure power systems against cyber-physical faults with cascading impacts: a system protection scheme application

The utilization levels of the transmission network can be enhanced by the use of automated protection schemes that rapidly respond to disturbances. However, such corrective systems may suffer from malfunctions that have the potential to exacerbate the impact of the disturbance. This paper addresses the challenge of jointly optimizing the dispatch of generators and protection settings in this context. This requires a holistic assessment of the cyber (protection logic) and physical (network) systems, considering the failures in each part and their interplay. Special protection schemes are used as a prototypical example of such a system. An iterative optimization method is proposed that relies on power system response simulations in order to perform detailed impact assessments and compare candidate solutions. The candidate solutions are generated on the basis of a security-constrained dispatch that also secures the system against a set of cyber failure modes. A case study is developed for a generation rejection scheme on the IEEE reliability test system (RTS): candidate solutions are produced based on a mixed integer linear programming optimisation model, and loss-of-load costs are computed using a basic cascading outage algorithm. It is shown that the partial security approach is able to identify solutions that provide a good balance of operational costs and loss-of-load risks, both in a fixed dispatch and variable dispatch context.

Design and analysis of a combined desalination and standalone CCHP (combined cooling heating and power) system integrating solar energy based on a bi-level optimization model

Water and energy supply are strongly interrelated on islands without power grid infrastructure and their efficient management can be achieved by integrating seawater desalination and solar energy into combined cooling, heating, and power (CCHP) systems. In this study, a bi-level optimization methodology is proposed to optimize a combined desalination and standalone CCHP system, which is assumed as installed on a remote South China Sea island. The traversing method and branch-and-bound method are used for solving the mixed-integer linear programming (MILP) optimization problem at the design and operation stages, respectively. The results indicate that the economic and environmental objectives determine the system configuration with the minimum and maximum capacity of each component. As the system configuration changes, the system energy efficiency exhibits a consistent change tendency with the carbon dioxide emission generally. It is also observed that the capacity of the electrical storage system (ESS) is no larger than that of the thermal storage system (TSS) because of the relative high cost-performance ratio of the ESS. The integrated desalination with the water tank proves to be effective for improving the system performance.

Effect of transmission impairments in CO-OFDM based Elastic Optical Network design

Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) based Elastic Optical Network (EON) is one of the emerging technologies being considered for next generation high data rate optical network systems. Routing and Spectrum Allocation (RSA) is an important aspect of EON. Apart from spectral fragmentation created due to spectrum continuity and contiguity constraints of RSA, transmission impairments such as shot noise, amplified spontaneous emission (ASE), beat noise due to coherent detection, crosstalk in cross-connect (XC), nonlinear interference, and filter narrowing, limit the transmission reach of optical signals in EON. This paper focuses on the off-line joint optimization of delay-bandwidth product, fragmentation and link congestion for RSA in CO-OFDM EON while considering the effect of physical layer impairments. First, we formulate an optimal Mixed Integer Linear Programming (MILP) that achieves load-balancing in presence of transmission impairments and minimizes delay-bandwidth product along with fragmentation. We next propose a heuristic algorithm for large networks with two different demand ordering techniques. We show the benefits of our algorithm compared to the existing load-balancing algorithm.

Probabilistic Under Frequency Load Shedding Considering RoCoF Relays of Distributed Generators

The activation of under frequency load shedding (UFLS) is the last automated action against the severe frequency drops in order to rebalance the system. In this paper, the setting parameters of a multistage load shedding plan are obtained and optimized using a discretized model of dynamic system frequency response. The uncertainties of system parameters including inertia time constant, load damping, and generation deficiency are taken into account. The proposed UFLS model is formulated as a mixed-integer linear programming optimization problem to minimize the expected amount of load shedding. The activation of rate-of-change-of-frequency relays as the anti-islanding protection of distributed generators is considered. The Monte Carlo simulation method is utilized for modeling the uncertainties of system parameters. The results of probabilistic UFLS are then utilized to design four different UFLS strategies. The proposed dynamic UFLS plans are simulated over the IEEE 39-bus and the large-scale practical Iranian national grid.

Energy Systems Integration in Smart Districts: Robust Optimisation of Multi-Energy Flows in Integrated Electricity, Heat and Gas Networks

Smart districts can provide flexibility from emerging distributed multi-energy technologies, thus bringing benefits to the district and the wider energy system. However, due to nonlinearity and modeling complexity, constraints associated with the internal energy network (e.g., electricity, heat, and gas) and operational uncertainties (for example, in energy demand) are often overlooked. For this purpose, a robust operational optimization framework for smart districts with multi-energy devices and integrated energy networks is proposed. The framework is based on two-stage iterative modeling that involves mixed integer linear programming (MILP) and linear approximations of the nonlinear network equations. In the MILP optimization stage, the time-ahead set points of all controllable devices (e.g., electrical and thermal storage) are optimized considering uncertainty and a linear approximation of the integrated electricity, heat, and gas networks. The accuracy of the linear model is then improved at a second stage by using a detailed nonlinear integrated network model, and through iterations between the models in the two stages. To efficiently model uncertainty and improve computational efficiency, multi-dimensional linked lists are also used. The proposed approach is illustrated with a real U.K. district; the results demonstrate the model’s ability to capture network limits and uncertainty, which is critical to assess flexibility under stressed conditions.

Competition and cooperation for intermodal container transhipment: A network optimization approach

This study presents an analysis of cross-border competition and cooperation between ports in Bangladesh and India. Nepal and Bhutan are countries without access to seaports — two landlocked countries in South Asia, depending solely on the Indian port of Kolkata for their international seaborne trade. Alternatives do exist in the Bangladeshi ports of Chittagong and Mongla but these are not exploited, in spite of trade agreements that allow access to a third country's port, and/or crossing the land of a third, intermediate, country. We formulate a mixed integer linear programming optimization model to find the optimum economic benefit of port users (serving Bhutan, Nepal and Northeast India) and port authorities (Chittagong, Kolkata, Mongla), were Indian and Bangladeshi ports to cooperate in serving intermodal transhipment traffic. Our results show that port users would benefit greatly from such a cooperation, in terms of reduced transportation costs, although Kolkata Port Authority (KPA) would suffer a revenue loss for which it ought to be somehow compensated. Sensitivity analyses considering equal terminal handling charges (THC) for transhipment container at the three ports, as well as different capacity and demand volatilities are also carried out, to establish the robustness of any strategic decisions that might be made on the basis of our findings. Finally, we show that inland transportation costs determine container transhipment demand to distant hinterlands, rather than THC at ports.

Mixed Integer Linear Programming Optimization of Gas Supply to a Local Market.

Remote or stranded areas that cannot be supplied by natural gas through transmission pipelines can access gas through terminals for liquefied natural gas (LNG), from where LNG is distributed by trucks or compressed and regasified into regional distribution networks. The gas supply may be further augmented by local biogas or synthetic natural gas. A model for optimization of such regional gas supply chains is presented in the paper, considering a combination of pipeline and truck delivery to a set of customers with given energy demands. After linearization, the task is formulated as a mixed integer linear programming (MILP) problem and is solved by state-of-the-art software. The model is illustrated on a regional energy supply problem considering seasonal variations in the demands. The results of the study demonstrate the role of the price of the local and alternative fuels and the price margins at which it is feasible to build an extensive pipeline network instead of supplying the fuel by trucks to storages connected to pipeline islands. The findings also give information about the influence on investment versus operation costs on the optimal design of the supply chain. The sensitivity of the optimal supply chain on the price of local and alternative fuels as well as on the unit price of pipes and storage tanks is studied to illustrate how optimization can be used to shed light on the feasibility of investment in new infrastructure and to support the decision making processes in the energy sector.

Mixed-Integer Linear Programming-Based Splitting Strategies for Power System Islanding Operation Considering Network Connectivity

An efficient splitting strategy is important for the islanding operation of power systems. In this paper, a mixed-integer linear programming (MILP)-based splitting method is proposed. First, the graph theory is employed to transform the splitting problem into a graph partition problem. Then, the graph partition problem is modeled as an MILP optimization problem with consideration to the network connectivity of all subgraphs. The MILP-based splitting strategy can be efficiently computed with existing commercial solvers, and the multiple optimal solutions can be captured with the recursive process. Compared with the splitting methods in the literature, the proposed method is more flexible and efficient, such that the users can select the optimal solution from multiple solutions with different interests and heuristic splitting rules (e.g., with the minimum amount of switched lines). Finally, the effectiveness of the proposed method has been verified with IEEE 30-, 118-, and 300-bus test systems.

Robust optimisation‐based state estimation considering parameter errors for systems observed by phasor measurement units

This study presents a new robust state estimation (SE) approach for power systems that are monitored by synchronised phasor measurements. The proposed robust SE utilises the least absolute value (LAV) of residuals to determine the system state. Although conventional deterministic LAV-based SE is robust against bad measurements, it is vulnerable with respect to the network parameters’ errors. In other words, the conventional LAV-SE method is not robust against the network parameters’ errors and these errors can make the SE results inaccurate. The proposed robust SE aims at solving this problem of the conventional LAV-SE. Robust optimisation, strong duality theorem, and Big-M linearisation technique have been used to construct the proposed SE approach, which is robust against the network parameters’ errors. Additionally, the proposed robust SE is finally formulated as a tractable mixed-integer linear programming optimisation problem. Comprehensive numerical experiments and a probabilistic evaluation approach are presented to evaluate the effectiveness of the proposed robust SE compared to the conventional deterministic SE in the presence of the uncertainty source of network parameters’ errors.

GreenTouch GreenMeter Core Network Energy-Efficiency Improvement Measures and Optimization

In this paper, we discuss energy-efficiency improvements in core networks obtained as a result of work carried out by the GreenTouch consortium over a five-year period. A number of techniques that yield substantial energy savings in core networks were introduced, including (i) the use of improved network components with lower power consumption, (ii) putting idle components into sleep mode, (iii) optically bypassing intermediate routers, (iv) the use of mixed line rates, (v) placing resources for protection into a low power state when idle, (vi) optimization of the network physical topology, and (vii) the optimization of distributed clouds for content distribution and network equipment virtualization. These techniques are recommended as the main energy-efficiency improvement measures for 2020 core networks. A mixed integer linear programming optimization model combining all the aforementioned techniques was built to minimize energy consumption in the core network. We consider group 1 nations' traffic and place this traffic on a US continental network represented by the AT&T network topology. The projections of the 2020 equipment power consumption are based on two scenarios: a business as usual (BAU) scenario and a GreenTouch (GT) (i.e., BAU + GT) scenario. The results show that the 2020 BAU scenario improves the network energy efficiency by a factor of 4.23 x compared with the 2010 network as a result of the reduction in the network equipment power consumption. Considering the 2020 BAU + GT network, the network equipment improvements alone reduce network power by a factor of 20 x compared with the 2010 network. Including of all the BAU + GT energy-efficiency techniques yields a total energy efficiency improvement of 315×. We have also implemented an experimental demonstration that illustrates the feasibility of energy-efficient content distribution in IP/WDM networks.

Resilience‐based framework for switch placement problem in power distribution systems

Optimal placement of switches can play a key role in providing resilience to power distribution systems against major faults caused by natural disasters. This study presents a resilience-based framework for optimal switch placement in distribution systems being consistent with the expansion plans of distributed generation units. At first, the impact of hurricanes on distribution system components is modelled using the geographic information system of distribution grid and the strength of components against extreme weather-related events. Then, a new resiliency index is proposed to assess the resilience of distribution grids. This index is involved in a mathematical model of the switch placement problem and the obtained formulation is modelled as a mixed integer linear programming optimisation problem. The presented framework is implemented on two test systems, i.e. an illustrative test system and Bus 4 of the Roy Billinton test system. The results prove the effectiveness of this approach to improving the resiliency of distribution systems.

Mixed-integer linear programming method for multi-degree and multi-hoist cyclic scheduling with time windows

ABSTRACTMulti-degree cyclic hoist scheduling and multi-hoist cyclic scheduling are both capable of improving the throughput in an automatic electroplating line. However, previous research on integrated multi-degree and multi-hoist cyclic scheduling is rather limited. This article develops an optimal mixed-integer linear programming model for the integrated multi-degree and multi-hoist cyclic scheduling with time window constraints. This model permits overlap on hoist coverage ranges, and it proposes new formulations to avoid hoist collisions, by which time window constraints and tank capacity constraints are also formulated. A set of available benchmark instances and newly generated instances are solved using the CPLEX solver to test the performance of the proposed method. Computational results demonstrate that the proposed method outperforms the zone partition heuristic without overlapping, and the throughputs are improved by a significant margin using the proposed method, especially for large-size instances.