Integer Linear Programming Method Research Articles

Regional waste heat valorisation: A mixed integer linear programming method for energy service companies

A Mixed Integer Linear Programming method for the optimal valorisation of regional waste heat, formulated for energy service companies, is proposed in this work. The model provides a framework to simultaneously optimise the multi-period exchange of waste heat between regional thermal sources and sinks, as well as the selection of the backup heating technology. Given the pre-defined cost contributions of the involved sources, the sinks, the heat transport infrastructures and the heating technologies, the configuration is optimised by maximising the system profitability. The approach accounts for variations of temperature levels and heat loads across periods for the same sources and sinks, considers specific energy prices for multiple competing sinks and provides a predesign of the waste heat distribution network considering standard pipe sizes.The method is applied to the southern region of Luxembourg, composed of two steel production plants (heat sources), as well as three factories and nine towns (heat sinks). The impact of the waste heat buying price on the profits, revenues, valorised heat and electricity production quantities is assessed. For prices between 0 and 5 €/MWh, electricity production is a viable solution, while for prices between 0 and 25 €/MWh, the heat can be valorised in the urban systems.

Combining an Extended SMAA-2 Method with Integer Linear Programming for Task Assignment of Multi-UCAV under Multiple Uncertainties

Uncertainty should be taken into account when establishing multiobjective task assignment models for multiple unmanned combat aerial vehicles (UCAVs) due to errors in the target information acquired by sensors, implicit preferences of the commander for operational objectives, and partially known weights of sensors. In this paper, we extend the stochastic multicriteria acceptability analysis-2 (SMAA-2) method and combine it with integer linear programming to achieve multiobjective task assignment for multi-UCAV under multiple uncertainties. We first represent the uncertain target information as normal distribution interval numbers so that the values of criteria (operational objectives) concerned can be computed based on the weighted arithmetic averaging operator. Thus, we obtain multiple criteria value matrices for each UCAV. Then, we propose a novel aggregation method to generate the final criteria value matrix based on which the holistic acceptability indices are computed by the extended SMAA-2 method. On this basis, we convert the task assignment model with uncertain parameters into an integer linear programming model without uncertainty so as to implement task assignment using the integer linear programming method. Finally, we conduct a case study and demonstrate the feasibility of the proposed method in solving the multiobjective task assignment problem multi-UCAV under multiple uncertainties.

Impact of generation mix flexibility on the integration of variable renewable energies

Worldwide, renewable energies are witnessing a huge expansion especially for power generation driven by different factors including the increased demand on fossil fuels and the depletion of its resources, the increase in its cost and the need to preserve the environment. Variable Renewable Energies (VRE) especially depending on wind and solar resources are intermittent by nature and this intermittency can have severe impacts on the operation of the power systems. Power systems are thus required to have a sufficient degree of flexibility to deal with this intermittency especially in the generation side. This paper introduces a hybrid Flexibility Enhanced Priority List-Mixed Integer Linear Programming (FEPL-MILP) method to solve the Unit Commitment (UC) problem and study the impact of the generation mix flexibility on the integration of renewable energies. Results show that, increasing the flexibility of the thermal energy mix used for power generation will have positive technical and economic impacts on the integration of renewable energies into the power system.Keywords: Intermittency, Generation Mix, Flexibility, Unit Commitment

Limits and potentials of Mixed Integer Linear Programming methods for optimization of polygeneration energy systems

The simultaneous production of different energy vectors from hybrid polygeneration plants is a promising way to increase energy efficiency and facilitate the development of distributed energy systems. The inherent complexity of polygeneration energy systems makes their economic, environmental and energy performance highly dependent on system synthesis, equipment selection and capacity, and operational strategy. Mixed Integer Linear Programming (MILP) is the state of the art approach to tackle the optimization problem of polygeneration systems. The guarantee of finding global optimality in linear problems and the effectiveness of available commercial solvers make MILP very attractive and widely used in optimization problems of polygeneration systems. Nevertheless, several drawbacks affect the MILP formulation, such as: the impossibility of taking into account nonlinear effects; the necessity of considering all the time periods at once; the risk of high-dimensionality of the problem. To tackle these limitations, several techniques have been developed, such as: piecewise linearization methods; rolling horizon approaches; dimensionality reduction by means of energy demands clustering algorithms. In this paper, limits and potentials of MILP methods for the optimization problem of polygeneration energy systems are reviewed and discussed.

A superstructure optimization approach for process synthesis under complex reaction networks

In this work, we present mixed integer linear programming methods for the synthesis of processes that involve complex reaction networks. Specifically, we consider the modeling of reactors and interconnecting streams in systems where the composition of the reactor inlet streams can vary substantially, thereby making the determination of the limiting component as well as the calculation of the stream heating/cooling and power requirements challenging. First, towards the modeling of reactors, we develop an extent-based method which detects the limiting reactant of each reaction occurring in parallel with others, based on the inlet flows of the reactants. Second, we develop a computationally tractable method for the calculation of the work and heating/cooling duty needed to condition any stream of a process based on simple calculations that can be performed offline. Finally, we present how the two aforementioned components can be integrated in an optimization model generated based on a process superstructure. We demonstrate the application of the developed methods for the synthesis of a biorefinery.

0–1 linear integer programming method for granule knowledge reduction and attribute reduction in concept lattices

Knowledge reduction is one of the key issues in formal concept analysis, and there have been many studies on this topic. Granule knowledge reduction and attribute reduction are two of the most important knowledge reduction in formal concept analysis. Firstly, theorem to character granule knowledge reduction is given, and granule knowledge reduction method in concept lattices based on 0–1 linear integer programming is proposed in this paper. Then, characterization theorems of three types attributes are obtained in attribute reduction, and attribute reduction method in concept lattices based on 0–1 linear integer programming is proposed.

An inexact two-stage fractional energy systems planning model

In this study, an inexact two-stage fractional energy systems planning model (ITF-ESP) is developed through an integration of interval-parameter programming (IPP), two-stage stochastic programming (TSP), fractional programming (FP), and mixed integer linear programming (MILP) methods. Since the proposed model could not be solved directly, it is converted into two interactive sub-models. In order to obtain more precise interval solutions, the sub-model corresponding to f−is solved first. The developed ITF-ESP model is considered as an efficient approach to address dual-objective optimization problems involving capacity expansion issues and policy scenario analysis, as well as uncertainties described as intervals and probability distributions. Effectiveness of the ITF-ESP model is demonstrated through a case study within a Chinese context. The results indicate that although the non-renewable technologies would still play a major role in electricity generation, the renewable technologies are becoming increasingly significant. Comparisons of the ITF-ESP model and the least-cost model are conducted to illustrate the advantages of the proposed ITF-ESP model in reflecting trade-offs between economic development and environmental protection. In addition, compared with the chance-constrained two-stage fractional optimization model (CTFO), interval solutions obtained from the ITF-ESP model can provide multiple alternative management plans in terms of electricity generation and capacity expansion.

Energy-Efficient Scheduling of Periodic Applications on Safety-Critical Time-Triggered Multiprocessor Systems

Energy optimization for periodic applications running on safety/time-critical time-triggered multiprocessor systems has been studied recently. An interesting feature of the applications on the systems is that some tasks are strictly periodic while others are non-strictly periodic, i.e., the start time interval between any two successive instances of the same task is not fixed as long as task deadlines can be met. Energy-efficient scheduling of such applications on the systems has, however, been rarely investigated. In this paper, we focus on the problem of static scheduling multiple periodic applications consisting of both strictly and non-strictly periodic tasks on safety/time-critical time-triggered multiprocessor systems for energy minimization. The challenge of the problem is that both strictly and non-strictly periodic tasks must be intelligently addressed in scheduling to optimize energy consumption. We introduce a new practical task model to characterize the unique feature of specific tasks, and formulate the energy-efficient scheduling problem based on the model. Then, an improved Mixed Integer Linear Programming (MILP) method is proposed to obtain the optimal scheduling solution by considering strict and non-strict periodicity of the specific tasks. To decrease the high complexity of MILP, we also develop a heuristic algorithm to efficiently find a high-quality solution in reasonable time. Extensive evaluation results demonstrate the proposed MILP and heuristic methods can on average achieve about 14.21% and 13.76% energy-savings respectively compared with existing work.

Retracted Article: Performance benefits of regeneration flexibility and modulation convertibility in elastic optical networks

In planning of the elastic optical networks (EONs), the traditional approach of regeneration node(s) number minimization and the assumption of same modulation format over every segment of lightpath results in the (i) utilization of modulation formats which are less spectrally-efficient, and (ii) unneeded resource(s) loss over shorter route segments which may use modulation formats that are more spectrally-efficient. In this work, we investigate the performance benefits that can be obtained by the introduction of intentional signal regeneration, modulation and spectrum conversion in non-transparent (i.e., translucent) EONs which are based on super-channel transmission. We examine and compare three different cases that may be used to provision the lightpaths which are translucent viz., a basic case of regenerator(s) minimization, and two cases which provision flexible signal regeneration and modulation conversion. For the aforementioned, we develop the routing and spectrum allocation with transceiver and regeneration allocation (RSAwTCRA) problem which, apart from the traditional RSA constraints, also accounts for the (i) regeneration site(s) selection, (ii) modulation format(s) adaptation, and (iii) transceiver(s) assignment to the lightpaths. We develop (i) an integer linear programming method to formulate the RSAwTCRA optimization problem and, (ii) a heuristic (scalable) algorithm to generate the RSAwTCRA solutions. Our simulation results demonstrate that with deliberate signal regeneration and optical carriers’ modulation format(s) adaptation, gains in both, the spectrum and transceiver(s) utilization are achievable for the networks with long distances; however, the savings are negligible for the network with small distances.

Routing, Spectrum, and Core Assignment in SDM-EONs With MCF: Node-Arc ILP/MILP Methods and an Efficient XT-Aware Heuristic Algorithm

In this paper, we focus on the static routing, spectrum, and core assignment (RSCA) problem in spacedivision multiplexing (SDM)-based elastic optical networks (EONs) with multi-core fiber (MCF). In RSCA problems, it is a challenging task to control the inter-core interference, called inter-core crosstalk (XT), within an acceptable level and simultaneously maximize the spectrum utilization. We first consider XT in a worst interference scenario (i.e., XTunaware), which can simplify the RSCA problem. In this scenario, we formulate the RSCA problem using a nodearc- based integer linear programming (ILP) method in which the numbers of both variables and constraints are greatly reduced compared with previous ILP methods, thereby leading to a significant improvement in convergence efficiency. Then, we consider the XT strictly (i.e., XT-aware) and formulate the problem using a mixed integer linear programming (MILP) method, which is an extension of the above node-arc-based ILP method. It is more suitable for different XT thresholds and/or geographically large networks, in that it has a higher degree of generalizability. Finally, we propose an XT-aware-based heuristic algorithm. The simulation results demonstrate that our heuristic algorithm achieves higher spectrum efficiency, higher degree of generalizability, and higher computational efficiency than the existing heuristic algorithm(s).

Mixed integer linear programming and heuristic methods for feature selection in clustering

This paper studies the problem of selecting relevant features in clustering problems, out of a data-set in which many features are useless, or masking. The data-set comprises a set U of units, a set V of features, a set R of (tentative) cluster centres and distances for every , , . The feature selection problem consists of finding a subset of features such that the total sum of the distances from the units to the closest centre is minimised. This is a combinatorial optimisation problem that we show to be NP-complete, and we propose two mixed integer linear programming formulations to calculate the solution. Some computational experiments show that if clusters are well separated and the relevant features are easy to detect, then both formulations can solve problems with many integer variables. Conversely, if clusters overlap and relevant features are ambiguous, then even small problems are unsolved. To overcome this difficulty, we propose two heuristic methods to find that, most of the time, one of them, called q-vars, calculates the optimal solution quickly. Then, the q-vars heuristic is combined with the k-means algorithm to cluster some simulated data. We conclude that this approach outperforms other methods for clustering with variable selection that were proposed in the literature.

Mathematical model of parking space unit for triangular parking area

Parking space unit (PSU) is an effective measure for the area size of a vehicle, including the free space and the width of the door opening of the vehicle (car). This article discusses a mathematical model for parking space of vehicles in triangular shape area. An optimization model for triangular parking lot is developed. Integer Linear Programming (ILP) method is used to determine the maximum number of the PSU. The triangular parking lot is in isosceles and equilateral triangles shape and implements four possible rows and five possible angles for each field. The vehicles which are considered are cars and motorcycles. The results show that the isosceles triangular parking area has 218 units of optimal PSU, which are 84 units of PSU for cars and 134 units of PSU for motorcycles. Equilateral triangular parking area has 688 units of optimal PSU, which are 175 units of PSU for cars and 513 units of PSU for motorcycles.

Optimization flow model for handling car flows at the marshalling yard

Mathematical modeling is widely used in studies of operational planning in railway transport. Mainly heuristic algorithms and simulation modeling is used in short-term planning at marshalling yards. There is an opportunity to improve the quality of planning using strict optimization models. The objective of the study was to find a way to optimize the multi-terminal transport flows of the complex structure by the example of operational planning for handling car flows at the marshalling yard. The process model was built on the basis of Mixed Integer Linear Program (MILP) method. The article provides the mathematical setting and describes results of calculations of the reference example. The LpSolve application package was used. The technological effect is estimated through checking the optimal solution on the simulation model.

Optimal design of a coproduction system of electricity and hydrogen to manage imbalances resulting from forecast errors in photovoltaic outputs

Renewable power sources are increasing mainly because of economic institutions such as renewable portfolio standard or feed-in tariff program. In Japan, the feed-in tariff program triggered explosive growth of photovoltaic systems because of its high tariff level. Although mass introduction of photovoltaic systems certainly contributes to reduce CO2 emissions, it causes instability issues in power systems. One of the most serious issues is management of imbalances resulting from forecast errors in photovoltaic outputs. On the other hand, power-to-gas technologies are attracting our attention, since these technologies could convert surplus of renewable energy to other energy carriers. In particular, hydrogen is efficiently produced from electricity using electrolysis. We could use hydrogen to manage the imbalances by the system, in which uncertain parts of photovoltaic outputs are used to produce hydrogen. In this paper, we propose a coproduction system of electricity and hydrogen to reduce the imbalances. For this purpose, a novel mathematical model is developed, in which we determine the structure of the coproduction system with a mixed integer linear programming method. Evaluated results indicated that the coproduction system is economical under appropriate capacity of the electrolyzer.

A linear programming computational framework integrates phosphor-proteomics and prior knowledge to predict drug efficacy

BackgroundIn recent years, the integration of ‘omics’ technologies, high performance computation, and mathematical modeling of biological processes marks that the systems biology has started to fundamentally impact the way of approaching drug discovery. The LINCS public data warehouse provides detailed information about cell responses with various genetic and environmental stressors. It can be greatly helpful in developing new drugs and therapeutics, as well as improving the situations of lacking effective drugs, drug resistance and relapse in cancer therapies, etc.ResultsIn this study, we developed a Ternary status based Integer Linear Programming (TILP) method to infer cell-specific signaling pathway network and predict compounds’ treatment efficacy. The novelty of our study is that phosphor-proteomic data and prior knowledge are combined for modeling and optimizing the signaling network. To test the power of our approach, a generic pathway network was constructed for a human breast cancer cell line MCF7; and the TILP model was used to infer MCF7-specific pathways with a set of phosphor-proteomic data collected from ten representative small molecule chemical compounds (most of them were studied in breast cancer treatment). Cross-validation indicated that the MCF7-specific pathway network inferred by TILP were reliable predicting a compound’s efficacy. Finally, we applied TILP to re-optimize the inferred cell-specific pathways and predict the outcomes of five small compounds (carmustine, doxorubicin, GW-8510, daunorubicin, and verapamil), which were rarely used in clinic for breast cancer. In the simulation, the proposed approach facilitates us to identify a compound’s treatment efficacy qualitatively and quantitatively, and the cross validation analysis indicated good accuracy in predicting effects of five compounds.ConclusionsIn summary, the TILP model is useful for discovering new drugs for clinic use, and also elucidating the potential mechanisms of a compound to targets.

Penjadwalan Untuk Memininimalkan Total Tardiness Dengan Metode Integer Linear Programming

Production scheduling is an important thing done in the company so that consumer demand is met on time. PT Mitra Mulia Makmur implements the scheduling principle of First Come First Serve in producing plastic container products. The scheduling applied is not yet effective and efficient because there are some late consumer demands. The delay in consumer demand is due to longer processing time than the specified time limit. In the study using Integer Linear Programming (ILP) method to minimize total tardiness (total tardiness). ILP was chosen as a method of solving delay problems. ILP can help the company’s decision-making process to achieve a purpose function by considering the constraints or constraints in the company. Linear Integer Programming method with the help of LINGO 16.0 software can produce improvements.

Application of a Double-Sided Chance-Constrained Integer Linear Program for Optimization of the Incremental Value of Ecosystem Services in Jilin Province, China

The Interconnected River System Network Project (IRSNP) is a significant water supply engineering project, which is capable of effectively utilizing flood resources to generate ecological value, by connecting 198 lakes and ponds in western Jilin, northeast China. In this article, an optimization research approach has been proposed to maximize the incremental value of IRSNP ecosystem services. A double-sided chance-constrained integer linear program (DCCILP) method has been proposed to support the optimization, which can deal with uncertainties presented as integers or random parameters that appear on both sides of the decision variable at the same time. The optimal scheme indicates that after rational optimization, the total incremental value of ecosystem services from the interconnected river system network project increased 22.25%, providing an increase in benefits of 3.26 × 109 ¥ compared to the original scheme. Most of the functional area is swamp wetland, which provides the greatest ecological benefits. Adjustment services increased obviously, implying that the optimization scheme prioritizes ecological benefits rather than supply and production services.

Performance benefits of regeneration flexibility and modulation convertibility in elastic optical networks

In planning of the elastic optical networks (EONs), the traditional approach of regeneration node(s) number minimization and the assumption of same modulation format over every segment of lightpath results in the (i) utilization of modulation formats which are less spectrally-efficient, and (ii) unneeded resource(s) loss over shorter route segments which may use modulation formats that are more spectrally-efficient. In this work, we investigate the performance benefits that can be obtained by the introduction of intentional signal regeneration, modulation and spectrum conversion in non-transparent (i.e., translucent) EONs which are based on super-channel transmission. We examine and compare three different cases that may be used to provision the lightpaths which are translucent viz., a basic case of regenerator(s) minimization, and two cases which provision flexible signal regeneration and modulation conversion. For the aforementioned, we develop the routing and spectrum allocation with transceiver and regeneration allocation (RSAwTCRA) problem which, apart from the traditional RSA constraints, also accounts for the (i) regeneration site(s) selection, (ii) modulation format(s) adaptation, and (iii) transceiver(s) assignment to the lightpaths. We develop (i) an integer linear programming method to formulate the RSAwTCRA optimization problem and, (ii) a heuristic (scalable) algorithm to generate the RSAwTCRA solutions. Our simulation results demonstrate that with deliberate signal regeneration and optical carriers’ modulation format(s) adaptation, gains in both, the spectrum and transceiver(s) utilization are achievable for the networks with long distances; however, the savings are negligible for the network with small distances.

Techno-economic optimization of hybrid photovoltaic/wind generation together with energy storage system in a stand-alone micro-grid subjected to demand response

Regarding the importance of supplying energy to regions that are far from power systems, this study is devoted to analyzing and modeling of a stand-alone micro-grid. In spite of many studies in the case of demand response programming for optimal management and operation cost reduction of the micro-grids, and regarding the importance of size optimization of micro-grids, this paper seeks to examine and investigate the ability of demand response programming in the case of component size optimization of a micro-grid. Due to deficiency or unavailability of dispatchable energy recourses, only the nondispatchable renewable energy resources (wind and solar energy) are considered to supply the required energy. Applied strategy for effective component size optimization as well as relevant costs reduction is implemented by reducing or eliminating the mismatch between the generation and consumption profiles by time shift and schedule of dispatchable loads. Furthermore, the effect of demand response utilization on loss of generated energy reduction is studied. The optimized results with and without demand response are extracted and compared to each other.For each case, the optimum configuration was determined. Obtained results indicated that application of the demand response program, reduced the number of required batteries, the required inverter and photovoltaic cells capacity, and, consequently, the total net present costs. Furthermore, demand response implementation reduced the peak of consumed loads and increased the consumed load factor and correlation factor. The micro-grid components have been modeled mathematically within the framework of the mixed integer linear programming method. The optimization program has been performed by HOMER software together with GAMS software via the CPLEX solver.

A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy

Abstract Under the background of a low carbon economy, this paper examines the impact of carbon tax policy on supply chain network emission reduction. The integer linear programming method is used to establish a supply chain network emission reduction such a model considers the cost of CO2 emissions, and analyses the impact of different carbon price on cost and carbon emissions in supply chains. The results show that the implementation of a carbon tax policy can reduce CO2 emissions in building supply chain, but the increase in carbon price does not produce a reduction effect, and may bring financial burden to the enterprise. This paper presents a reasonable carbon price range and provides decision makers with strategies towards realizing a low carbon building supply chain in an economical manner.