Linear Programming Scheme Research Articles

Integral techno-economic design & operational optimization for district heating networks with a Mixed Integer Linear Programming strategy

The Netherlands, with over 90% of homes heated by natural gas is currently in the early phases of the heat transition to find alternative solutions towards 2050. According to ambitions of the Dutch government up to 50% of future implemented heating systems in the built environment will use District Heat Networks. The investment-heavy nature for District Heating System (DHS) makes it challenging to establish viable business-cases as supply-side parties require security of demand. However, resident participation is lacking as there is no integral estimate for the cost of heat over the lifetime in the early planning phase. This paper proposes a network integral techno-economic optimization with minimal a-priori assumptions. An integral network cost optimization enables to achieve a considerably more reliable cost of heat in the early planning phase. Both the investments and operational strategy are optimized with a Mixed Integer Linear Programming approach that captures the physics as well as the financial choices. Linearization of the physics are chosen to have a conservative impact on the costs estimates. The end scenario network is designed where the placement and size of sources, storage components and pipes are optimized together with the operational strategy, e.g. thermal allocation time-series, for all assets. The workflow was applied to a greenfield network for the Dutch municipality of Rijswijk. It was shown that a 18% reduction in Total Cost of Ownership in the primary grid could be achieved by introducing decentralized sources, decentralized storages and seasonal storage.

Memory event-triggered scheme of positive systems: A dynamic weighted method

A novel memory event-triggered scheme for positive systems is proposed in this paper. To address the conservatism of the existing memory event-triggered scheme, the weight parameter on the left side of the memory event-triggered scheme is replaced with a dynamic function. This modification results in a dynamic weighted memory event-triggered scheme that can be applied in both continuous-time and discrete-time contexts. By adjusting the weight dynamically based on the system operation, the scheme can respond more effectively to changes in the system state. Compared to the memory event-triggered scheme, a more flexible balance is achieved between improving system performance and saving system resources. A joint design that combines the dynamic weighted memory event-triggered scheme and positive systems is presented for continuous linear systems, with the controller gain obtained by a linear programming strategy. The proposed co-design scheme is subsequently extended to discrete positive systems. To demonstrate the effectiveness of the proposed method, two practical applications are presented.

AoI Minimization Scheme for Short-Packet Communications in Energy-Constrained IIoT

This paper is motivated by the requirement of high information freshness in the industrial Internet of Things (IIoT). An industrial robot sends short status packets to a control center (CC), and the timeliness of status updates is measured by the age of information (AoI). Due to the dynamic change of the wireless channel, the robot needs to send a pilot for channel estimation during each coherence time. Considering the robot is energy-limited, we investigate the average AoI minimization scheme for short packet communications under the average power consumption constraint. By rationally analyzing state transitions, we first formulate the problem as a constrained Markov Decision Process, and obtain the optimal solution through linear programming (LP). Then, for the problem of high computational complexity caused by too many variables in LP, we propose a heuristic threshold-based status update scheme by exploiting the threshold structure of the optimal solution. Simulation results show that the LP scheme can effectively minimize the average AoI and the threshold-based scheme can achieve near-optimal performance. Interestingly, we find that when the channel suffers from severe fading, at the end of a coherence time, the robot does not send status packets even if the information at the CC is particularly stale.

Probabilistic Control of Heterogeneous Swarms Subject to Graph Temporal Logic Specifications: A Decentralized and Scalable Approach

We develop a probabilistic control algorithm, GTLProCo, for swarms of agents with heterogeneous dynamics and objectives, subject to high-level task specifications. The resulting algorithm not only achieves decentralized control of the swarm but also significantly improves scalability over state-of-the-art existing algorithms. Specifically, we study a setting in which the agents move along the nodes of a graph, and the high-level task specifications for the swarm are expressed in a recently-proposed language called graph temporal logic (GTL). By constraining the distribution of the swarm over the nodes of the graph, GTL can specify a wide range of properties, including safety, progress, and response. GTLProCo, with a computational complexity agnostic to the number of agents comprising the swarm, controls the density distribution of the swarm in a decentralized and probabilistic manner. To this end, it synthesizes a time-varying Markov chain modeling the time evolution of the density distribution under the GTL constraints. We first identify a subset of GTL, namely reach-avoid specifications, for which we can reduce the synthesis of such a Markov chain to either linear or semi-definite programs. Then, in the general case, we formulate the synthesis of the Markov chain as a mixed-integer nonlinear program (MINLP).We exploit the structure of the problem to provide an efficient sequential mixed-integer linear programming scheme with trust regions to solve the MINLP. We empirically demonstrate that our sequential scheme is at least three orders of magnitude faster than off-the-shelf MINLP solvers and illustrate the effectiveness of GTLProCo in several swarm scenarios.

Task-guided IRL in POMDPs that scales

In inverse reinforcement learning (IRL), a learning agent infers a reward function encoding the underlying task using demonstrations from experts. However, many existing IRL techniques make the often unrealistic assumption that the agent has access to full information about the environment. We remove this assumption by developing an algorithm for IRL in partially observable Markov decision processes (POMDPs). We address two limitations of existing IRL techniques. First, they require an excessive amount of data due to the information asymmetry between the expert and the learner. Second, most of these IRL techniques require solving the computationally intractable forward problem—computing an optimal policy given a reward function—in POMDPs. The developed algorithm reduces the information asymmetry while increasing the data efficiency by incorporating task specifications expressed in temporal logic into IRL. Such specifications may be interpreted as side information available to the learner a priori in addition to the demonstrations. Further, the algorithm avoids a common source of algorithmic complexity by building on causal entropy as the measure of the likelihood of the demonstrations as opposed to entropy. Nevertheless, the resulting problem is nonconvex due to the so-called forward problem. We solve the intrinsic nonconvexity of the forward problem in a scalable manner through a sequential linear programming scheme that guarantees to converge to a locally optimal policy. In a series of examples, including experiments in a high-fidelity Unity simulator, we demonstrate that even with a limited amount of data and POMDPs with tens of thousands of states, our algorithm learns reward functions and policies that satisfy the task while inducing similar behavior to the expert by leveraging the provided side information.

Mathematical Method to Construct Linear Programming Scheme of Football Training

Abstract Linear programming is a widely applicable mathematical operation method. In this paper, two solutions of linear programming and state parameter extraction can be used to simplify the inequality group and transfer the high-dimensional state utility function in football. This can speed up the generation of joint strategies for football teams in the game. This paper uses the free-kick technical football cooperation as an example to conduct an empirical study on the linear programming method of state parameters. In this paper, combined with the traditional motion information modeling method, a free ball path planning based on the linear programming gradient method is established. At the same time, this paper adopts an asymptotic method based on linear programming to solve the trajectory of any football. Finally, an experimental study on the linear programming gradient method for state feature vectorization is carried out. Experiments verify the effectiveness of this method. The mathematical model accurately predicts the linear programming of football training.

Optimal Annual Operational Cost of a Hybrid Renewable-Based Microgrid to Increase the Power Resilience of a Critical Facility

With the rapid increment of power outages related to extreme natural disasters such as wildfires and severe storms, microgrids have the potential to enhance resilience locally. Traditionally, grid-connected microgrids are investigated from an economic perspective only, without focusing on resilience solutions benefits during grid interruptions. Hence, the presented work proposes a technical and economic evaluation of an airport grid-connected microgrid consisting of solar photovoltaic (PV), energy storage system, and diesel generator to enhance airport power resilience under different power interruption scenarios. A modified mixed-integer linear programming scheme was introduced to minimize the total annual operating cost of the proposed resilient system. The optimal resilient microgrid components sizing and dispatching were investigated with and without a monetary assigned value for resilience as a service. Moreover, the microgrid survivability during solar performance change was investigated. The possible load increment from electric ground support equipment deployment was considered. The results show that the proposed microgrid can achieve an annual operational cost reduction while ensuring a continuous power supply for all considered outage scenarios. The operational cost saving varies between 20% and 22%. The duration of the outage and critical load level have a higher impact on microgrid sizing and dispatching.

Individualizable Vehicle Lane Keeping Assistance System Design: A Linear-Programming-Based Model Predictive Control Approach

Model predictive control (MPC), a control technique that can systematically and explicitly cope with system constraints, has become increasingly prevalent in the field of automotive engineering. Respecting the advanced driver-assistance systems (ADAS) design, the MPC has found its applications in various kinds of ground vehicular lane-keeping assistance systems (LKAS). In this paper, an MPC-based LKAS is synthesized by leveraging the linear programming (LP) methodology. Compared to the conventional MPC-based LKAS that is based on quadratic programming (QP), the LP alternative is less computationally demanding, which is desired for commercial vehicular electronic control units. Besides, the LP scheme enables the designer to formulate the MPC's performance criterion in the sense of L1/L∞ norms, which differs from the QP's L2-norm-based measure. The proposed LP-based MPC-LKAS is examined in CarSim-Simulink joint simulations and its performance is compared with a QP-based solution.

Improvement in Co-Operative Spectrum Sensing Using ILP and GA in Cognitive Radio Network

Wireless technologies have grown at a speed and with the passing year, it shows clearly that their consumers are also increasing, that increment in wireless spectrum consumer increases the demand for spectrum. But for our wireless systems, the spectrum is divided into two categories: the first is licensed and the second is unlicensed. Licensed spectrum is used by authorized users and unlicensed spectrum is free for all users. But most of the time it is shown the hat licensed spectrum may not be properly utilized by primary users (PUs), at that time spectrum band is free. To mitigate that inappropriate use of spectrum cognitive radio (CR) network is used. In CR there is one challenge that among the CR node some nodes experience an impact of multipath and shadowing, and another is to sense the spectrum under a lower signal to noise ratio. To overcome the effect of multipath and shadowing co-operative spectrum sensing has been used but it has large energy utilization. This extra energy is consumed in sensing the spectrum and reporting each nodes local decision to Fusion Centre (FC). In this paper we discuss three different schemes for total sensing time and energy decrement or throughput improvement. Here we go after for the genetic algorithm and integer linear programming scheme for overall energy minimization and throughput maximization.

Performances of energy management strategies for a Photovoltaic/Battery microgrid considering battery degradation

Several energy management strategies, of increasing complexity, are compared in term of cost benefit for a Photovoltaic /battery system providing electricity to an accommodation building with an electric vehicle. Rule based control methods with or without production forecasting are implemented and compared to a linear programming strategy used as a reference. The improvement in term of gain between simplest and reference methods is about 27%. It appears that the battery cycles number differs greatly (up to 55%), leading to a more or less rapid ageing. Battery degradation models are thus added and a corresponding cost is introduced in the strategy benefit. The results, depending on the initial battery cost, are significantly impacted, changing the relevance of the control strategies.

Renewable Energy Communities business models under the 2020 Italian regulation

Recently in Italy several regulation actions have been setup defining the Renewable Energy Communities implementation. Beyond the regulatory aspects of the legislation, the definition of economic incentives has open the possibility for the evaluation of the business models of the Renewable Energy Community initiative. The present work is focused on a methodology aimed at the sizing of the active part of an energy community: a solar photovoltaic system with electrochemical energy storage. It develops a multicriteria optimisation procedure by evaluating two independent and normalised key performance indices: self consumption and self sufficiency of the energy community. These two KPIs are evaluated on a hourly based energy balance by minimising the power flow to/from the electrical grid through a Mixed Integer Linear Programming scheme. Results obtained by changing the PV and the energy storage sizes are mapped in a Pareto plane and their distance from “utopia point” are evaluated. Economic indicators are then used to pick up the most performing configuration. Three different options of business model are considered on the optimal point: one where the Renewable Energy Community is taking on itself all the capital expenditure for photovoltaic and battery, a second one where an independent company is acting as a “technological partner” acquiring and managing the assets, sharing with the community the revenues and one intermediate case where costs and revenues are shared between community and developer. The procedure is applied to a real test case of an energy community located in the north-western region of Italy. Results show both positive economic and environmental performances, where the internal rate of return is greater than 11% and CO2 emission reduction is close to 45% for all the configurations, making attractive the exploitation of REC in the Italian context.

Covering problems with polyellipsoids: A location analysis perspective

In this paper we analyze the extension of the classical smallest enclosing disk problem to the case of the location of a polyellipsoid to fully cover a set of demand points in Rd. We prove that the problem is polynomially solvable in fixed dimension and analyze mathematical programming formulations for it. We also consider some geometric approaches for the problem in case the foci of the polyellipsoids are known. Extensions of the classical algorithm by Elzinga-Hearn are also derived for this new problem. Moreover, we address two extensions of the problem, as the case where the foci of the enclosing polyellipsoid are not given and have to be determined among a potential set of points or the induced covering problems when instead of polyellipsoids, one uses ordered median polyellipsoids. For these problems we also present Mixed Integer (Non) Linear Programming strategies that lead to efficient ways to solve it. Extensive computational experiments on different datasets show the usefulness of our solution methods.

Optimal Design of a Sustainable Hydrogen Supply Chain Network: Application in an Airport Ecosystem

Hydrogen and fuel cell technologies are one solution foraddressing the challenges that major airports are facing today, such asupward price trends of liquid hydrocarbon fuels, greenhouse gasemission regulations, and stricter noise and air pollutant emissionregulations, especially for on-ground pollution. An airport can also beviewed as the center of a hydrogen ecosystem, around which multiplehydrogen users could be clustered, with cost sharing of hydrogenproduction and storage occurring among users. The main novelty of thepresent work is the design of a hydrogen infrastructure irrigated by theairport ecosystem that satisfies the airport ecosystem energy needs. Forthis purpose, the model development is based on a multiobjectiveoptimization framework designed to consider four echelons: energysources, hydrogen production, transportation, and storage. Themultiperiod problem is then solved using thee-constraint method.Two objective functions are involved, that is, the total daily cost (TDC) of the network and an environmental indicator basedon the global warming potential. The second innovative contribution is to model the demand uncertainty using fuzzy conceptsfor a hydrogen supply chain design. Because hydrogen demand is one the most significant parameters, the uncertainty of thedemand has been considered using a proposed fuzzy linear programming strategy. The solutions are compared with the originalcrisp model, giving more robustness to the proposed approach. This work has been performed in the framework of the Hyportmeta-project and, in particular, within the“H2modeling”project. This paper focuses on a hydrogen airport ecosystem located inthe department of Hautes-Pyrenees (France). However, the developed methodology could be extended to other hydrogenecosystems for which deployment involves a multiperiod multi-objective formulation under an uncertain demand

A Pipeline Approach to Free‐Description Question Answering in Chinese Gaokao Reading Comprehension

This study attempted to answer complicated free-description questions in Chinese Gaokao Reading comprehension (RC) tasks. We found that quite a few questions can be answered by extracting sentences from the document and combining them, so we used a pipeline approach with two components: Answer sentence extraction (ASE) and Answer sentence fusion (ASF). Semantic vector similarity and topical distribution similarity were explored for ASE. Integer linear programming strategy was used for ASF, which combined dependencies with the language model, based on word importance. As a first step towards the new challenge, we obtained some encouraging results on actual exam questions in Chinese subject's RC tasks of Beijing Gaokao, which helped us obtain insights into techniques needed to solve real-word complex questions.

Low-Complexity Approximate Convolutional Neural Networks.

In this paper, we present an approach for minimizing the computational complexity of the trained convolutional neural networks (ConvNets). The idea is to approximate all elements of a given ConvNet and replace the original convolutional filters and parameters (pooling and bias coefficients; and activation function) with an efficient approximations capable of extreme reductions in computational complexity. Low-complexity convolution filters are obtained through a binary (zero and one) linear programming scheme based on the Frobenius norm over sets of dyadic rationals. The resulting matrices allow for multiplication-free computations requiring only addition and bit-shifting operations. Such low-complexity structures pave the way for low power, efficient hardware designs. We applied our approach on three use cases of different complexities: 1) a "light" but efficient ConvNet for face detection (with around 1000 parameters); 2) another one for hand-written digit classification (with more than 180 000 parameters); and 3) a significantly larger ConvNet: AlexNet with million matrices. We evaluated the overall performance on the respective tasks for different levels of approximations. In all considered applications, very low-complexity approximations have been derived maintaining an almost equal classification performance.

Whole-Body Kinematic Control of Nonholonomic Mobile Manipulators Using Linear Programming

This paper presents some improvements to the robot kinematic control strategy based on linear programming, as well as its application to a nonholonomic mobile manipulator. In addition to being computationally efficient, this approach enables the inclusion of inequality and equality constraints in the system control inputs and has formal guarantee of stability. We first propose a new positive definite function of the error variation to avoid joint movements when the robot end-effector stabilizes at a point different from the desired one. In addition, the nonholonomic constraint of the mobile base is imposed as an equality constraint, and inequality constraints are defined to avoid both violation of joint limits and collisions between the mobile base and obstacles in the plane. Last, a performance comparison between the linear programming strategy and an approach based on the pseudoinverse of the whole-body Jacobian matrix is presented. Experimental results show that the controller based on linear programming has low computational cost, and the robot is able to control its end-effector without colliding with obstacles in the plane and without violating its joints limits. However, it tends to generate more abrupt control signals than the continuous controller based on the pseudoinverse of the whole-body Jacobian matrix.

High-accuracy variable-phase filter design utilising iterative linear-programming strategy

ABSTRACTThis paper proposes an iterative strategy employing the linear programming (LP) method for the design of an all-pass variable-phase (AP-VP) digital filter in the minimax error sense. Mathematically, designing an AP-VP digital filter belongs to a non-linear optimisation problem. The novel LP design method first reduces this non-linear minimisation problem to a linear minimisation problem and then solves the linearised optimisation problem iteratively via using the LP method. The iterative LP-solving scheme is able to reduce the largest design errors significantly and thus can get a considerable accuracy improvement as compared to the noniterative one. We will utilise three design examples to show that this iterative scheme can get much better design results (much smaller maximum errors) than the noniterative method in the literature. Therefore, this iterative LP design strategy can significantly enhance the performance of the AP-VP digital filter.

Fuzzy Bi-Objective Production-Distribution Planning Problem under the Carbon Emission Constraint

This study addresses the design of a four-stage production distribution system under a carbon emission constraint. The first stage contains a set of established retail outlets. The second stage consists of a set of possible distribution centers. The third stage is comprised of a set of manufacturing units. The final and fourth stage involves a set of suppliers. We propose a bi-objective optimization problem with a mixed-integer linear programming scheme for maximizing the total profits while minimizing the cumulative shortages in a multi-period planning horizon with inaccurate information on raw material resources. We also propose a two-phase approach to solve the proposed model and obtain a Pareto-optimal solution. The effectiveness of the solution method for obtaining the fuzzy efficient solution is demonstrated with computational experiments. Sensitivity analysis is used for examining the effect of the carbon emission constraint on the optimal decisions.

Efficient pre‐equalisation strategies for the downlink of a multi‐carrier code division multiple‐access wireless network

In this study, the problem of optimal synthesis of pre-equalisation factors for a multi-carrier code division multiple-access wireless network is studied under different quality of service (QoS) restrictions and performance objectives. The downlink is particularly addressed, where the QoS is evaluated by the signal-to-interference-noise ratio (SINR) after signal detection by matched filtering. First, the minimum energy formulation under inequality QoS constraints is analysed, and it was concluded that the optimal performance is always achieved at the lower bounds. Next, the minimisation of the peak magnitude of the pre-equalisation factors was addressed by an optimal synthesis scheme through the infinity norm, where a linear programming strategy is proposed by using an upper bound. Finally, by combining the minimum energy and minimum peak strategies, the minimisation of an upper bound on the peak-to-average-power ratio (PAPR) is suggested, which can be solved through quadratic programming by incorporating the QoS constraints. The new synthesis schemes take into account two important transmitter-based properties: peak magnitude and PAPR. These ideas were extensively validated in simulation, where the synthesis schemes were compared by Monte Carlo tests at different load and noise levels, and objective SINRs.

An efficient Resource Management to optimize the placement of hardware task on FPGA in the RVC framework

Dynamic partial reconfiguration (DPR) functionality allows implementing multi-tasks applications by exchanging tasks in a design at run-time. It is a promising solution to enhance system performances. But, the effective use of DPR is often hampered by the complexity added to the system design process. In this paper, we investigate the implementation of a multi-tasks applications using the DPR in the RVC framework. We present a resource management method which includes three steps: partitioning the application in HW/SW tasks, divided the FPGA in static and dynamic regions and placement the tasks on FPGA. The proposed method is based on using linear programming strategy to find the optimal placement of hardware tasks. We take into account the heterogeneity aspect of the device. The goal is to minimize the resource utilization and fragmentation. We use RVC technology which is based on a specific language for writing dataflow models called RVC-CAL. This language describes the application as set of blocks called actors connected through a network. To test the efficiency of our approach, we exploit the decoder MPEG-4 SP described in RVC-CAL. We measure the quality of placement in terms of tasks rejection, execution time and resource wastage. Application of different data combinations and a comparison with the state-of-the art method show the high performance of the proposed approach.