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An overview is presented of the numerical solution of constrained minimization problems. Attention is given to both primal and indirect (linear programs and unconstrained minimizations) methods of solution.
The indirect synthesis method is developed and shown to be capable of leading a near-optimal design of multidegree-of-freedom and multidesign-element transient nonlinear dynamical systems. The basis of the approach is to select the open design parameters such that the response of the portion of the system being designed approximates the limiting performances solution. The limiting performance problem can be formulated as one of linear programming by replacing all portions of the system subject to transient disturbances by control forces and supposing that the remaining portions are linear as are the overall kinematic constraints. One then selects the design parameters that respond most closely to the limiting performance solution, which can be achieved by unconstrained curve-fitting techniques.
The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.
This paper presents a dual-strategy approach to optimizing charging and discharging schedules for school bus fleets, using the limited charging infrastructure effectively. We aim to ensure that each bus is fully charged for daily operations and aids in grid stability during peak demand. The first strategy utilizes linear programming to schedule overnight charging at available station sockets and strategic discharging during peak periods, efficiently coordinating limited resources. The second strategy employs metaheuristic techniques for continuous optimization, focusing on precise power requirements and offering greater flexibility than the linear model.
The Deep Space Network (DSN) is a network of tracking stations, located throughout the globe, used to track spacecraft for NASA's interplanetary missions. This paper describes a computer program, DSNTRAK, which provides an optimum daily tracking schedule for the DSN given the view periods at each station for a mission set of n spacecraft, where n is between 2 and 6. The objective function is specified in terms of relative total daily tracking time requirements between the n spacecraft. Linear programming is used to maximize the total daily tracking time and determine an optimal daily tracking schedule consistent with DSN station capabilities. DSNTRAK is used as part of a procedure to provide DSN load forecasting information for proposed future NASA mission sets.
A description and applications of a computer capability for determining the ultimate optimal behavior of a dynamically loaded structural-mechanical system are presented. This capability provides characteristics of the theoretically best, or limiting, design concept according to response criteria dictated by design requirements. Equations of motion of the system in first or second order form include incompletely specified elements whose characteristics are determined in the optimization of one or more performance indices subject to the response criteria in the form of constraints. The system is subject to deterministic transient inputs, and the computer capability is designed to operate with a large linear programming on-the-shelf software package which performs the desired optimization. The report contains user-oriented program documentation in engineering, problem-oriented form. Applications cover a wide variety of dynamics problems including those associated with such diverse configurations as a missile-silo system, impacting freight cars, and an aircraft ride control system.
We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace--Beltrami operator on functions and the Laplacian on powers of the cotangent bundle. Our approach employs linear programming techniques to derive rigorous bounds by leveraging two types of spectral identities. The first type, inspired by the conformal bootstrap, arises from the consistency of the spectral decomposition of the product of Laplace eigensections, and involves the Laplacian spectra as well as integrals of triple products of eigensections. We formulate these conditions in the language of representation theory of PSL 2 (C) and use them to prove upper bounds on the first and second Laplacian eigenvalues. The second type of spectral identities follows from the Selberg trace formula. We use them to find upper bounds on the spectral gap of the Laplace--Beltrami operator on hyperbolic 3-orbifolds, as well as on the systole length of hyperbolic 3-manifolds, as a function of the volume. Further, we prove that the spectral gap λ 1 of the Laplace--Beltrami operator on all closed hyperbolic 3-manifolds satisfies λ 1 < 47.32. Along the way, we use the trace formula to estimate the low-energy spectra of a large set of example orbifolds and compare them with our general bounds, finding that the bounds are nearly sharp in several cases.
By generalizing the unconstrained p-hub approach for the park-and-ride (P&R) facility location problem under the multinomial logit demand function, the capacitated p-hub approach for the problem under the nested logit demand function captures a broader range of real-world cases. To solve this problem optimally, we introduce a mixed-integer linear program and accelerate its solution by enhancing the branch-and-cut procedure. To address the problem at a large scale, we introduce two other polyhedral approaches: variable neighborhood search (VNS) and adaptive randomized rounding (ARR). Downtown areas in Seoul have a high modal share of public transportation and congested road traffic, yet P&R has not been widely implemented. Therefore, we apply the ARR procedure to solve a real-world problem using traffic and geographic data from the Seoul metropolitan area. ARR performs better than VNS and addresses real-world cases. The solutions obtained by ARR present a phased expansion plan that encourages policymakers to start installing a small number of P&Rs immediately.
Previous approaches to dispatching nuclear integrated energy systems (NIES) have focused on the profitability and flexibility of these systems to operate on energy grids with highly variable pricing. However, due to the complexity involved in modeling and designing these systems, there has been less emphasis on ensuring that these dispatch strategies are physically achievable. It is imperative to develop methods that allow the system to remain within the desired NIES operating conditions and perform this based on realistic limited forecasted information. This research employs next generation artificial intelligence, namely deep reinforcement learning (DRL), and a dynamic system model written in Modelica to find a safe and profitable dispatch strategy for a solar nuclear hybrid design. The DRL agent is shown to find a novel dispatch strategy that manages both power ramping and power levels while respecting operational limits. This DRL-based dispatch is compared to other dispatching strategies including an optimal design solution from mixed integer linear programming (MILP). It is found that incorporating the physics of such a tightly coupled NIES limits the profitability of the MILP-based dispatch strategy. As a result, the MILP solution overestimates the design’s generated revenue. In contrast, DRL significantly reduces the number of breaches of safe operational conditions during energy arbitrage while maintaining profitability. Furthermore, this work paves the way for a more detailed assessment of NIES profitability and could be used to aid operator decisions on future NIES projects.
The conversion of carbon dioxide (CO 2 ) into jet fuel holds significant potential for reducing CO 2 emissions, providing an alternative to carbon-based resources, and offering a renewable means of energy storage. The objective of this study is to conduct a techno-economic analysis and optimize the supply chain network for converting CO 2 to jet fuel in the United States, aiming to minimize total costs while assessing the environmental and economic feasibility of two CO 2 conversion pathways. This first pathway is based on Fischer-Tropsch synthesis (FTS), and the other one is based on the valorization and upgrading of light methanol (MeOH). Incorporating spatial and techno-economic data, a mixed-integer linear programming model was developed to select source plants and conversion pathways, locations of conversion refinery sites, and the amount of captured CO 2 across the United States. The optimal results indicate that the FTS pathway is adopted at all selected refineries when the hydrogen price is 1000 dollars/t and the operating cost, mainly electricity used in conversion, is reduced to 5 % of its current level. Under this scenario, the total annual profit is 8 billion dollars, and the net carbon emissions are -88,783,284 tons. The sensitivity analyses reveal that the prices of electricity and hydrogen significantly contribute to total production costs. The CO 2 recycle percentage of the FTS pathway influences the choice of applied pathways at refineries. Additionally, a higher conversion rate holds a substantial promise for reducing the total production cost and can make the MeOH pathway a viable choice.
Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.
Integrating genome-scale metabolic networks with reactive transport models (RTMs) provides a detailed description of the dynamic changes in microbial growth and metabolism. Despite promising demonstrations in the past, computational inefficiency has been pointed out as a critical issue to overcome because it requires repeated application of linear programming (LP) to obtain flux balance analysis (FBA) solutions in every time step and spatial grid. To address this challenge, we propose a new simulation method where we train and validate artificial neural networks (ANNs) using randomly sampled FBA solutions and incorporate the resulting surrogate FBA model (represented as algebraic equations) into RTMs as source/sink terms. We demonstrate the efficiency of our method via a case study of Shewanella oneidensis MR-1. During aerobic growth on lactate, S. oneidensis produces metabolic byproducts (such as pyruvate and acetate), which are subsequently consumed as alternative carbon sources when the preferred nutrients are depleted. To effectively simulate these complex dynamics, we used a cybernetic approach that models metabolic switches as the outcome of dynamic competition among multiple growth options. In both zero-dimensional batch and one-dimensional column configurations, the ANN-based surrogate models achieved substantial reduction of computational time by several orders of magnitude compared to the original LP-based FBA models. Moreover, the ANN models produced robust solutions without any special measures to prevent numerical instability. These developments significantly promote our ability to utilize genome-scale networks in complex, multi-physics, and multi-dimensional ecosystem modeling.
Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.
The need for distributed and adaptable energy resources that can handle the growing unpredictability in both supply and demand is rising as the power system continues to modernize. In order to satisfy those needs and maintain grid resilience, nuclear power plants can dynamically control their output, despite typically being used as baseload generators. By incorporating energy storage and renewable energy sources, nuclear integrated energy systems are designed to satisfy the electrical and thermal demands of different end-user applications while ensuring flexible power operation. These systems generate revenue by participating in both wholesale and ancillary services electricity markets, as well as commodity markets for various byproducts generated from coupled industrial processes. This study addresses the economic dispatch efficiency of a tightly coupled nuclear integrated energy system comprising a gigawatt-scale light water reactor, commercialized in the U.S., a high-temperature steam electrolysis unit, a district heating network, and specified electrical loads. To demonstrate the nuclear power plant’s flexibility within the day-ahead unit commitment and economic dispatch framework, while maintaining equilibrium even during periods of refueling outages, this paper develops a mixed-integer linear programming framework that models the subsystems and components of its nuclear steam supply system. A systematic comparative analysis of flexible versus baseload nuclear power plant operation under varying levels of renewable energy integration indicates that flexible operation enhances system profitability by more than 18% while also increasing energy storage utilization, improving reactor responsiveness to load fluctuations, and allowing for greater participation across numerous electricity markets.
Many recent efforts in developing hardware-accelerated spiking neural networks (SNNs) are characterized by deep co-design between algorithms, architectures, and devices. Architectural advances overcome device constraints by coupling together many small resistive-RAM (ReRAM) crossbars via a network-on-chip (NoC) for neuromorphic component operation. Concurrently, improved SNN training methods increase accuracy and structural sparsity in networks despite growing problem sizes. Finally, compilers leverage these attributes to minimize area and inter-crossbar communication while mapping large SNNs to sophisticated architectures. However, for compiler-driven co-design to realize increasingly complex and profitable optimizations, a compile-time view of power consumption is critical. We present PowerMappeR to express and optimize over mapping-, architecture-, and device-specific power consumption information. By modeling the dynamic power of well-established components, we develop an integer linear programming (ILP)-based, encoding-agnostic, parametric power estimation model. Using this model, we demonstrate practical improvements in area and inter-crossbar communication by 0%–9.5% and 1.4%–5.1%, respectively. We also limit hotspot formation during optimization, achieving comparable or better results in targeted metrics with up to 96.4%–97.1% restriction of hotspot magnitude. Finally, we introduce profile-guided formulations to reduce worst-case and expected-case hotspot magnitude by 40.7%–69.5% and 40.6%–56.3%, respectively. Optimizing worst-case hotspot magnitude incidentally improves expected-case magnitude by 10.85%–33.45%. Reciprocally, optimizing expected-case magnitude incidentally improves worst-case magnitude by 4.33%–39.87%. Validation against hardware simulators confirms that PowerMappeR can decrease dynamic power consumption by 12.6%–27.3%.
Electrification of heavy-duty (HD) vehicles marks an important milestone and technical challenge in the electric vehicle (EV) industry and the public grid. However, implementing EV charging at this scale will necessitate that traditional truck stops be updated with EV charging infrastructure that could represent 10's of MW in electricity consumption. Furthermore, as the transportation sector is represented as critical infrastructure, supporting resiliency considerations in EV charging infrastructure will be critical. This paper proposes an optimization-based approach for optimally designing a MW-scale microgrid charging network. This approach transforms conventional designed truck stops into a reliable HDEV charging stations capable of overnight slow charging and 30-minute to 1 hour fast charging. Using a mixed-integer linear program formulation blending capacity planning and reliability constraints, an optimal network configuration can be solved for a proposed EV charging station that includes photovoltaic and battery energy storage capabilities.
Here, we consider a distribution network integrating demand response (DR) participants in the presence of uncertain renewable suppliers and outdoor temperatures. A bilevel optimization model is proposed to capture the intricate dynamics between price-incentivized DR participants and distribution system operations, including energy procurement and active/reactive power flows. The model is formulated as a distributional robust bilevel optimization using Wasserstein metrics. We show favorable data-driven properties including out-of-sample guarantee and asymptotic consistency. Furthermore, we present a tractable mixed-integer linear programming reformulation and characterize the worst-case distribution. Computational experiments are conducted on a modified 33-bus system. Our findings underscore the efficacy of the pricing strategies derived from the proposed bilevel optimization model. These strategies not only effectively manage DR participants' behavior but also bring equity considerations among households with various characteristics to light. The results contribute to a deeper understanding of the interplay between distribution system operators and DR participants.
Recent advances in smart inverters offer opportunities to mitigate adverse grid impacts caused by high penetrations of distributed photovoltaics (PV) in distribution grids, such as voltage violations. Here, this paper proposes a novel measurement-driven optimal power flow (OPF)-based distributed energy resource management system (DERMS) voltage regulation via recursive sensitivity estimation informed coordinated control of distributed PV inverters. The proposed approach leverages available grid and controllable DER measurements, eliminating reliance on system model information while being adaptive and robust to volatile operating conditions. A mean-corrected recursive ridge regression (MCRRR) algorithm is proposed for sensitivity estimation, continuously refining the sensitivity model through a closed-form solution. It effectively manages varying grid operating conditions, such as changes in power injections and topology reconfiguration, to facilitate a time-varying update of the Load Sensitivity Factors (LSF). The proposed approach is formulated as a linear programming (LP) problem and is thus scalable to larger-scale distribution systems. Its effectiveness and efficiency are demonstrated on a realistic distribution feeder with high PV penetrations in Southern California, USA.