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Results for “Mixed integer optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Measure this, not that: Optimizing the cost and model-based information content of measurements

Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. Here, this work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) to optimize the selection of measurements. The solver MindtPy is modified to support calculating the D-optimality objective and its gradient via an external package, scipy, using the grey-box module in Pyomo. The new approach is demonstrated in two case studies: estimating highly correlated kinetics from a batch reactor and estimating transport parameters in a large-scale rotary packed bed for CO 2 capture. Both case studies show how examining the Pareto optimal trade-offs between information content measured by A- and D-optimality versus measurement budget offers practical guidance for selecting measurements for scientific experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Substation-Level Grid Topology Optimization Using Bus Splitting: Preprint

Operations of substation circuit breakers are of high significance for performing system maintenance and topology optimization. Bus splitting is one type of topology changes where the two bus-bars at a substation become electrically disconnected after certain actions of circuit breakers. As these events involve detailed substation modeling, they are not typically considered in power system routine operation and control. In this paper, an improved substation-level topology optimization is developed by expanding traditional line switching with breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bi-linear terms in the resultant topology optimization model. Thus, a tractable mixed-integer linear program formulation is presented which can be efficiently solved for real-time control. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the performance and economic benefits of the proposed topology optimization approach.

bus split↗
DOE OSTI2024

Grid-Aware Charging and Operational Optimization for Mixed-Fleet Public Transit

The rapid growth of urban populations and the increasing need for sustainable transportation solutions have prompted a shift towards electric buses in public transit systems. However, the effective management of mixed fleets consisting of both electric and diesel buses poses significant operational challenges. One major challenge is coping with dynamic electricity pricing, where charging costs vary throughout the day. Transit agencies must optimize charging assignments in response to such dynamism while accounting for secondary considerations such as seating constraints. This paper presents a comprehensive mixed-integer linear programming (MILP) model to address these challenges by jointly optimizing charging schedules and trip assignments for mixed (electric and diesel bus) fleets while considering factors such as dynamic electricity pricing, vehicle capacity, and route constraints. We address the potential computational intractability of the MILP formulation, which can arise even with relatively small fleets, by employing a hierarchical approach tailored to the fleet composition. By using real-world data from the city of Chattanooga, Tennessee, USA, we show that our approach can result in significant savings in the operating costs of the mixed transit fleets.

Sen, Rishav↗
DOE OSTI2021

POINT: Partially Observable Imitation Network for Traffic Signal Control

Smart traffic signals bring together transportation infrastructure and advance technologies to improve the mobility and efficiency of urban transportation network. Adaptive traffic signal control studies can be categorized into modeling-based approaches and learning-based approaches. In order to take advantages of these two systems, this study developed an offline-online combined Partial Observable Imitation Network for Traffic signal control (POINT). In the offline system, the traffic signal timing optimization problem was formulated as a Mixed Integer Nonlinear Programming (MINLP) given complete traffic information, i.e., second-by-second speeds and locations of all vehicles. Furthermore, the objective of MINLP is to minimize total travel delays considering individual vehicle trajectories under Connected Vehicle (CV) environment. The calculated optimal solutions under various traffic conditions were considered as the ”expert” decisions. In the online system, an imitation neural network model was developed to learn the ”expert” signal plans generated from offline system. Given partial observable traffic conditions in real time, e.g., the aggregate-level of traffic volume, the POINT model can compute the signal timing parameters in the online system. The numerical results demonstrated that the proposed method outperformed other state-of-the-art signal control method under high and unbalanced traffic demand levels in terms of reducing travel delays and queue length.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Coordinated Optimization and Control of Residential Solid State Power Substations in Electrical Distribution Network

This paper proposes a computationally efficient mixed integer linear programming (MILP) model for the coordinated optimization of solid-state power substations (SSPSs) in a feeder considering the full unbalanced three-phase structure of the distribution grid and its characteristics. The proposed model determines the optimal real and reactive power of each SSPS at the point of common coupling (PCC) that minimizes the operating cost and maximizes the system performance, e.g., voltage regulation and phase balancing. To improve the computational efficiency, an inscribed octagon is introduced to approximate the quadratic capacity constraints of components. Numerical simulation results show the effectiveness of the proposed model and significant improvements in voltage profiles and power imbalance between phases.

Liu, Guodong↗
DOE OSTI2022

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using neural networks. These neural networks can be exactly transformed into mixed integer linear programs and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the neural network. Accordingly, this paper develops a technique for training an "optimally compact'' neural network, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We demonstrate the use of this neural network as an approximator of the nonlinear power flow equations by embedding it in the AC unit commitment problem, transforming the problem from a mixed integer nonlinear program into a more manageable mixed integer linear program. We use the 14-, 57-, and 89-bus networks as test cases and compare the AC-feasibility of commitment decisions resulting from the neural network, DC, and linearized power flow approximations. Our results show that the neural network model outperforms both the DC and linearized power flow approximations when embedded in the unit commitment problem. The neural network formulation most often selects a feasible unit commitment schedule, and furthermore, it only s

AC power flow↗
DOE OSTI2023

Series FACTS Devices for Increasing Resiliency in Severe Weather Conditions

Severe weather conditions are low-probability, high-impact events that affect grid operations. The majority of power outages are caused by severe weather conditions. Grid resiliency to weather events can be enhanced by decreasing the reliance on its affected sections. One way to do this is to reduce the power flow through lines vulnerable to severe weather. If a line is disconnected, its initial power flow is distributed through the neighbor lines, which may cause congestion in the grid. FACTS devices can be used to control the power flow of lines that have a higher chance of power outages. Most previous works do not consider weather events in power flow control. In this work, a linearized optimal power flow (OPF)–based algorithm is developed to minimize the real power flow of vulnerable lines considering the thermal limits of lines to prevent infeasible solutions; the simulation is fast, making it suitable for large-scale systems. The proposed optimization problem is presented as a mixed-integer linear program (MILP), making it capable of using short-term load forecasting due to its high solution speed. The proposed optimization problem considers multiple lines with different outage probabilities and the uncertainties of the weather forecast. Moreover, it estimates the power reduction in vulnerable lines due to changes in the series FACTS devices. The performance of the proposed optimization problem is tested on IEEE 14-, 30-, and 118-bus systems for several scenarios. The results are validated with the AC power flow results from MATPOWER.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists of choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to the nonconvex AC power flow constraints, and bilevel solution approaches commonly apply a convex relaxation or approximation to allow for tractable bilevel reformulations at the cost of underestimating some power system vulnerabilities. Our main contribution is to provide an alternative branch-and-bound algorithm whose upper bounding mechanism (in a maximization context) is based on a reformulation that avoids relaxation of the AC power flow constraints in the lower-level defender problem. Lower bounding is provided with semidefinite programming (SDP) relaxed solutions to the lower-level problem. We establish finite termination with guarantees of either a globally optimal solution to the original bilevel problem, or a globally optimal solution to the SDP-relaxed bilevel problem which is included in a vetted list of upper-level attack solutions, at least one of which is a globally optimal solution to the bilevel problem. We demonstrate through computational experiments applied to IEEE case instances both the relevance of our contribution, and the effectiveness of our contributed algorithm for identifying power system vulnerabilities without resorting to convex relaxations of the lower-level problem. We conclude with a discussion of future extensions and improvements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A mathematical programming approach for the optimal placement of flame detectors in petrochemical facilities

Flame detectors provide an important layer of protection for personnel in petrochemical plants, but effective placement can be challenging. A mixed-integer nonlinear programming formulation is proposed for optimal placement of flame detectors while considering non-uniform probabilities of detection failure. We show that this approach allows for the placement of fire detectors using a fixed sensor budget and outperforms models that do not account for imperfect detection. In this study, we develop a linear relaxation to the formulation and an efficient solution algorithm that achieves global optimality with reasonable computational effort. We integrate this problem formulation into the Python package, Chama, and demonstrate the effectiveness of this formulation on a small test case and on two real-world case studies using the fire and gas mapping software, Kenexis Effigy.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Optimizing design and dispatch of a renewable energy system with combined heat and power

We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Optimal Renewable Resource Allocation and Load Scheduling of Resilient Communities

This paper presents a methodology for enhancing community resilience through optimal renewable resource allocation and load scheduling in order to minimize unserved load and thermal discomfort. The proposed control architecture distributes the computational effort and is easier to be scaled up than traditional centralized control. The decentralized control architecture consists of two layers: The community operator layer (COL) allocates the limited amount of renewable energy resource according to the power flexibility of each building. The building agent layer (BAL) addresses the optimal load scheduling problem for each building with the allowable load determined by the COL. Both layers are formulated as a model predictive control (MPC) based optimization. Simulation scenarios are designed to compare different combinations of building weighting methods and objective functions to provide guidance for real-world deployment by community and microgrid operators. The results indicate that the impact of power flexibility is more prominent than the weighting factor to the resource allocation process. Allocation based purely on occupancy status could lead to an increase of PV curtailment. Further, it is necessary for the building agent to have multi-objective optimization to minimize unserved load ratio and maximize comfort simultaneously.

model predictive control↗
DOE OSTI2021

Modular supply chain optimization considering demand uncertainty to manage risk

Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. We report the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.

42 ENGINEERING↗
DOE OSTI2020

Multistage distributionally robust mixed-integer programming with decision-dependent moment-based ambiguity sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Furthermore, our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Refueling infrastructure planning in intercity networks considering route choice and travel time delay for mixed fleet of electric and conventional vehicles

The range anxiety has been a major factor that affects the market acceptance of electric vehicles. Even with the recent development of battery technologies, a lack of charging stations and range anxiety are still significant concerns, specifically for intercity trips. This calls for more investments in building charging stations and advancing battery technologies to increase the market share of electric vehicles and improve sustainability. This study suggests a configuration for plug-in electric vehicle charging infrastructure to support long-distance intercity trips of electric vehicles at the network level. A model is proposed to minimize the total system cost including infrastructure investment (building charging stations/spots) and travel time delays (charging time, waiting time in the queue, and detour time to access charging stations). This study fills existing gaps in the literature by capturing realistic patterns of travel demand and considering flow-dependent charging delays at charging stations. Furthermore, the proposed model, which is formulated as a mixed-integer program with nonlinear constraints, solves the optimization problem at the network level. At the network level, impacts of charging station locations on the traffic assignment problem with a mixed fleet of electric and conventional vehicles need to be considered. To this end, a traffic assignment module is integrated with a simulated annealing algorithm. The numerical experiments show a satisfactory application of the model for a full-scale case study (intercity network in Michigan). The solution quality and efficiency of the proposed solution algorithm are evaluated against those of an enumeration approach for a small case study. The results suggest that even for the current market share and charging stations’ setting, a significant investment is needed to support intercity trips without range anxiety issues and with acceptable delays. Additionally, through sensitivity analyses, the required infrastructure and battery investments to support intercity trips with acceptable delays are established for hypothetical increased market shares and battery size in the future.

42 ENGINEERING↗
DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗