Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “mixed integer program (MIP)”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Model-Based Framework to Optimize Charger Station Deployment for Battery Electric Vehicles

The development of battery electric vehicles (BEVs) is accelerating due to their environmental advantages over gasoline and diesel-powered vehicles, including a decrease in air pollution and an increase in energy efficiency. The deployment of charging infrastructure will need to increase to keep pace with demand, especially for large commercial vehicles for which few public chargers currently exist. In this paper, a new flexible framework is proposed for optimizing the placement of charging stations for BEVs, within which different physical models and optimization techniques may be used. Furthermore, a set of metrics is suggested to help enforce complex constraints and facilitate direct comparison between different optimization techniques. Unlike many existing charger placement techniques, the proposed method directly considers the historical driving patterns on a vehicle-by-vehicle basis, using transparent models to assess impacts of candidate charger placements, thus improving the explainability of the results. In the developed framework, modeled BEVs are first generated along the road network to mimic historical traffic data and are simulated traveling along a given route according to a simplified vehicle model. During the simulation, the charger placement problem is initially relaxed to allow vehicles to charge at any node along the road network, and vehicle states are tracked to assess areas of high charging demand. Charging stations are then placed based on the results of the relaxed simulation, and suggested placements are evaluated via road network simulation with fixed charger locations. This proposed framework is applied to a sample problem of placing charging stations along five major highway corridors for Class 8 over-the-road electric trucks. A novel mixed integer programming (MIP) formulation is proposed to optimize charger placements based upon the expected charging demand. Constraints were imposed on the final placement results to limit expected wait times at each station and ensure a minimum threshold of trucking routes are viable for BEVs. The results demonstrate the flexibility and potential effectiveness of the developed model-based framework for scalable charger station deployment.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2014

Poster — Thur Eve — 69: Computational Study of DVH-guided Cancer Treatment Planning Optimization Methods

Purpose: To compare methods to incorporate the Dose Volume Histogram (DVH) curves into the treatment planning optimization. Method: The performance of three methods, namely, the conventional Mixed Integer Programming (MIP) model, a convex moment-based constrained optimization approach, and an unconstrained convex moment-based penalty approach, is compared using anonymized data of a prostate cancer patient. Three plans we generated using the corresponding optimization models. Four Organs at Risk (OARs) and one Tumor were involved in the treatment planning. The OARs and Tumor were discretized into total of 50,221 voxels. The number of beamlets was 943. We used commercially available optimization software Gurobi and Matlab to solve the models. Plan comparison was done by recording the model runtime followed by visual inspection of the resulting dose volume histograms. Conclusion: We demonstrate the effectiveness of the moment-based approaches to replicate the set of prescribed DVH curves. The unconstrained convex moment-based penalty approach is concluded to have the greatest potential to reduce the computational effort and holds a promise of substantial computational speed up.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TH-EF-BRB-04: 4π Dynamic Conformal Arc Therapy Dynamic Conformal Arc Therapy (DCAT) for SBRT

Purpose: To develop an efficient and effective trajectory optimization methodology for 4π dynamic conformal arc treatment (4π DCAT) with synchronized gantry and couch motion; and to investigate potential clinical benefits for stereotactic body radiation therapy (SBRT) to breast, lung, liver and spine tumors. Methods: The entire optimization framework for 4π DCAT inverse planning consists of two parts: 1) integer programming algorithm and 2) particle swarm optimization (PSO) algorithm. The integer programming is designed to find an optimal solution for arc delivery trajectory with both couch and gantry rotation, while PSO minimize a non-convex objective function based on the selected trajectory and dose-volume constraints. In this study, control point interaction is explicitly taken into account. Beam trajectory was modeled as a series of control points connected together to form a deliverable path. With linear treatment planning objectives, a mixed-integer program (MIP) was formulated. Under mild assumptions, the MIP is tractable. Assigning monitor units to control points along the path can be integrated into the model and done by PSO. The developed 4π DCAT inverse planning strategy is evaluated on SBRT cases and compared to clinically treated plans. Results: The resultant dose distribution of this technique was evaluated between 3D conformal treatment plan generated by Pinnacle treatment planning system and 4π DCAT on a lung SBRT patient case. Both plans share the same scale of MU, 3038 and 2822 correspondingly to 3D conformal plan and 4π DCAT. The mean doses for most of OARs were greatly reduced at 32% (cord), 70% (esophagus), 2.8% (lung) and 42.4% (stomach). Conclusion: Initial results in this study show the proposed 4π DCAT treatment technique can achieve better OAR sparing and lower MUs, which indicates that the developed technique is promising for high dose SBRT to reduce the risk of secondary cancer.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Design Considerations for GPU-based Mixed Integer Programming on Parallel Computing Platforms

Mixed Integer Programming (MIP) is a powerful abstraction in combinatorial optimization that finds real-life application across many significant sectors. The recent proliferation of graphical processing unit (GPU)-based accelerated computing architectures in large-scale parallel computing or supercomputing presents new opportunities as well as challenges in the advancement of MIP solver technology to effectively use the new accelerated computing platforms and scale to large parallel systems. Here, we recount the conventional processor-based strategies and focus on configurations where the most promising intersection lies between parallel MIP solver approaches and the specific strengths of accelerated parallel platforms. We note that the best potential lies in solving problems whose individual matrix sizes (of the linear program relaxation) fit entirely within one accelerator's memory and whose branch-and-bound (or branch-and-cut) trees cannot be fully contained within a small number of computational nodes. Additionally, we identify ideal features of computational linear algebra support on GPU accelerators that would help advance this direction of scalable parallel solution of MIP problems on GPU-based accelerated computing architectures.

Perumalla, Kalyan↗
DOE OSTI2016

Electric Grid Expansion Planning with High Levels of Variable Generation

Renewables are taking a large proportion of generation capacity in U.S. power grids. As their randomness has increasing influence on power system operation, it is necessary to consider their impact on system expansion planning. To this end, this project studies the generation and transmission expansion co-optimization problem of the US Eastern Interconnection (EI) power grid with a high wind power penetration rate. In this project, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. This study analyzed a time series creation method to capture the diversity of load and wind power across balancing regions in the EI system. The obtained time series can be easily introduced into the MIP co-optimization problem and then solved robustly through available MIP solvers. Simulation results show that the proposed time series generation method and the expansion co-optimization model and can improve the expansion result significantly after considering the diversity of wind and load across EI regions. The improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare. This study shows that modelling load and wind variations and diversities across balancing regions will produce significantly different expansion result compared with former studies. For example, if wind is modeled in more details (by increasing the number of wind output levels) so that more wind blocks are considered in expansion planning, transmission expansion will be larger and the expansion timing will be earlier. Regarding generation expansion, more wind scenarios will slightly reduce wind generation expansion in the EI system and increase the expansion of other generation such as gas. Also, adopting detailed wind scenarios will reveal that it may be uneconomic to expand transmission networks for transmitting a large amount of wind power through a long distance in the EI system. Incorporating more details of renewables in expansion planning will inevitably increase the computational burden. Therefore, high performance computing (HPC) techniques are urgently needed for power system operation and planning optimization. As a scoping study task, this project tested some preliminary parallel computation techniques such as breaking down the simulation task into several sub-tasks based on chronology splitting or sample splitting, and then assigning these sub-tasks to different cores. Testing results show significant time reduction when a simulation task is split into several sub-tasks for parallel execution.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Managing time-substitutable electricity usage using dynamic controls

A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Managing time-substitutable electricity usage using dynamic controls

A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Managing time-substitutable electricity usage using dynamic controls

A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Ghosh, Soumyadip↗
DOE OSTI2023

Learning to Branch with Interpretable Machine Learning Models

Machine learning is being increasingly used in improving decisions made within branch-and-bound algorithms for solving mixed-integer programs (MIPs). Branching is a key component in branch-and-bound algorithms, this work presents IDAES-core project update on building simple and interpretable machine learning models for branching and improving decision-making tools applied for the optimization of advanced energy systems.

Bayramoglu, Selin↗
DOE OSTI2024

Integrated solution techniques for security constrained unit commitment problem

Apparatus and methods are disclosed for solving Mixed Integer Programming (MIP) problems, such as Security Constrained Unit Commitment (SCUC) problems used by power grid authorities to perform day-ahead market clearing. In certain examples, a plurality of threads of a software tool implementing a concurrent optimizer can be executed concurrently and sequentially to generate new solutions to a SCUC problem for an upcoming planning horizon. Data can be shared among the concurrently executing threads, such as intermediate/incumbent solutions and hints regarding the fixing of variables and constraints to reduce the size of the SCUC problem. In some examples, the threads are seeded with historical solutions from prior planning horizons. The software tool can select a best solution from the solutions generated by the threads, and determine dispatch instructions for a device coupled to the power grid for the upcoming planning horizon based at least in part on the selected solution.

Pan, Feng↗
DOE OSTI2021

Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design

Microgrids are frequently employed in remote regions, in part because access to a larger electric grid is impossible, difficult, or compromises reliability and independence. Although small microgrids often employ spot generation, in which a diesel generator is attached directly to a load, microgrids that combine these individual loads and augment generators with photovoltaic cells and batteries as a distributed energy system are emerging as a safer, less costly alternative. In this work, we present a model that seeks the minimum-cost microgrid design and ideal dispatched power to support a small remote site for one year with hourly fidelity under a detailed battery model; this mixed-integer nonlinear program (MINLP) is intractable with commercial solvers but loosely coupled with respect to time. A mixed-integer linear program (MIP) approximates the model, and a partitioning scheme linearizes the bilinear terms. We introduce a novel policy for loosely coupled MIPs in which the system reverts to equivalent conditions at regular time intervals; this separates the problem into subproblems that we solve in parallel. We obtain solutions within 5% of optimality in at most six minutes across 14 MIP instances from the literature and solutions within 5% of optimality to the MINLP instances within 20 minutes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift. Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

Machine Learning↗
DOE OSTI2021

Hybrid Imitation Learning for Real-Time Service Restoration in Resilient Distribution Systems

Self-healing capability is a critical factor for a resilient distribution system, which requires intelligent agents to automatically perform service restoration online, including network reconfiguration and reactive power dispatch. Here, the article proposes the imitation learning framework for training such an agent, where the agent will interact with an expert built based on the mixed-integer program to learn its optimal policy, and therefore significantly improve the training efficiency compared with exploration-dominant reinforcement learning (RL) methods. This significantly improved training efficiency makes the training problem under N-k scenarios tractable. A hybrid policy network is proposed to handle tie-line operations and reactive power dispatch simultaneously to further improve the restoration performance. The 33-bus and 119-bus systems with N-k disturbances are employed to conduct the training. The results indicate that the proposed method outperforms traditional RL algorithms such as the deep-Q network.

42 ENGINEERING↗
DOE OSTI2015

Chance-Constrained Transmission Switching With Guaranteed Wind Power Utilization

Due to the significant variability and uncertainty of wind power over short time scales, high penetration of wind power can be problematic in an electric grid. One of the critical issues is how to keep increasing wind penetration without jeopardizing grid security and reliability. This paper explores the possibility of changing transmission network topology, by transmission switching, to accommodate higher utilization of wind power and reduce the generation costs of thermal units. Considering the uncertainty in wind power output, we use chance constraints to ensure that the wind energy utilized exceeds a minimal usage level at a certain probability. We develop a deterministic approximation approach using sample average approximation and provide a strong extended formulation. Numerical results show the potential benefit the proposed model can achieve.

17 WIND ENERGY↗
DOE OSTI2015

Stochastic Optimization for Unit Commitment-A Review

Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC's birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Probabilistic Forecasting of Generators Startups and Shutdowns in the MISO System Based on Random Forest

Solving security constrained unit commitment (SCUC) problems to plan an economical generation schedule for day-head electricity market has been an important research topic in recent years. Mixed integer programming method (MIP), the-state-of-art approach for solving SCUC problem, is known computationally hard when the number of binary status variables is large. In this paper, a machine learning-based algorithm - random forest (RF), was applied to forecast the startups (SU) and shutdowns (SD) hours of generators, based on historical hourly system condition observations in the Midcontinent Independent System Operator (MISO) system. The main purpose is to reduce the number of binary status variables, by fixing the SU/SD hours to a narrow range of high confidence. This would significantly reduce the size of the decision space, and therefore speed up SCUC solutions with reduced uncertainty.

Lin, Xinming↗
DOE OSTI2019

A Bi-Level Formulation And Solution Method For The Integration Of Process Design And Scheduling

Design and operation decisions of manufacturing plants can often be expressed within a hierarchical structure, where optimal decisions at lower operating level provide constraints for the decision raking at a higher decision level. In this work, we are addressing the case of a hierarchical design and scheduling optimization problem. The integration of design and scheduling decisions can play a big role in designing economically profitable plants and improving their operational performance. This problem can be expressed as a bi-level problem, where design related decisions occur at the upper level and operational scheduling decisions at the lower level. Since discrete decisions are involved in both optimization levels, the resulting formulation typically corresponds to bi-level mixed-integer programming problems (B-MIP). The solution of B-MIP problems is very challenging, and typically requires the use of global optimization techniques, with many algorithms not able to guarantee feasibility. To overcome the challenges in solving this class of problems we propose the use of a multi-parametric based algorithm for the solution of bi-level mixed-integer linear and quadratic programming problems, capable of providing the exact and global solution. The main idea of this approach is to treat the lower scheduling problem as a multi-parametric programming problem in which the design decisions are considered as parameters. Here, the resulting parametric solutions can then be substituted into the upper level design problem, which can be solved as a set of single-level deterministic programming problems. Through the developed formulation and algorithm we are able to supply the decision makers with the exact solution of the integrated design and scheduling problem.

42 ENGINEERING↗