scholarly journals Nonlinear Hybrid Planning with Deep Net Learned Transition Models and Mixed-Integer Linear Programming

2017 ◽  
Author(s):  
Buser Say ◽  
Ga Wu ◽  
Yu Qing Zhou ◽  
Scott Sanner
Keyword(s):  
Network Models ◽  
Mixed Integer ◽  
State Transitions ◽  
Transition Model ◽  
Model Learning ◽  
Mixed Integer Linear Program ◽  
Monte Carlo Tree Search ◽  
Deep Network ◽  
Transition Models ◽  
Network Transition

In many real-world hybrid (mixed discrete continuous) planning problems such as Reservoir Control, Heating, Ventilation and Air Conditioning (HVAC), and Navigation, it is difficult to obtain a model of the complex nonlinear dynamics that govern state evolution. However, the ubiquity of modern sensors allow us to collect large quantities of data from each of these complex systems and build accurate, nonlinear deep network models of their state transitions. But there remains one major problem for the task of control -- how can we plan with deep network learned transition models without resorting to Monte Carlo Tree Search and other black-box transition model techniques that ignore model structure and do not easily extend to mixed discrete and continuous domains? In this paper, we make the critical observation that the popular Rectified Linear Unit (ReLU) transfer function for deep networks not only allows accurate nonlinear deep net model learning, but also permits a direct compilation of the deep network transition model to a Mixed-Integer Linear Program (MILP) encoding in a planner we call Hybrid Deep MILP Planning (HD-MILP-PLAN). We identify deep net specific optimizations and a simple sparsification method for HD-MILP-PLAN that improve performance over a naive encoding, and show that we are able to plan optimally with respect to the learned deep network.

scholarly journals Scalable Planning with Deep Neural Network Learned Transition Models

2020 ◽  
Vol 68 ◽  
pp. 571-606
Author(s):  
Ga Wu ◽  
Buser Say ◽  
Scott Sanner
Keyword(s):  
Neural Network ◽  
Deep Neural Network ◽  
Mixed Integer ◽  
Transition Model ◽  
Model Learning ◽  
Deep Network ◽  
Continuous State ◽  
Deep Networks ◽  
Transition Models ◽  
Planning Problems

In many complex planning problems with factored, continuous state and action spaces such as Reservoir Control, Heating Ventilation and Air Conditioning (HVAC), and Navigation domains, it is difficult to obtain a model of the complex nonlinear dynamics that govern state evolution. However, the ubiquity of modern sensors allows us to collect large quantities of data from each of these complex systems and build accurate, nonlinear deep neural network models of their state transitions. But there remains one major problem for the task of control – how can we plan with deep network learned transition models without resorting to Monte Carlo Tree Search and other black-box transition model techniques that ignore model structure and do not easily extend to continuous domains? In this paper, we introduce two types of planning methods that can leverage deep neural network learned transition models: Hybrid Deep MILP Planner (HD-MILP-Plan) and Tensorflow Planner (TF-Plan). In HD-MILP-Plan, we make the critical observation that the Rectified Linear Unit (ReLU) transfer function for deep networks not only allows faster convergence of model learning, but also permits a direct compilation of the deep network transition model to a Mixed-Integer Linear Program (MILP) encoding. Further, we identify deep network specific optimizations for HD-MILP-Plan that improve performance over a base encoding and show that we can plan optimally with respect to the learned deep networks. In TF-Plan, we take advantage of the efficiency of auto-differentiation tools and GPU-based computation where we encode a subclass of purely continuous planning problems as Recurrent Neural Networks and directly optimize the actions through backpropagation. We compare both planners and show that TF-Plan is able to approximate the optimal plans found by HD-MILP-Plan in less computation time. Hence this article offers two novel planners for continuous state and action domains with learned deep neural net transition models: one optimal method (HD-MILP-Plan) and a scalable alternative for large-scale problems (TF-Plan).

scholarly journals Investment Incentives in Competitive Electricity Markets

2018 ◽  
Vol 8 (10) ◽  
pp. 1978 ◽  
Author(s):  
Jaber Valinejad ◽  
Taghi Barforoshi ◽  
Mousa Marzband ◽  
Edris Pouresmaeil ◽  
Radu Godina ◽  
...  
Keyword(s):  
Electricity Markets ◽  
Electricity Market ◽  
Planning Horizon ◽  
Optimization Method ◽  
Design Criterion ◽  
Mixed Integer ◽  
Investment Incentives ◽  
Mixed Integer Linear Program ◽  
Interconnected Power System ◽  
The Impact

This paper presents the analysis of a novel framework of study and the impact of different market design criterion for the generation expansion planning (GEP) in competitive electricity market incentives, under variable uncertainties in a single year horizon. As investment incentives conventionally consist of firm contracts and capacity payments, in this study, the electricity generation investment problem is considered from a strategic generation company (GENCO) ′ s perspective, modelled as a bi-level optimization method. The first-level includes decision steps related to investment incentives to maximize the total profit in the planning horizon. The second-level includes optimization steps focusing on maximizing social welfare when the electricity market is regulated for the current horizon. In addition, variable uncertainties, on offering and investment, are modelled using set of different scenarios. The bi-level optimization problem is then converted to a single-level problem and then represented as a mixed integer linear program (MILP) after linearization. The efficiency of the proposed framework is assessed on the MAZANDARAN regional electric company (MREC) transmission network, integral to IRAN interconnected power system for both elastic and inelastic demands. Simulations show the significance of optimizing the firm contract and the capacity payment that encourages the generation investment for peak technology and improves long-term stability of electricity markets.

On the Simulation of Unsteady Turbulence and Transition Effects in a Multistage Low Pressure Turbine: Part III — Comparison of Harmonic Balance and Full Wheel Simulation

2018 ◽  
Author(s):  
Edmund Kügeler ◽  
Georg Geiser ◽  
Jens Wellner ◽  
Anton Weber ◽  
Anselm Moors
Keyword(s):  
Harmonic Balance ◽  
Leading Edge ◽  
Suction Side ◽  
Low Pressure ◽  
Transition Model ◽  
Higher Harmonics ◽  
Low Pressure Turbine ◽  
The Third ◽  
Transition Effects ◽  
Transition Models

This is the third part of a series of three papers on the simulation of turbulence and transition effects in a multistage low pressure turbine. The third part of the series deals with the detailed comparison of the Harmonic Balance calculations with the full wheel simulations and measurements for the two-stage low-pressure turbine. The Harmonic Balance simulations were carried out in two confingurations, either using only the 0th harmonic in the turbulence and transition model or additional in all harmonics. The same Menter SST two-equation k–ω turbulence model along with Menter and Langtrys two-equation γ–Reθ transition model is used in the Harmonic Balance simulation as in the full wheel simulations. The measurements on the second stator ofthe low-pressure turbine have been carried out separately for downstream and upstream influences. Thus, a dedicated comparison of the downstream and upstream influences of the flow to the second stator is possible. In the Harmonic Balance calculations, the influences of the not directly adjacent blade, i.e. the first stator, were also included in the second stator In the first analysis, however, it was shown that the consistency with the full wheel configuration and the measurement in this case was not as good as expected. From the analysis ofthe full wheel simulation, we found that there is a considerable variation in the order ofmagnitude ofthe unsteady values in the second stator. In a further deeper consideration of the configuration, it is found that modes are reflected in upstream rows and influences the flow in the second stator. After the integration of these modes into the Harmonic Balance calculations, a much better agreement was reached with results ofthe full wheel simulation and the measurements. The second stator has a laminar region on the suction side starting at the leading edge and then transition takes place via a separation or in bypass mode, depending on the particular blade viewed in the circumferential direction. In the area oftransition, the clear difference between the calculations without and with consideration ofthe higher harmonics in the turbulence and transition models can be clearly seen. The consideration ofthe higher harmonics in the turbulence and transition models results an improvement in the consistency.

Optimizing Location and Relocation of Response Units in Guarding Critical Facilities

2005 ◽  
Vol 1923 (1) ◽  
pp. 127-136 ◽  
Author(s):  
Aamod Sathe ◽  
Elise Miller-Hooks
Keyword(s):  
Transportation Network ◽  
Computational Effort ◽  
Optimal Location ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Public And Private ◽  
Emergency Operations ◽  
Response Unit ◽  
Critical Facilities ◽  
Military Units

The ability to locate military units or equipment, police forces, and first responders optimally and to relocate idle units quickly in response to changing conditions is crucial to a country's ability to guard its critical facilities. Such facilities include vital components of the transportation infrastructure, government and monumental buildings, locations of large gatherings, emergency operations centers, and public and private utilities and communications facilities. In this paper, the problem of making optimal location and relocation decisions for a fixed fleet of response units in a transportation network, where travel conditions are uncertain, is addressed. A mixed integer linear program with multiple objectives (maximize secondary coverage and minimize cost) is presented. Because exact solution of such problems may require considerable computational effort, a metaheuristic based on the principles of genetic algorithms is proposed. The heuristic seeks the set of Pareto-optimal location and relocation decisions for each network state. All facilities of concern must be covered by at least one response unit. If the state of the network changes so that coverage is lost (e.g., travel times increase or a response unit is no longer available), one or more of the response units must be relocated. These relocation decisions are also addressed.

scholarly journals Locating Multiple Size and Multiple Type of Charging Station for Battery Electricity Vehicles

2018 ◽  
Vol 10 (9) ◽  
pp. 3267 ◽  
Author(s):  
Shaohua Cui ◽  
Hui Zhao ◽  
Huijie Wen ◽  
Cuiping Zhang
Keyword(s):  
Travel Time ◽  
Electric Vehicles ◽  
Sensitivity Analyses ◽  
Mixed Integer ◽  
Range Limit ◽  
Mixed Integer Linear Program ◽  
Charging Station ◽  
Different Types ◽  
Initial Charge ◽  
Charging Stations

As environmental and energy issues have attracted more and more attention from the public, research on electric vehicles has become extensive and in-depth. As driving range limit is one of the key factors restricting the development of electric vehicles, the energy supply of electric vehicles mainly relies on the building of charging stations, battery swapping stations, and wireless charging lanes. Actually, the latter two kinds of infrastructure are seldom employed due to their immature technology, relatively large construction costs, and difficulty in standardization. Currently, charging stations are widely used since, in the real world, there are different types of charging station with various levels which could be suitable for the needs of network users. In the past, the study of the location charging stations for battery electric vehicles did not take the different sizes and different types into consideration. In fact, it is of great significance to set charging stations with multiple sizes and multiple types to meet the needs of network users. In the paper, we define the model as a location problem in a capacitated network with an agent technique using multiple sizes and multiple types and formulate the model as a 0–1 mixed integer linear program (MILP) to minimize the total trip travel time of all agents. Finally, we demonstrate the model through numerical examples on two networks and make sensitivity analyses on total budget, initial quantity, and the anxious range of agents accordingly. The results show that as the initial charge increases or the budget increases, travel time for all agents can be reduced; a reduction in range anxiety can increase travel time for all agents.

scholarly journals Clearing Kidney Exchanges via Graph Neural Network Guided Tree Search (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13989-13990
Author(s):  
Zeyu Zhao ◽  
John P. Dickerson
Keyword(s):  
Neural Network ◽  
Independent Set ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Tree Search ◽  
Scalable Algorithms ◽  
Monte Carlo Tree Search ◽  
Kidney Exchange ◽  
Stage Renal Disease

Kidney exchange is an organized barter market that allows patients with end-stage renal disease to trade willing donors—and thus kidneys—with other patient-donor pairs. The central clearing problem is to find an arrangement of swaps that maximizes the number of transplants. It is known to be NP-hard in almost all cases. Most existing approaches have modeled this problem as a mixed integer program (MIP), using classical branch-and-price-based tree search techniques to optimize. In this paper, we frame the clearing problem as a Maximum Weighted Independent Set (MWIS) problem, and use a Graph Neural Network guided Monte Carlo Tree Search to find a solution. Our initial results show that this approach outperforms baseline (non-optimal but scalable) algorithms. We believe that a learning-based optimization algorithm can improve upon existing approaches to the kidney exchange clearing problem.

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