Control co-design of commercial building chiller plant using Bayesian optimization
Not Available
Bhattacharya, Arnab↗
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Results for “Mixed integer optimization”
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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↗
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↗
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↗
Transmission Grid Resiliency Investment Optimization Model With SOCP Recovery Planning
Not Available
24 POWER TRANSMISSION AND DISTRIBUTION↗
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↗
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↗
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↗
Dynamic Programming Method to Optimally Select Power Distribution System Reliability Upgrades
Not Available
42 ENGINEERING↗
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↗
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↗
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↗
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↗
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↗
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↗
Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation
In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.
97 MATHEMATICS AND COMPUTING↗
Optimization Routine for Generating Medical Kits for Spaceflight Using the Integrated Medical Model
The Integrated Medical Model (IMM) is a MATLAB model that provides probabilistic assessment of the medical risk associated with human spaceflight missions.Different simulations or profiles can be run in which input conditions regarding both mission characteristics and crew characteristics may vary. For each simulation, the IMM records the total medical events that occur and “treats” each event with resources drawn from import scripts. IMM outputs include Total Medical Events (TME), Crew Health Index (CHI), probability of Evacuation (pEVAC), and probability of Loss of Crew Life (pLOCL).The Crew Health Index is determined by the amount of quality time lost (QTL). Previously, an optimization code was implemented in order to efficiently generate medical kits. The kits were optimized to have the greatest benefit possible, given amass and/or volume constraint. A 6-crew, 14-day lunar mission was chosen for the simulation and run through the IMM for 100,000 trials. A built-in MATLAB solver, mixed-integer linear programming, was used for the optimization routine. Kits were generated in 10% increments ranging from 10%-100% of the benefit constraints. Conditions wheremass alone was minimized, volume alone was minimized, and where mass and volume were minimizedjointly were tested.
Medical Kit↗
Delivery drone route planning over a battery swapping network
Many enterprises invest on drone delivery research and development to drop off packages at consumers’ doorsteps in a matter of minutes. We study delivery drone route planning over a battery swapping network allowing farther reach by penetrating current battery capacity constraints. A mixed-integer nonlinear programming model is created to plan efficient drone routing over the swapping machines by minimizing the delivery lead time. We develop an exact solution method, evaluate its performance, and compare it with a straightforward nonlinear solver application. A case study highlights the applicability of the model. Data and source code to the solver are publicly shared.
drone battery swapping↗