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DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗

DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗

DOE OSTI2022

Feedback Control Approaches for Restoration of Power Grids from Blackouts

The automated restoration of power systems with variable energy resources is a timely problem to tackle. Automated restoration advice can support operators in deciding on strategic actions to restore power grids from a blackout with a mix of conventional and renewable generation resources. To this end, this paper frames the restoration process of power grids with solar resources as a nonlinear dynamic model with algebraic constraints in discrete time which is steered by feedback control loops. We discuss two feedback-control strategies based on greedy and reinforcement learning algorithms, and contrast their performance with restoration plans generated by a mixed-integer linear program. We found that the reinforcement learning algorithm infers restoration actions faster than the greedy one. However, the tuning process of the reinforcement learning parameters is slower than for the greedy one.

machine learning↗

DOE OSTI2021

Multilane Automated Driving With Optimal Control and Mixed-Integer Programming

Road vehicle lane changes often initiate traffic disturbances and can therefore impact road networks’ energy and time efficiency. Furthermore, unexpected changes in traffic conditions may also render lane changes counterproductive for the lane-changing vehicle. Vehicle-to-vehicle connectivity combined with anticipative control could address these challenges via improved lane change decisions by automated vehicles. In a move toward this objective, receding horizon control cast as a mixed-integer quadratic program is used to plan lane changing and acceleration in a coupled optimization. A long-term pacing module, based on Pontryagin’s minimum principle from optimal control theory, sets terminal and input references for receding horizon control to target a user’s expected travel time. To remove nonlinear vehicle dynamics from the receding horizon controller, lane change commands are passed to a pure pursuit steering module whose response is approximated by a second-order linear model. Here, comparison against a rule-based reactive algorithm in arterial and highway scenarios shows an 8.9%–13.7% reduction in energy consumption and a 5.2%–10.3% reduction in the travel time, along with navigational improvements.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Piecewise polyhedral formulations for a multilinear term

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

42 ENGINEERING↗

DOE OSTI2020

An Optimization-Based Planning Tool for On-Demand Mobility Service Operations

Regions worldwide are adopting and exploring low-speed automated electric shuttle (AES) service as an on-demand shared mobility service in dense geofenced urban areas. Building on this concept, the National Renewable Energy Laboratory (NREL) recently developed the Automated Mobility District (AMD) toolkit. The AMD toolkit—comprising of a travel micro-simulation model and an energy estimation model—estimates the mobility and energy impacts of a given shuttle configuration within an AMD. Early-stage AMD deployments need to find optimal operational configurations that include: (a) passenger capacity of an AES, (b) time-dependent routes, and (c) fleet size (AES units) to satisfy the demand for the region. This research extends the AMD toolkit functionality by developing an optimization-based planning module that will assist in the operations of AES units. We developed a constrained mixed-integer program accounting for passenger waiting time, battery range, and passenger capacity of AES units. For scalability, we demonstrated the Tabu search-based solution technique for a real-world network—a proposed AMD deployment in Greenville, South Carolina, USA. Compared to rule-based operations, our developed solution yields higher travel time and energy savings for the network at different demand levels. The sensitivity analyses for waiting time thresholds indicate nonlinearity in the system performance, underscoring the need to meet shared-use mobility user-level expectations. The developed optimization framework can be adapted and extended to accommodate different categories of shared-use on-demand mobility services.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

DOE OSTI2019

Designing Metabolic Division of Labor in Microbial Communities

ABSTRACT Microbes face a trade-off between being metabolically independent and relying on neighboring organisms for the supply of some essential metabolites. This balance of conflicting strategies affects microbial community structure and dynamics, with important implications for microbiome research and synthetic ecology. A “gedanken” (thought) experiment to investigate this trade-off would involve monitoring the rise of mutual dependence as the number of metabolic reactions allowed in an organism is increasingly constrained. The expectation is that below a certain number of reactions, no individual organism would be able to grow in isolation and cross-feeding partnerships and division of labor would emerge. We implemented this idealized experiment using in silico genome-scale models. In particular, we used mixed-integer linear programming to identify trade-off solutions in communities of Escherichia coli strains. The strategies that we found revealed a large space of opportunities in nuanced and nonintuitive metabolic division of labor, including, for example, splitting the tricarboxylic acid (TCA) cycle into two separate halves. The systematic computation of possible solutions in division of labor for 1-, 2-, and 3-strain consortia resulted in a rich and complex landscape. This landscape displayed a nonlinear boundary, indicating that the loss of an intracellular reaction was not necessarily compensated for by a single imported metabolite. Different regions in this landscape were associated with specific solutions and patterns of exchanged metabolites. Our approach also predicts the existence of regions in this landscape where independent bacteria are viable but are outcompeted by cross-feeding pairs, providing a possible incentive for the rise of division of labor. IMPORTANCE Understanding how microbes assemble into communities is a fundamental open issue in biology, relevant to human health, metabolic engineering, and environmental sustainability. A possible mechanism for interactions of microbes is through cross-feeding, i.e., the exchange of small molecules. These metabolic exchanges may allow different microbes to specialize in distinct tasks and evolve division of labor. To systematically explore the space of possible strategies for division of labor, we applied advanced optimization algorithms to computational models of cellular metabolism. Specifically, we searched for communities able to survive under constraints (such as a limited number of reactions) that would not be sustainable by individual species. We found that predicted consortia partition metabolic pathways in ways that would be difficult to identify manually, possibly providing a competitive advantage over individual organisms. In addition to helping understand diversity in natural microbial communities, our approach could assist in the design of synthetic consortia.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗

DOE OSTI2019

OPERATIONAL TOPOLOGY ESTIMATION OF THREE PHASE UNBALANCED POWER DISTRIBUTION SYSTEMS WITH OUTAGES

Distribution grid, in general, is constructionally loopy but a radially operated network. Opening and closing of suitable tie-switches allows transition from one radial topology to another. Tie-switches ensure reliability and provide restoration paths when faults (outages) occur. The estimation of the system's current operational topology is a precursor to implementing any optimal control actions (during normal operation) or restorative actions (during outage condition). The existing literature in topology detection suffers with several limitations including: (1) computationally intensive nonlinear formulations that are not scalable for large distribution systems, (2) methods requiring exhaustive search for the correct topology by enumerating the complete topological search space, and (3) approaches requiring large volumes of time-series measurements and are not applicable for estimating continuously changing operational topology. Furthermore, the existing literature on distribution grid topology estimation cannot be extended to estimate the operational topology during outage conditions. For operational topology estimation during outages, our objective is to estimate both energized radial feeder and the outaged sections. Starting with a radial topology, these methods identify outaged feeder sections and hence, are inapplicable when the current radial operational topology is not known. In this work, we present a mathematical programming approach to estimate the operational topology of a three-phase unbalanced power distribution system under both outage and normal operating conditions. The aforementioned limitations of existing literature were countered by modeling the problem as a mixed-integer linear programming (MILP) problem which minimizes the errors in available measurements while satisfying the power flow and structural constraints of the system. Specically, a minimum weighted least absolute value estimator is proposed that uses the instantaneous line flow measurements, historical/ forecasted load data, and ping measurements from a limited set of smart meters and solves an MILP to identify the operational topology based on a linearized three-phase unbalanced power flow model. The proposed approach is tested on IEEE 123-bus feeder and 1069 bus multi-feeder test system and the numerical results prove the applicability of the proposed method to large three phase unbalanced grids with high errors in measurements. It is observed that the approach performs well even at high percentages of measurement errors.

GANDLURU NAGA, ANANDINI↗

DOE OSTI2020

Approximating Trajectory Constraints With Machine Learning – Microgrid Islanding With Frequency Constraints

Here, we introduce deep earning aided constraint encoding to tackle the frequency-constraint microgrid scheduling problem. The nonlinear function between system operating condition and frequency nadir is approximated by using a neural network, which admits an exact mixed-integer formulation (MIP). This formulation is then integrated with the scheduling problem to encode the frequency constraint. With the stronger representation power of the neural network, the resulting commands can ensure adequate frequency response in a realistic setting in addition to islanding success. The proposed method is validated on a modified 33-node system. Successful islanding with a secure response is simulated under the scheduled commands using a detailed three-phase model in Simulink. The advantages of our model are particularly remarkable when the inertia emulation functions from wind turbine generators are considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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 OSTI2024

Solving the Grid Optimization Competition Challenge 3 Problem

The Grid Optimization Competition Challenge 3 Problem posed a multiperiod security-constrained unit commitment problem with base-case AC power flow. The problem formulation includes binary unit commitment decisions, nonlinear AC power flow and balance, dispatchable loads, and linearized contingency real power flow, among other features. This talk will present a modified consensus ADMM algorithm, which splits the problem into mixed-integer linear and nonlinear components, as a heuristic solution method for this large-scale mixed integer nonlinear program. We will present some computational results from the competition for our implementation and reflect on the challenges of participating the grid optimization competition.

AC power flow↗