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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Connected Vehicle-Based Traffic Signal Coordination

This study presents a connected vehicles (CVs)-based traffic signal optimization framework for a coordinated arterial corridor. The signal optimization and coordination problem are first formulated in a centralized scheme as a mixed-integer nonlinear program (MINLP). The optimal phase durations and offsets are solved together by minimizing fuel consumption and travel time considering an individual vehicle’s trajectories. Due to the complexity of the model, we decompose the problem into two levels: an intersection level to optimize phase durations using dynamic programming (DP), and a corridor level to optimize the offsets of all intersections. In order to solve the two-level model, a prediction-based solution technique is developed. The proposed models are tested using traffic simulation under various scenarios. Compared with the traditional actuated signal timing and coordination plan, the signal timing plans generated by solving the MINLP and the two-level model can reasonably improve the signal control performance. When considering varies vehicle types under high demand levels, the proposed two-level model reduced the total system cost by 3.8% comparing to baseline actuated plan. MINLP reduced the system cost by 5.9%. It also suggested that coordination scheme was beneficial to corridors with relatively high demand levels. For intersections with major and minor street, coordination conducted for major street had little impacts on the vehicles at the minor street.

42 ENGINEERING↗
DOE OSTI2019

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

We develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several large-scale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Generalized mathematical models in design optimization

The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

Papalambros, Panos Y.↗
DOE OSTI2019

From graphical to model-based distillation column design: A McCabe-Thiele-inspired mathematical programming approach

We propose a mixed-integer nonlinear programming (MINLP) model for simple and complex distillation column design and optimization. The model is based upon the concepts and equations underpinning the McCabe-Thiele method. Generalizing this method, we introduce material balances at various locations of the column and employ binary variables to determine the optimal number of trays and optimal feed locations. We model the vapor–liquid equilibrium using continuous piecewise linear approximating functions. The model is extended to account for multicomponent mixtures and non-constant-molar overflow. We also discuss how to estimate the minimum number of trays and the minimum reflux ratio.

42 ENGINEERING↗
NASA NTRS1973

A method for digital image registration using a mathematical programming technique

A new algorithm based on a nonlinear programming technique to correct the geometrical distortions of one digital image with respect to another is discussed. This algorithm promises to be superior to existing ones in that it is capable of treating localized differential scaling, translational and rotational errors over the whole image plane. A series of piece-wise 'rubber-sheet' approximations are used, constrained in such a manner that a smooth approximation over the entire image can be obtained. The theoretical derivation is included. The result of using the algorithm to register four channel S065 Apollo IX digitized photography over Imperial Valley, California, is discussed in detail.

Yao, S. S.↗
DOE OSTI2024

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗
NASA NTRS2022

Alternative regularizations for Outer-Approximation algorithms for convex MINLP

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Convex Mixed-integer nonlinear programming↗
NASA NTRS2024

A Convexification-Based Outer-Approximation Method for Convex and Nonconvex MINLP

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer-Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a Branch-and-Bound method for both convex and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have been developed and incorporated into the open-source Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were conducted, validating the effectiveness and reliability of our proposed algorithms. These tests highlight the improvements achieved by incorporating convexification and domain reduction techniques into the Outer-Approximation and Branch-and-Bound methods.

Optimization↗
DOE OSTI2021

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↗
DOE OSTI2023

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Here, in this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Technique for Optimization Design of the Flow Path of a Main Oil Pump

A method for the design of the flow path of a main oil pump by means of which the geometry of the flow path may be optimized to achieve maximum energy efficiency of the pump is given. The method is based on mathematical simulation of the hydrodynamic processes that occur in the flow path of a pump using the ANSYS system of finite-element analysis combined with methods of nonlinear programming.

42 ENGINEERING↗
NASA NTRS1989

An algorithm for the solution of dynamic linear programs

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

Psiaki, Mark L.↗
DOE OSTI2018

Constructing the Pareto front for multi-objective Markov chains handling a strong Pareto policy approach

In this paper, we present a multi-objective solution of the Pareto front for a certain class of discrete-time ergodic controllable Markov chains. For solving the problem, we transform the original multi-objective problem into an equivalent nonlinear programming problem implementing the Lagrange principle. We then propose to adopt the Tikhonov’s regularization method to ensure the convergence of the cost functions to a unique point into the Pareto front. We show that Pareto policies are characterized as optimal policies. One of the fundamental problems related to the construction of the Pareto front is the existence and characterization of both, Pareto and strong Pareto policies. By introducing the Tikhonov’s regularizator, we ensure the existence of strong Pareto policies. This paper proposes a real solution to this problem. We formulate the original problem considering several constraints: (a) we employ the c-variable method for the introduction of linear constraints over the nonlinear problem and (b) restrict the cost functions, allowing points in the Pareto front to have a small distance from one another. The constraints imposed by the c-variable method make the problem computationally tractable and the restriction imposed by the small distance change ensures the continuation of the Pareto front. The resulting equation in this nonlinear system is an optimization problem for which the necessary and efficient condition of a minimum is solved using the projected gradient method. Moreover, we also prove the convergence conditions and compute the estimate rate of convergence of variables corresponding to the Lagrange principle and the Tikhonov’s regularization, respectively. We provide all the details needed to implement the proposed method in an efficient way. The usefulness of the method is successfully demonstrated by a numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems

Here we present a decomposition approach for obtaining good feasible solutions for the security-constrained, alternating-current, optimal power flow (SC-AC-OPF) problem at an industrial scale and under real-world time and computational limits. The approach was designed while preparing and participating in ARPA-E’s Grid Optimization Competition (GOC) Challenge 1. The challenge focused on a near-real-time version of the SC-AC-OPF problem, where a base operating point is optimized, taking into account possible single-element contingencies, after which the system adapts its operating point following the response of automatic frequency droop controllers and voltage regulators. Our solution approach for this problem relies on state-of-the-art nonlinear programming algorithms, and it employs nonconvex relaxations for complementarity constraints, a specialized two-stage decomposition technique with sparse approximations of recourse terms and contingency ranking and prescreening. The paper describes and justifies our approach and outlines the features of its implementation, including functions and derivatives evaluation, warm-starting strategies, and asynchronous parallelism. We discuss the results of the independent benchmark of our approach by ARPA-E’s GOC team in Challenge 1, where it was found to consistently produce high-quality solutions across a wide range of network sizes and difficulty, and conclude by outlining future extensions of the approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimizing Vehicle Fleet and Assignment for Concentrating Solar Power Plant Heliostat Washing

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. Furthermore, these solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

14 SOLAR ENERGY↗
DOE OSTI2018

Optimization of groundwater artificial recharge systems using a genetic algorithm: a case study in Beijing, China

An optimization approach is used for the operation of groundwater artificial recharge systems in an alluvial fan in Beijing, China. The optimization model incorporates a transient groundwater flow model, which allows for simulation of the groundwater response to artificial recharge. The facilities’ operation with regard to recharge rates is formulated as a nonlinear programming problem to maximize the volume of surface water recharged into the aquifers under specific constraints. This optimization problem is solved by the parallel genetic algorithm (PGA) based on OpenMP, which could substantially reduce the computation time. To solve the PGA with constraints, the multiplicative penalty method is applied. In addition, the facilities’ locations are implicitly determined on the basis of the results of the recharge-rate optimizations. Two scenarios are optimized and the optimal results indicate that the amount of water recharged into the aquifers will increase without exceeding the upper limits of the groundwater levels. Optimal operation of this artificial recharge system can also contribute to the more effective recovery of the groundwater storage capacity.

58 GEOSCIENCES↗