Advances in Generalized Disjunctive and Mixed-Integer Nonlinear Programming Algorithms and Software for Superstructure Optimization.
Abstract not provided.
Bernal, David↗
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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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Decomposition Strategies for Non-convex Nonlinear Programs.
Abstract not provided.
Rodriguez, Jose Santiago↗
Mixed-Integer Nonlinear Programming Applications: Pyomo Tools and Tailored Strategies.
Abstract not provided.
Laird, Carl Damon↗
A Nonlinear Programming Framework for Estimating Spatial Coupling and Seasonal Transmission Parameters in Disease Transmission.
Abstract not provided.
Laird, Carl↗
Mathematical Programming Models for Shale Oil & Gas Development: A Review and Perspective
Here, in this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming
In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.
97 MATHEMATICS AND COMPUTING↗
DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, developers manual.
The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes.
97 MATHEMATICS AND COMPUTING↗
DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's reference manual.
The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications.
97 MATHEMATICS AND COMPUTING↗
DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual.
The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the DAKOTA software and provides capability overviews and procedures for software execution, as well as a variety of example studies.
97 MATHEMATICS AND COMPUTING↗
Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software
the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.
97 MATHEMATICS AND COMPUTING↗
A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming
We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.
97 MATHEMATICS AND COMPUTING↗
Data-driven simultaneous process optimization and adsorbent selection for vacuum pressure swing adsorption
Technologies for post-combustion carbon capture are essential for the reduction of greenhouse gas emissions to the atmosphere. However, they are still associated with high costs and energy consumption. Intensified processes for carbon capture have the potential to overcome these challenges due to their higher efficiency, lower capital cost, and increased operational flexibility. Here, this work investigates simultaneous optimization of process conditions and adsorbent selection for a modular Vacuum Pressure-Swing Adsorption system designed for CO 2 capture. Both surrogate-based Nonlinear Programming and Mixed-Integer Nonlinear Programming approaches are applied and compared in terms of computational efficiency and solution accuracy. Moreover, process performance results are examined by applying several data analytics techniques to gain insights into the material-process correlations. Data-driven classifiers and neural networks can accurately predict whether a material is likely to satisfy purity, recovery, and energy constraints when operated at optimal process conditions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Comprehensive assessment of deep reinforcement learning approaches for economic dispatch in nuclear-driven microgrids
As the electrical grid integrates more variable renewable energy sources such as wind and solar, the demand for distributed and flexible systems to address this increased variability becomes critical. Nuclear-driven microgrids provide a promising solution by offering stable generation to complement intermittent renewables, ensuring grid reliability and operating efficiency. This paper proposes a recurrent deep reinforcement learning framework for optimal economic dispatch in a nuclear-powered microgrid integrating renewable energy sources, small modular reactors, battery storage systems, and balance-of-plant dynamics. A three-agent control architecture is developed, where demand and renewable energy agents act as forecasters, and a reinforcement learning-based dispatch agent performs real-time energy allocation. A nonlinear programming formulation is first used to generate an optimal baseline for benchmarking. The proposed dispatch controller, based on Proximal Policy Optimization enhanced with Long Short-Term Memory networks, exploits temporal correlations in system dynamics by taking advantage of the time series used as inputs to improve policy robustness under uncertainty. Comparative analysis against established deep reinforcement learning methods, including Proximal Policy Optimization with a feedforward architecture, Soft Actor-Critic, and Twin Delayed Deep Deterministic Policy Gradient, demonstrates superior performance. Numerical results indicate that the proposed controller achieves a 0.39% cost reduction relative to the nonlinear programming benchmark and outperforms other learning-based methods by generating additional revenue of up to 0.35%. All reinforcement learning controllers compute dispatch actions in less than 0.3 s, resulting in a computational speedup of more than three orders of magnitude over the nonlinear programming baseline. The findings of this paper highlight their applicability for real-time operation and control in nuclear-integrated microgrids under volatile operating conditions.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A superstructure-based optimal synthesis of PSA cycles for post-combustion CO2 capture
Recent developments have shown pressure/vacuum swing adsorption (PSA/VSA) to be a promising option to effectively capture CO2 from flue gas streams. In most commercial PSA cycles, the weakly adsorbed component in the mixture is the desired product, and enriching the strongly adsorbed CO2 is not a concern. On the other hand, it is necessary to concentrate CO2 to high purity to reduce CO2 sequestration costs and minimize safety and environmental risks. Thus, it is necessary to develop PSA processes specifically targeted to obtain pure strongly adsorbed component. A multitude of PSA/VSA cycles have been developed in the literature for CO2 capture from feedstocks low in CO2 concentration. However, no systematic methodology has been suggested to develop, evaluate, and optimize PSA cycles for high purity CO2 capture. This study presents a systematic optimization-based formulation to synthesize novel PSA cycles for a given application. In particular, a novel PSA superstructure is presented to design optimal PSA cycle configurations and evaluate CO2 capture strategies. The superstructure is rich enough to predict a number of different PSA operating steps. The bed connections in the superstructure are governed by time-dependent control variables, which can be varied to realize most PSA operating steps. An optimal sequence of operating steps is achieved through the formulation of an optimal control problem with the partial differential and algebraic equations of the PSA system and the cyclic steady state condition. Large-scale optimization capabilities have enabled us to adopt a complete discretization methodology to solve the optimal control problem as a largescale nonlinear program, using the nonlinear optimization solver IPOPT. The superstructure approach is demonstrated for case studies related to post-combustion CO2 capture. In particular, optimal PSA cycles were synthesized, which maximize CO2 recovery for a given purity, and minimize overall power consumption. The results show the potential of the superstructure to predict PSA cycles with up to 98% purity and recovery of CO2. Moreover, for recovery of around 85% and purity of over 90%, these cycles can recover CO2 from atmospheric flue gas with a low power consumption of 465 kWh tonne 1 CO2. The approach presented is, therefore, very promising and quite useful for evaluating the suitability of different adsorbents, feedstocks, and operating strategies for PSA, and assessing its usefulness for CO2 capture.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Optimal Network Topology for Node-Breaker Representations With AC Power Flow Constraints
It has been demonstrated that network topology optimization (NTO) may change the topology of power system networks, and consequently, provide additional flexibility to reduce network congestion and violations. Most NTO problems are formulated based on the bus-branch model in which it is challenging to represent a realistic picture of all substation configurations. In this paper, we explore advantages of substation reconfiguration modeling based on node-breaker representations for NTO problem with full nonlinear alternating current power flow. It also proposes a tailored solution algorithm to solve this nonconvex mixed-integer nonlinear programming through the outer approximation method. The proposed solution approach iterates between a mixed-integer linear programming and a nonlinear subproblem. Additional enhancements to further accelerate the iteration process are illustrated. Numerical case studies demonstrate the relative economic and operational impact of optimal network topology with node-breaker representations.
42 ENGINEERING↗
Subdifferential of Optimal Value Functions in Nonlinear Infinite Programming
This paper presents an exact formula for computing the normal cones of the constraint set mapping including the Clarke normal cone and the Mordukhovich normal cone in infinite programming under the extended Mangasarian-Fromovitz constraint qualification condition. Then, we derive an upper estimate as well as an exact formula for the limiting subdifferential of the marginal/optimal value function in a general Banach space setting.
97 MATHEMATICS AND COMPUTING↗
Designing a drone delivery network with automated battery swapping machines
Drones are projected to alter last-mile delivery, but their short travel range is a concern. In this study, we propose a drone delivery network design using automated battery swapping machines (ABSMs) to extend ranges. The design minimizes the long-term delivery costs, including ABSM investment, drone ownership, and cost of the delivery time, and locates ABSMs to serve a set of customers. We build a mixed-integer nonlinear program that captures the nonlinear waiting time of drones at ABSMs. To solve the problem, we create an exact solution algorithm that finds the globally optimal solution using a derivative-supported cutting-plane method. To validate the applicability of our program, we conduct a case study on the Chicago Metropolitan area using cost data from leading ABSM manufacturer and geographical data from the planning and operations language for agent-based regional integrated simulation (more commonly known as POLARIS). A sensitivity analysis identifies that ABSM service times and costs are the key parameters impacting the long-term adoption of drone delivery.
25 ENERGY STORAGE↗