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DOE OSTI2019

The Quantum Alternating Operator Ansatz on Maximum k -Vertex Cover

The Quantum Alternating Operator Ansatz is a generalization of the Quantum Approximate Optimization Algorithm (QAOA) designed for finding approximate solutions to combinatorial optimization problems with hard constraints. In this paper, we study Maximum k-Vertex Cover under this ansatz due to its modest complexity, while still being more complex than the well studied problems of Max-Cut and Max E3-LIN2. Our approach includes (i) a performance comparison between easy-to-prepare classical states and Dicke states as starting states, (ii) a performance comparison between two XY -Hamiltonian mixing operators: the ring mixer and the complete graph mixer, (iii) an analysis of the distribution of solutions via Monte Carlo sampling, and (iv) the exploration of efficient angle selection strategies.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2005

Low-thrust orbit transfer optimization with refined Q-law and multi-objective genetic algorithm

An optimization method for low-thrust orbit transfers around a central body is developed using the Q-law and a multi-objective genetic algorithm. in the hybrid method, the Q-law generates candidate orbit transfers, and the multi-objective genetic algorithm optimizes the Q-law control parameters in order to simultaneously minimize both the consumed propellant mass and flight time of the orbit tranfer. This paper addresses the problem of finding optimal orbit transfers for low-thrust spacecraft.

low-thrust orbit transfer↗

DOE OSTI2020

Dynamic optimization and economic evaluation of flexible heat integration in a hybrid concentrated solar power plant

Hybridization of concentrated solar power (CSP) plants provides flexibility in operation that can drastically improve the solar-to-electric (STE) efficiency and levelized cost of electricity (LCOE) relative to standalone CSP plants. Flexible heat integration (FHI) is a novel concept where the collection and integration of CSP within a power plant is modified relative to the amount of solar energy available. FHI improves the thermal efficiency of a hybrid solar tower steam Rankine cycle power plant but leads to increased pumping needs due to continuously elevated molten salt flow rates through the collection system, which can negatively impact STE efficiency. The present work is carried out to maximize the STE efficiency of a hybrid CSP plant utilizing FHI by employing a dynamic optimization framework where a genetic algorithm optimizes the operation of the plant over a given solar irradiance profile. The study concerns a plant hypothetically located in Salt Lake City, Utah. Here, the optimization results confirm the accuracy of a predictive heuristic where the preferred operation of the plant can be estimated relative to local peaks in the incident power generated by the heliostat collection field. The optimized FHI operation demonstrates a yearly STE efficiency of 13.8%, whereas the equivalent base-level hybrid and solar-only plants exhibit solar efficiencies of 13.4% and 11.2%, respectively. Economic analysis shows that FHI reduces yearly natural gas costs, leading to a $\$0.5$/MWh reduction in LCOE relative to the base-level hybrid configuration. Overall, the results show that hybrid FHI schemes exhibit economic benefits along with observed thermodynamic improvements.

14 SOLAR ENERGY↗

DOE OSTI2023

A decision support tool for e-waste recycling operations using the hen-and-chicks bio-inspired optimization metaheuristic

E-waste from end-of-life electrical and electronic devices is one of the fastest growing waste streams from households and businesses. E-waste recycling yields environmental sustainability and economic benefits. Due to continuous changes in e-waste types and compositions, recycling businesses face challenges to optimize their operational configuration to achieve better economic and environmental performance. To help e-waste recyclers mitigate this problem, we have developed a modular decision support tool called the Comprehensive Manufacturing Assessment Tool (CMAT) that can simulate both e-waste recycling operations and economics. This tool can give valuable insights regarding the profitability of the entire operation and different e-waste types. In addition, a new bio-inspired metaheuristic optimization algorithm, hen-and-chicks optimization (HACO), was developed to assign manpower to different workstations to maximize operational efficiencies. According to the results of our case study, laptops, desktops, and computer peripherals are the three electronic waste products that produce the most profit. Our examination of the sensitivity of material prices shows that the price of steel has the most significant influence on total profit, because it is the most widely used material in the majority of electronic devices. We have released the decision support tool as open-source software under a general public license. It could be customized for other recycling industries beyond e-waste to achieve business sustainability by making their operations more efficient.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2019

Optimization of processor allocation for domain decomposed Monte Carlo calculations

Load imbalance plagues domain decomposed Monte Carlo calculations when sources are not uniform. Parallel efficiency for domain decomposed Monte Carlo transport calculations improves through a nonuniform allocation of processors over subdomains. In this work, we optimize the allocation with runtime diagnostics collected during a calibration step, then complete the full calculation. The diagnostic-based approach is compared to implicit filtering, an optimization algorithm for bound constrained noisy optimization problems. Finally, we consider both forward and hybrid radiation transport calculations to measure performance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

LOGOS

LOGOS is a software package which contains a set of discrete optimization models that can be employed for capital budgeting optimization problems. More specifically, provided a set of items (characterized by cost and reward values) and constraints, these models select the best combination of items which maximizes overall reward and satisfies the provided constraints. The developed models are based on different versions of the knapsack optimization algorithms. Two main classes of optimization models have been initially developed: deterministic and stochastic. Stochastic optimization models evolve deterministic models by explicitly considering data uncertainties (associated to constraints or item cost and reward). These models can be employed as stand-alone models or interfaced with the INL developed RAVEN code to propagate data uncertainties and analyze the generated data (i.e., sensitivity analysis).

Wang, Congjian↗

DOE OSTI2017

Ultra-short beam expander with segmented curvature control: the emergence of a semi-lens

We introduce direct curvature control in designing a segmented beam expander, and explore novel design possibilities for ultra-compact beam expanders. Assisted by the particle swarm optimization algorithm, we search for an optimal curvature-controlled multi-segment taper that maintains width continuity. Counterintuitively, the optimization yields a structure with abrupt width discontinuity and width compression features. Through spatial phase and parameterized analysis, a semi-lens feature is revealed that helps to flatten the wavefront at the output end for higher coupling efficiency. Such functionality cannot be achieved by normal tapers in a short distance. The structure is fabricated and characterized experimentally. By a figure of merit that accounts for expansion ratio, length, and efficiency, this structure outperforms an adiabatic taper by 9 times.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Furthermore, extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

HERON as a Tool for LWR Market Interaction in a Deregulated Market

This document reports the development of HERON (Holistic Energy Resource Optimization Network), a newly-developed RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization, to technoeconomic analysis in a deregulated market. A short description of the HERON plugin is provided, and the release process is described. HERON as a plugin enables RAVEN to perform stochastic technoeconomic analysis of grid-energy systems in a generic approach. The primary function of HERON is to generate the complex RAVEN workflows necessary to optimize component capacities under stochastic systems. HERON is capable of analyzing systems with complex components transferring a variety of commodities, including production components and varied markets. HERON is capable of optimizing high-resolution dispatch for such systems and guiding stochastic optimization algorithms in RAVEN for finding optimal component capacities. In particular, this document demonstrates the application of HERON to systems with deregulated markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

Crystal Structure Prediction of Binary Alloys via Deep Potential

Predicting crystal structure has been a challenging problem in physics and materials science for a long time. A reliable energy calculation engine combined with an efficient global search algorithm, such as particle swarm optimization algorithm or genetic algorithm, is needed to conduct crystal structure prediction. In recent years, machine learning-based interatomic potential energy surface models have been proposed, potentially allowing us to perform crystal structure prediction for systems with the accuracy of density functional theory (DFT) and the speed of empirical force fields. In this paper, we employ a previously developed Deep Potential model to predict the intermetallic compound of the aluminum–magnesium system, and find six meta-stable phases with negative or nearly zero formation energy. In particular, Mg 12 Al 8 shows excellent ductility and Mg 5 Al 27 has a high Young's modulus. Based on our benchmark results, we propose a relatively robust structure screening criterion that selects potentially stable structures from the Deep Potential-based convex hull and performs DFT refinement. By using this criterion, the computational cost needed to construct the convex hull with ab initio accuracy can be dramatically reduced.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2000

First-Order Frameworks for Managing Models in Engineering Optimization

Approximation/model management optimization (AMMO) is a rigorous methodology for attaining solutions of high-fidelity optimization problems with minimal expense in high- fidelity function and derivative evaluation. First-order AMMO frameworks allow for a wide variety of models and underlying optimization algorithms. Recent demonstrations with aerodynamic optimization achieved three-fold savings in terms of high- fidelity function and derivative evaluation in the case of variable-resolution models and five-fold savings in the case of variable-fidelity physics models. The savings are problem dependent but certain trends are beginning to emerge. We give an overview of the first-order frameworks, current computational results, and an idea of the scope of the first-order framework applicability.

Alexandrov, Natlia M.↗

NASA NTRS2010

Aircraft Trajectory Optimization and Contrails Avoidance in the Presence of Winds

There are indications that persistent contrails can lead to adverse climate change, although the complete effect on climate forcing is still uncertain. A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectories are developed by solving a non-linear optimal control problem with path constraints. The regions of airspace favorable to persistent contrails formation are modeled as penalty areas that aircraft should avoid and are adjustable. The tradeoff between persistent contrails formation and additional fuel consumption is investigated, with and without altitude optimization, for 12 city-pairs in the continental United States. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a two percent increase in total fuel consumption can reduce the total travel times through contrail regions by more than six times. Allowing further increase in fuel consumption does not seem to result in proportionate decrease in contrail travel times.

Ng, Hok K.↗

NASA NTRS2010

Concepts and Challenges for Environmentally Friendly En Route Operations

A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectory is derived using Singular Perturbation Method. The regions of airspace favorable to persistent contrails formation are modeled as high-risk areas that aircraft should avoid and are adjustable. The tradeoffs between persistent contrails formation and additional travel time are investigated for wind-optimal trajectories and various contrails-avoidance trajectories at 10 different cruising altitudes for flights departing from Chicago and San Diego to New York. The additional travel times required for avoiding 100% persistent contrails formation at various flight altitudes ranged from approximately 0% to 4.3% for flights from Chicago to New York. For flights between San Diego and New York, additional traveling times vary between 1.3% and 5% depending on the cruise altitude and the percentage of contrail avoidance. Talk will present the results of aircraft fuel consumptions that are proportional to the travel time for cruising aircraft.

Sridhar, Banavar↗

NASA NTRS2012

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

Mixed Integer Programming↗

DOE OSTI2023

A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- ${\boldsymbol{\mathcal{C}^2}}$ Objective

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- ${\boldsymbol{\mathcal{C}^2}}$ objective functions is proposed and analyzed. Upper- ${\boldsymbol{\mathcal{C}^2}}$ is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- ${\boldsymbol{\mathcal{C}^2}}$ objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- ${\boldsymbol{\mathcal{C}^2}}$ problems and a real-world optimal power flow problem used in current power grid industry practices.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Aerodynamic Shape Optimization Using Evolutionary Algorithms

A method for aerodynamic shape optimization based on an evolutionary algorithm approach is presented and demonstrated. Results are presented for a number of model problems to access the effect of algorithm parameters on convergence efficiency and reliability. A transonic viscous airfoil optimization problem, both single and two-objective variations, is used as the basis for a preliminary comparison with an adjoint-gradient optimizer. The evolutionary algorithm is coupled with a transonic full potential flow solver and is used to optimize the inviscid flow about transonic wings including multi-objective and multi-discipline solutions that lead to the generation of pareto fronts. The results indicate that the evolutionary algorithm approach is easy to implement, flexible in application and extremely reliable.

Holst, Terry L.↗

DOE OSTI2025

RxnRover/CyRxnOpt

CyRxnOpt aims to provide a single software interface to various optimization algorithms, mainly designed for chemical process optimization applications. CyRxnOpt generalizes the optimization process into four high-level “phases”: Installation, Configuration, Training, and Prediction. This allows developers to program to a general interface for each phase of the optimization, simplifying the development of user-friendly tools to lower the barrier of entry into chemical process optimization, especially for automated laboratory workflows which can greatly benefit from access to various optimization techniques. It is also designed so researchers can easily add new or existing algorithms into existing workflows in a user-friendly manner.

Kulathunga, Dulitha Prasanna [Iowa State Universit↗

NASA NTRS1980

Algorithm for fixed-range optimal trajectories

An algorithm for synthesizing optimal aircraft trajectories for specified range was developed and implemented in a computer program written in FORTRAN IV. The algorithm, its computer implementation, and a set of example optimum trajectories for the Boeing 727-100 aircraft are described. The algorithm optimizes trajectories with respect to a cost function that is the weighted sum of fuel cost and time cost. The optimum trajectory consists at most of a three segments: climb, cruise, and descent. The climb and descent profiles are generated by integrating a simplified set of kinematic and dynamic equations wherein the total energy of the aircraft is the independent or time like variable. At each energy level the optimum airspeeds and thrust settings are obtained as the values that minimize the variational Hamiltonian. Although the emphasis is on an off-line, open-loop computation, eventually the most important application will be in an on-board flight management system.

Lee, H. Q.↗