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DOE OSTI2016

Limited‐memory adaptive snapshot selection for proper orthogonal decomposition

Summary Reduced order models are useful for accelerating simulations in many‐query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models (ROMs) can have prohibitively expensive memory and floating‐point operation costs in high‐performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time‐stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition‐based ROMs, and memory usage is minimized by computing the singular value decomposition using a single‐pass incremental algorithm. Results for a viscous Burgers' test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full‐order model is recovered to within discretization error. A parallel version of the resulting method can be used on supercomputers to generate proper orthogonal decomposition‐based ROMs, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space. Copyright © 2016 John Wiley & Sons, Ltd.

Oxberry, Geoffrey M.↗

DOE OSTI2016

Accelerating the Mining of Influential Nodes in Complex Networks through Community Detection

Computing the set of influential nodes with a given size to ensure maximal spread of influence on a complex network is a challenging problem impacting multiple applications. A rigorous approach to influence maximization involves utilization of optimization routines that comes with a high computational cost. In this work, we propose to exploit the existence of communities in complex networks to accelerate the mining of influential seeds. We provide intuitive reasoning to explain why our approach should be able to provide speedups without significantly degrading the extent of the spread of influence when compared to the case of influence maximization without using the community information. Additionally, we have parallelized the complete workflow by leveraging an existing parallel implementation of the Louvain community detection algorithm. We then conduct a series of experiments on a dataset with three representative graphs to first verify our implementation and then demonstrate the speedups. Our method achieves speedups ranging from 3x - 28x for graphs with small number of communities while nearly matching or even exceeding the activation performance on the entire graph. Complexity analysis reveals that dramatic speedups are possible for larger graphs that contain a correspondingly larger number of communities. In addition to the speedups obtained from the utilization of the community structure, scalability results show up to 6.3x speedup on 20 cores relative to the baseline run on 2 cores. Finally, current limitations of the approach are outlined along with the planned next steps.

community detection↗

DOE OSTI2017

ParSplice, Version 1

The ParSplice code implements the Parallel Trajectory Splicing algorithm described in [1]. This method is part of the Accelerated Molecular Dynamics family of techniques developed in Los Alamos National Laboratory over the last 16 years. These methods aim at generating high-quality trajectories of ensembles of atoms in materials. ParSplice uses multiple independent replicas of the system in order to parallelize the generation of such trajectories in the time domain, enabling simulations of systems of modest size over very long timescales. ParSplice includes capabilities to store configurations of the system, to generate and distribute tasks across a large number of processors, and to harvest the results of these tasks to generate long trajectories. ParSplice is a management layer that orchestrate large number of calculations, but it does not perform the actual molecular dynamics itself; this is done by external molecular dynamics engines. [1] Danny Perez, Ekin D Cubuk, Amos Waterland, Efthimios Kaxiras, Arthur F Voter, Long-time dynamics through parallel trajectory splicing, Journal of chemical theory and computation 12, 18 (2015)

Perez, Danny↗

DOE OSTI2017

ParSplice, Version 1

Perez, Danny↗

DOE OSTI2018

A Methodology for the Rapid Development of Scalable HPC Data Services

There is growing evidence in the scientifc computing community that parallel file systems are not sufficient for all HPC storage workloads. This realization has motivated extensive research in new storage system designs. The question of which alternative we should turn towards implies that there could be a single answer satisfying a wide range of very diverse applications. We argue that such a generic solution does not exist. Instead, custom data services should be designed and tailored to the needs of specific applications on specific hardware. Furthermore, custom data services should be designed in close collaboration with users. In this paper, we present a methodology for the rapid development of such data services. This methodology promotes the design of reusable building blocks that can be composed together efficiently through a runtime based on high-performance threading, tasking, and remote procedure calls. We illustrate the success of our methodology by showcasing three examples of data services designed from the same building blocks, yet targeting entirely different applications.

Dorier, Mattieu↗

DOE OSTI2017

CEED-MS8:Initial Integration of CEED Software in ECP Applications

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone we report on the initial integration of CEED software in the selected first-wave ECP/CEED apps and the continued exploration of other ECP applications as second-wave (milestone CEED-MS23) and third-wave (milestone CEED-MS35) ECP/CEED application candidates. An extensive evaluation of various approaches for GPU acceleration of the CEED computational motives is also a major focus of the report, both in the settings of CEED’s Nekbone and Laghos miniapps, as well as versions of CEED’s bake-off problems (introduced in milestone CEED-MS6). The first-wave ECP applications targeted for coupling with CEED software include the ExaSMR and MARBL applications. We also report on near-term collaboration with the seed-funded Urban Systems project, as well as engagements with ACME, ExaAM, GEOS and the Application Assessment and Proxy App projects. The ExaSMR project involves coupled thermal-hydraulics/neutronics, with the latter based on Monte Carlo methods and the former based on high-order discretizations of the Navier-Stokes and energy equations for accurate simulation of turbulent transport. The project requires fast and efficient turbulence simulation capabilities that will scale to exascale platforms. Work within CEED will ensure that all aspects of the Nek5000 workflow scale to the target problem space, which involves > 10 10 degrees of freedom in typical production runs. CEED’s goal is to provide implementations that perform with maximum attainable efficiency and deliver low turn-around times. A deliverable for this milestone is beta-release of the GPU-based variant of Nek5000. MARBL is targeting high-energy-density physics problems, including single fluid multi-material hydrodynamics and radiation/magnetic diffusion simulation, with applications in inertial confined fusion, pulsed power experiments, and equation of state/material strength analysis. The code uses high-order methods based arbitrary Lagrangian-Eulerian, direct Eulerian, and unstructured adaptive mesh refinement. A deliverable for this milestone is collaboration with MARBL for improved performance based on partially-assembled operators. The Urban exascale project is planning to couple real-time data with high performance simulations to study particulate transport in cities. Nek5000 will be used for large eddy and RANS (Reynolds-averaged Navier-Stokes) simulations of turbulent transport in these domains. Areas where the CEED team is aiding the Urban Canyon group include creating high-order meshes for urban geometries and developing boundary conditions appropriate for simulations close to real-life urban conditions. The software artifacts delivered as part of this milestone include GPU-enabled versions of the Nekbone and Laghos miniapps, which are provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY17, including: the CEED first annual meeting and participation of CEED researchers in a variety of outreach activities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion 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 exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Collaborative simulations and experiments for a novel yield model of coal devolatilization in oxy-coal combustion conditions

Oxy-coal combustion is an emerging low-cost “clean coal” technology for emissions reduction and Carbon Capture and Sequestration (CCS). The use of Computational Fluid Dynamics (CFD) tools is crucial for the development of cost-effective oxy-fuel technologies and the minimization of environmental concerns at industrial scale. The coupling of detailed chemistry models and CFD simulations is still challenging, especially for large-scale plants, because of the high computational efforts required. The development of scale-bridging models is therefore necessary, to find a good compromise between computational efforts and the physical-chemical modeling precision. This paper presents a procedure for scale-bridging modeling of coal devolatilization, in the presence of experimental error, that puts emphasis on the thermodynamic aspect of devolatilization, namely the final volatile yield of coal, rather than kinetics. The procedure consists of an engineering approach based on dataset consistency and Bayesian methodology including Gaussian-Process Regression (GPR). Experimental data from devolatilization tests carried out in an oxy-coal entrained flow reactor were considered and CFD simulations of the reactor were performed. Jointly evaluating experiments and simulations, a novel yield model was validated against the data via consistency analysis. In parallel, a Gaussian-Process Regression was performed, to improve the understanding of the uncertainty associated to the devolatilization, based on the experimental measurements. Potential model forms that could predict yield during devolatilization were obtained. The set of model forms obtained via GPR includes the yield model that was proven to be consistent with the data. Finally, the overall procedure has resulted in a novel yield model for coal devolatilization and in a valuable evaluation of uncertainty in the data, in the model form, and in the model parameters.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2017

XPRESS: eXascale PRogramming Environment and System Software

The XPRESS project is the research and development of a complete software architecture for Exascale computing. The four major R&D thrusts include: 1) an Exascale lightweight kernel operating system (LXK), based on the Kitten operating system (OS), to manage billion way hardware parallelism, management of faults and power, management of global virtual name space, and other features of future system architectures; 2) a runtime system (HPX-5), co-designed with LXK, based on the ParalleX execution model that supports dynamic resource management and task scheduling; 3) system interfaces for interoperability between the runtime system and both the OS and the runtime system (RIOS); 4) compilation strategies and systems to translate MPI and OpenMP legacy codes to a form that can be run with performance at least as good as a native code implementation. The software architecture development has been driven by performance evaluation of mini-applications developed at Department of Energy Co-Design Centers as well as ancillary in-house developed applications and benchmarks. Research on the ParalleX execution model has been driven by the development of formal semantics and model checkers for the execution model. The major components of the software architecture are: ParalleX execution model – guiding principles for co-design of components of the system stack with advances in locality management and task prioritization through introspection; HPX runtime system – support of application dynamic adaptive resource management, task scheduling, and introspective control policies; LXK operating system – lightweight kernel operating system for order-constant scalability and low/no noise to manage resources; RIOS – a realm of Exascale system operation unique in the XPRESS project that includes the relationship between the new generation of lightweight kernel operating systems and runtime system software; XPI advanced programming model – intermediate form and low-level (readable) programming interface reflecting the ParalleX model, providing a target for source-to- source high level parallel language translation, and supporting early direct programming experimentation and measurement; Performance models & metrics – providing parameters and their mutual sensitivities to guide co-design and quantify operational behavior; Legacy migration – ensuring seamless transition of legacy codes and programming methods to the future generation of ParalleX-based Exascale systems; . Experiments and evaluation – critical to determining degree of effectiveness and likelihood of ultimate success as well as guiding corrective design changes to achieve DOE objectives; and Applications – collaborations with Co-Design Centers and other mission critical codes. The exemplar implementation of the ParalleX execution model, HPX-5, has been released along with five fully ported applications (LULESH, HPCG, SSSP, WAMR, and DASHMM) and multiple microbenchmarks. Using these applications, the system architecture demonstrated dynamic load balancing through active migration, legacy code migration, and data-driven approaches to for graph-like applications. Crucially for Exascale and billion way parallelism, the needs and patterns of irregular applications in HPX-5 were addressed using local flow control rather than relying on globally synchronized data structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

A Scalable HPC Insider Threat Monitoring System

Cyber Equations, Inc. is reporting on the results of its DOE SBIR Phase I project for the development of a Scalable HPC Insider Threat Monitoring System. This final report to the Department of Energy for Task DE-FOA-0001618 covers the period from 02/21/2017 to 02/20/2018 and summarizes the larger research accomplishments, which can be divided in theoretical and laboratory experiments. One of the many challenges for the U.S. Department of Energy (DOE) is the support of the high-performance computing (HPC) centers while providing quality information services, strategic vision, leadership, technical expertise, and capabilities necessary to enable the DOE to deliver effective, efficient, economical, and secure HPC services. In order to realize a secure DOE laboratory enterprise, DOE facilities operations must counter a wide range of cyber insider threats, from unsophisticated adversaries up to advanced, nation state sponsored actors. The DOE laboratories also presents an enormous insider attack surface of an ever-growing number of computers, networks, and devices all running a myriad of software. In addition, the DOE laboratories are connected to a variety of external organizations which multiplies the possibility of insider threat. During this SBIR project Cyber Equations developed a strategic combination of supervised and unsupervised machine learning techniques to control scale and classify whether entities, such as hosts, actors, or documents, are showing suspicious insider behavior. We conducted experiments using real cyber data to show that changes in observable behavior (e.g., changes in outbound traffic patterns) are indicative of attacks executing (e.g., insiders exfiltrating data, bots calling home, or an attack spreading). The features and methods we use, have been used in the anomaly detection research and development community for a significant amount of time and robust implementations are openly available. K-Means clustering, Decision Trees, and Support Vector Machine based classifiers are readily available through the R language and open source H20 machine learning framework. The Cyber Equations approach is novel in its use of these classifiers combined with Hadoop based parallel processing technology. The five stages of processing used by CyberInsider improve scalability and reduce the high number of false positives normally associated with network anomaly detection. In summary, the Cyber Equations has successfully accomplished all of its Phase I tasks and demonstrated the feasibility of the Insider Threat Monitoring System.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Parallel membership queries on very large scientific data sets using bitmap indexes

© 2019 John Wiley & Sons, Ltd. Many scientific applications produce very large amounts of data as advances in hardware fuel computing and experimental facilities. Managing and analyzing massive quantities of scientific data is challenging as data are often stored in specific formatted files, such as HDF5 and NetCDF, which do not offer appropriate search capabilities. In this research, we investigated a special class of search capability, called membership query, to identify whether queried elements of a set are members of an attribute. Attributes that naturally have classification values appear frequently in scientific domains such as category and object type as well as in daily life such as zip code and occupation. Because classification attribute values are discrete and require random data access, performing a membership query on a large scientific data set creates challenges. We applied bitmap indexing and parallelization to membership queries to overcome these challenges. Bitmap indexing provides high performance not only for low cardinality attributes but also for high cardinality attributes, such as floating-point variables, electric charge, or momentum in a particle physics data set, due to compression algorithms such as Word-Aligned Hybrid. We conducted experiments, in a highly parallelized environment, on data obtained from a particle accelerator model and a synthetic data set.

Yildiz, Beytullah↗

DOE OSTI2015

POLARIS: Agent-based modeling framework development and implementation for integrated travel demand and network and operations simulations

Here, we discuss the development of an agent-based modelling software development kit, and the implementation and validation of a model using it that integrates dynamic simulation of travel demand, network supply and network operations. A description is given of the core utilities in the kit: a parallel discrete event engine, interprocess exchange engine, and memory allocator, as well as a number of ancillary utilities: visualization library, database IO library, and scenario manager. The overall framework emphasizes the design goals of: generality, code agility, and high performance. This framework allows the modeling of several aspects of transportation system that are typically done with separate stand-alone software applications, in a high-performance and extensible manner. The issue of integrating such models as dynamic traffic assignment and disaggregate demand models has been a long standing issue for transportation modelers. The integrated approach shows a possible way to resolve this difficulty. The simulation model built from the POLARIS framework is a single, shared-memory process for handling all aspects of the integrated urban simulation. The resulting gains in computational efficiency and performance allow planning models to be extended to include previously separate aspects of the urban system, enhancing the utility of such models from the planning perspective. Lastly, initial tests with case studies involving traffic management center impacts on various network events such as accidents, congestion and weather events, show the potential of the system.

42 ENGINEERING↗

DOE OSTI2024

Optimizing Distributed Training on Frontier for Large Language Models

Large language models (LLMs) have demonstrated remarkable success as foundational models, benefiting various downstream applications through fine-tuning. Loss scaling studies have demonstrated the superior performance of larger LLMs compared to their smaller counterparts. Nevertheless, training LLMs with billions of parameters poses significant challenges and requires considerable computational resources. For example, training a one trillion parameter GPT-style model on 20 trillion tokens requires a staggering 120 million exaflops. This research explores efficient distributed training strategies to extract this computation from Frontier, the world's first exascale supercomputer. We enable and investigate various model and data parallel training techniques, such as tensor parallelism, pipeline parallelism, and sharded data parallelism, to facilitate training a trillion-parameter model on Frontier. We empirically assess these techniques and their associated parameters to determine their impact on memory footprint, communication latency, and GPU's computational efficiency. We analyze the complex interplay among these techniques and find a strategy to combine them to achieve high throughput through hyperparameter tuning. We have identified efficient strategies for training large LLMs of varying sizes through empirical analysis and hyperparameter tuning. For 22 Billion, 175 Billion, and 1 Trillion parameters, we achieved GPU throughputs of 38.38%, 36.14%, and 31.96%, respectively. For the training of the 175 Billion parameter model and the 1 Trillion parameter model, we achieved 100% weak scaling efficiency on 1024 and 3072 Mi250X GPUs, respectively. We also achieved strong scaling efficiencies of 89% and 87% for these two models. We trained these models only tens of iterations instead of training till completion.

Yin, Junqi↗

DOE OSTI2021

High flux boiling heat transfer enhancement using triangle shaped vertical walls in two-phase microchannel heat exchangers

Two-phase heat exchangers allow heat loads to be dissipated with lower fluid flow rates without inducing thermal gradients, and high surface area microchannels further reduce the thermal resistance of these heat exchangers. However, there are many practical limits that prevent widespread use of two-phase microchannel heat exchangers. Many authors have looked to address these practical limits by treating the channel floors or creating artificial nucleation sites. Few works look to enhance heat transfer in the walls of channels with hydraulic diameters below 200 μm. This work is aimed at increasing the efficacy of high aspect ratio silicon microchannels that use R134a as the working fluid. The 125 parallel channels are 40 μm wide, 200 μm deep, and 2 mm long and contain a 15 μm wide, 150 μm long restriction at each inlet. The thermal resistance and dryout characteristics of traditional, plain-walled channels are compared to channels with 2 area enhancement patterns each of which increases the area available for heat transfer by 41%. Furthermore, a resistance to dryout is seen in both area-enhanced test sections, and a 15.5% reduction in thermal resistance is shown for the area-enhanced part with a 6 μm triangular pitch. Only a 7.8% performance increase is seen in the test section with a 3 μm pitch. Both area enhancement patterns induce an average 27% increase in pressure drop for all tests. Heat transfer characteristics are solved for using a finite element analysis (FEA) model. By examining heat transfer coefficients and local heat fluxes, it is postulated that the area enhancement reduces heat transfer coefficients and the performance increase is caused by increasing the number of active nucleation sites.

42 ENGINEERING↗

DOE OSTI2019

Cardinal: A Lower Length-scale Simulator for Fluoride Cooled High Temperature Reactors

The new DOE-NE “Center of Excellence for Thermal-fluids applications in Nuclear Energy” inaugurated in April 2018 considers and researches novel new solution strategies for historically challenging flow issues that still plague the current fleet of deployed Light Water Reactor (LWR) nuclear reactors as well as predicting various fluid flow and fluid related issues with advanced reactor technologies. Our advanced thermal-fluids research and development approach synergistically combines three natural, though overlapping, length and time scales in a hierarchal multi-scale approach to avoid the temptation and pitfalls of attempting to develop a single “solve all” algorithm for physical fluid flow problems that will span 109 in spatial and temporal scales. The demonstrate the multi-scale philosophy of the center we focus first on Fluoride Cooled High Temperature Reactors (FHRs), and in particular on the Berkeley’s PB-FHR design Mark-I design. The Fluoride salt cooled High temperature Reactor (FHR) is a class of advanced nuclear reactors that combine the robust coated particle fuel form from high temperature gas cooled reactors, direct reactor auxiliary cooling system (DRACS) passive decay removal of liquid metal fast reactors, and the transparent, high volumetric heat capacitance liquid fluoride salt working fluids - Flibe - from molten salt reactors. This combination of fuel and coolant enables FHRs to operate in a high-temperature low-pressure design space that has beneficial safety and economic implications. The PB-FHR reactor relies on a pebble bed approach and pebble bed reactors are in a sense the poster child for multiscale analysis. The lower length-scale simulator for pebble reactor cores comprises three physics: neutronics (OpenMC), thermal-fluids (Nek5000) and fuel performance (BISON). As part of center of excellence ongoing research efforts we have developed “Cardinal”, a new tool platform for lower length-scale simulation. Cardinal tightly couples all three physics and leverages advances in MOOSE such as the MultiApp system and the concept of MOOSE-wrapped Apps. Moreover it is designed from the ground-up to scale on massively parallel architectures and perform well on world-class super-computing architectures. In this report we describe the design of Cardinal and present a demo of the application of Cardinal to an FHR.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

Hyperspectral Image Classification Using Graph Clustering Methods

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classification of large datasets in high dimensions. This paper presents two classes of graph-based classification methods for hyperspectral imagery. Using the full dimensionality of the data, we consider a similarity graph based on pairwise comparisons of pixels. The graph is segmented using a pseudospectral algorithm for graph clustering that requires information about the eigenfunctions of the graph Laplacian but does not require computation of the full graph. We develop a parallel version of the Nyström extension method to randomly sample the graph to construct a low rank approximation of the graph Laplacian. With at most a few hundred eigenfunctions, we can implement the clustering method designed to solve a variational problem for a graph-cut-based semi-supervised or unsupervised classification problem. We implement OpenMP directive-based parallelism in our algorithms and show performance improvement and strong, almost ideal, scaling behavior. The method can handle very large datasets including a video sequence with over a million pixels, and the problem of segmenting a data set into a pre-determined number of classes.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Coupling Surface Flow with High-performance Subsurface Reactive Flow and Transport Code PFLOTRAN

Water exchange between the surface and subsurface is important for both water resource management and environmental protection. In this paper, we develop coupled surface and subsurface flow simulation capability in a parallel subsurface flow and reactive transport code PFLOTRAN. We sequentially couple the diffusion wave-based surface flow with the subsurface flow governedby the Richards equation in PFLOTRAN. These two flow domains are linked with a boundary condition switching method that ensures continuity of pressure and flux at the surface-subsurface interface. We verify the coupled code against other existing hydrologic models and observation data using a number of numerical experiments. The coupled hydrological model exhibits good performance in strong parallel scaling tests. The new coupled surface and subsurface simulator significantly advance community simulation capability towards improving integrated hydrologic and biogeochemical understanding of complex systems such as watersheds and river corridors. Keywords: Surface flow, Integrated hydrological modeling, Boundary condition switching, Parallel computing

Wu, Runjian↗

DOE OSTI2016

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.

97 MATHEMATICS AND COMPUTING↗