Carol Meyers

The complexity of welfare maximization in congestion games

We investigate issues of complexity related to welfare maximization in congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general congestion games, and we examine several variants of the problem concerning the structure of the game and the properties of its associated cost functions. Many of these problem variants turn out to be NP-hard, and some are hard to approximate to within any finite factor, unless P = NP. We also identify several versions of the problem that are solvable in polynomial time.

Parallel Strategies for Solving Large Unit Commitment Problems in the California ISO Planning Model

We present our study of solving large unit commitment problems in the California ISO planning model. The model calculates hourly day-ahead unit commitments, and all instances need to be solved close to optimality within an hour. It takes CPLEX, the current state-of-the-art solver, up to 5 and 10 hours to solve the deterministic instances and the 5-scenario stochastic instances, respectively. The 20-scenario instances are practically unsolvable as no feasible solutions are found after 24 hours.We consider improving solution times through distributed-memory parallelization. Prior techniques such as distributed branch- and-bound perform poorly for our problems. We propose coordinated concurrent search to solve the deterministic instances on a cluster. For stochastic instances, we propose parallelization strategy that combines scenario-based decomposition and asynchronous solves guided by intermediate results from progressive hedging. Our decomposition creates linear sub problems instead of quadratic ones that are oftentimes intractable. On a cluster of 16 IBM Power7 machines, our parallel implementation achieves on average 12.7 and 22 times speedup for the deterministic instances and the 5-scenario stochastic instances, respectively. All problems are solved within an hour to near optimality including the previously unsolvable 20-scenario stochastic instances.

An efficient approach for solving large stochastic unit commitment problems arising in a California ISO planning model

We describe our experience in obtaining significant computational improvements in the solution of large stochastic unit commitment problems. The model we use is a stochastic version of a planning model used by the California Independent System Operator, covering the entire WECC western regional grid. We solve daily hour-timestep stochastic unit commitment problems using a new progressive hedging approach that features linear subproblems and guided solves for finding feasible solutions. For stochastic problems with 5 scenarios, the algorithm produces near-optimal solutions with a 6 times improvement in serial solution time, and over 20 times improvement when run in parallel; for previously unsolvable stochastic problems, we obtain near-optimal solutions within a couple of hours. We note that although this algorithm is demonstrated for stochastic unit commitment problems, the algorithm itself is suitable for application to generic stochastic optimization problems.

High-performance computing for electric grid planning and operations

High-performance computing (HPC) is having a profound impact on scientific discovery and engineering in a variety of areas, and researchers are beginning to demonstrate how HPC can impact problems in energy grid planning and operations. Contemporary supercomputers can perform over 1015 floating point operations per second and have more than 1.4 petabytes of memory - roughly 5 orders of magnitude greater than a commodity PC workstation. This level of computing power changes the very nature of problems that can be solved. Researchers at LLNL have used HPC systems to accelerate execution of a renewables planning study, by solving a thousand unit commitment and dispatch problems in parallel; this generated new insights and allowed for a more detailed study than would have been otherwise achievable. Ongoing work at LLNL includes the development and testing of new parallel algorithms for unit commitment problems, including multi-scenario stochastic unit commitment. These algorithms will enable greater grid and time resolution and provide more accurate solutions because of the increase in model fidelity.