Richard Li-Yang Chen

Solving Truckload Procurement Auctions Over an Exponential Number of Bundles

Truckload carriers provide hundreds of billions of dollars worth of services to shippers in the United States alone each year. Internet auctions provide these shippers with a fast and easy way to negotiate potential contracts with a large number of carriers. Combinatorial auctions have the added benefit of allowing multiple lanes to be considered simultaneously in a single auction. This is important because it enables carriers to connect multiple lanes in continuous moves or tours, decreasing the empty mileage that must be driven, and therefore increasing overall efficiency. On the other hand, combinatorial auctions require bidding on an exponential number of bundles to achieve full economies of scope and scale, which is not tractable except for very small auctions. In most real-world auctions, bidding is instead typically limited to a very small subset of the potential bids. We present an implicit bidding approach to combinatorial auctions for truckload procurement that enables the complete set of all possible bids to be considered implicitly, without placing the corresponding burden of an exponential number of bids on the bidders or the auctioneer. We present the models needed to solve this problem. We then provide extensive computational results to demonstrate the tractability of our approach. Finally, we conclude with numerical analysis to assess the quality of the solutions that are generated and to demonstrate the benefits of our approach over existing bidding methods in practice.

Contingency-Risk Informed Power System Design

We consider the problem of designing (or augmenting) an electric power system at a minimum cost such that it satisfies the N-k-ε survivability criterion. This survivability criterion is a generalization of the well-known N-k criterion, and it requires that at least (1-εj) fraction of the steady-state demand be met after failures of j components, for j=0,1,...,k. The network design problem adds another level of complexity to the notoriously hard contingency analysis problem, since the contingency analysis is only one of the requirements for the design optimization problem. We present a mixed-integer programming formulation of this problem that takes into account both transmission and generation expansion. We propose an algorithm that can avoid combinatorial explosion in the number of contingencies, by seeking vulnerabilities in intermediary solutions and constraining the design space accordingly. Our approach is built on our ability to identify such system vulnerabilities quickly. Our empirical studies on modified instances of the IEEE 30-bus and IEEE 57-bus systems show the effectiveness of our methods. We were able to solve the transmission and generation expansion problems for k=4 in approximately 30 min, while other approaches failed to provide a solution at the end of 2 h.

Efficient Uncertainty Quantification in Stochastic Economic Dispatch

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate evaluations of expectations or higher order moments for quantities of interest, e.g., generating cost, can require a prohibitively large number of samples. We propose an alternative to Monte Carlo sampling based on polynomial chaos expansions. These representations enable efficient and accurate propagation of uncertainties in model parameters, using sparse quadrature methods. We also use Karhunen–Loève expansions for efficient representation of uncertain renewable energy generation that follows geographical and temporal correlations derived from historical data at each wind farm. Considering expected production cost, we demonstrate that the proposed approach can yield several orders of magnitude reduction in computational cost for solving stochastic economic dispatch relative to Monte Carlo sampling, for a given target error threshold.

k-edge Failure Resilient Network Design.

Abstract We design a network that supports a feasible multicommodity flow even after the failures of any k edges. We present a mixed-integer linear program (MILP), a cutting plane algorithm, and a column-and-cut algorithm. The algorithms add constraints to repair vulnerabilities in partial network designs. Empirical studies on previously unsolved instances of SNDlib demonstrate their effectiveness.

An implicit optimization approach for survivable network design

We consider the problem of designing a network of minimum cost while satisfying a prescribed survivability criterion. The survivability criterion requires that a feasible flow must still exists (i.e. all demands can be satisfied without violating arc capacities) even after the disruption of a subset of the networks arcs. Specifically, we consider the case in which a disruption (random or malicious) can destroy a subset of the arcs, with the cost of the disruption not to exceed a disruption budget. This problem takes the form of a tri-level, two-player game, in which the network operator designs (or augments) the network, then the attacker launches a disruption that destroys a subset of arcs, and then the network operator attempts to find a feasible flow over the residual network. We first show how this can be modeled as a two-stage stochastic program from the network operators perspective, with each of the exponential number of potential attacks considered as a disruption scenario. We then reformulate this problem, via a Benders decomposition, to consider the recourse decisions implicitly, greatly reducing the number of variables but at the expense of an exponential increase in the number of constraints. We next develop a cut-generation based algorithm. Rather than explicitly considering each disruption scenario to identify these Benders cuts, however, we develop a bi-level program and corresponding separation algorithm that enables us to implicitly evaluate the exponential set of disruption scenarios. Our computational results demonstrate the efficacy of this approach.

N-1-1 contingency-constrained optimal power flow by interdiction methods

N-1-1 contingency analysis considers the consecutive loss of two elements in a power system, with intervening time for operator adjustments; the associated reliability criterion was recently included in the NERC Standard TPL-001-1. In this paper, we introduce optimization models for N-1-1 contingency analysis, based on DC optimal power flow considerations. We use mixed-integer programming approaches to optimally model the system adjustments required to avoid potential cascading outages during the primary and secondary contingencies. Contingencies are determined via worst-case interdiction analysis. To facilitate operation during the secondary contingency, line overloads and load shedding are allowed. We test our models and algorithms on several IEEE test systems. Our computational experiments indicate potential for the models to augment comprehensive system operations models, such as unit commitment.

Contingency-constrained unit commitment with post-contingency corrective recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an

A scalable decomposition algorithm for PMU placement under multiple-failure contingencies

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