Models and Algorithms for Stochastic Network Design and Flow Problems: Applications in Truckload Procurement Auctions and Renewable Energy.

This dissertation presents novel mathematical models and algorithms for stochastic network design and flow (SNDF) problems: the optimal design and flow of a network under uncertainty to meet specific requirements while minimizing expected total cost. The focus of this dissertation is SNDF problems characterized by uncertainties in node supplies and/or demands and in arc capacities and/or costs. SNDF problems often have characteristics that render them difficult to model and computationally challenging to solve, including nonlinearities, probabilistic constraints, and stochastic parameters, all of which lead to large-scale, nonlinear, and discrete models. The work in this dissertation is motivated by problems in combinatorial truckload procurement auctions (CTPA) and wind farm network design (WFND). We use these two applications both for their own sake, as they present important and computationally challenging practical problems, and as a basis for the development of more general SNDF models and algorithmic approaches. In studying CTPA, we develop a novel bidding framework, the Implicit Bidding Approach (IBA), that permits the solution of fully-enumerated combinatorial auctions in a single round. Using IBA, we can circumvent the computational challenges of CTPAs by reposing the problem as a polynomially-sized integer multicommodity flow problem. We then extend our CTPA models to consider network uncertainties and show that the resulting model is a special case of a two-stage multicommodity flow problem (TS-MFP). We develop an efficient decomposition algorithm for solving problems in this class and provide extensive computational results to demonstrate its efficacy. In WFND, we present the integrated generation- and transmission- expansion planning problem for a network of interconnected wind farms. We develop an efficient decomposition algorithm for solving WFND problems and present computational results to demonstrate its efficacy. We then extend this model to include a probabilistic constraint on loss-of-load-expectation. We demonstrate that this model is extremely challenging and that direct applications of mathematical programming approaches are not viable. We present a hybrid algorithm, which we called Iterative Test-and-Prune (I-T&P), that leverages mathematical programming to solve a series of easy feasibility problems within a larger meta-search algorithm. Computational results for several test systems demonstrate the efficacy of I-T&P.Ph.D.Industrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/76005/1/richchen_1.pd

Automated Markets and Trading Agents

Computer automation has the potential, just starting to be realized, of transforming the design and operation of markets, and the behaviors of agents trading in them. We discuss the possibilities for automating markets, presenting a broad conceptual framework covering resource allocation as well as enabling marketplace services such as search and transaction execution. One of the most intriguing opportunities is provided by markets implementing computationally sophisticated negotiation mechanisms, for example combinatorial auctions. An important theme that emerges from the literature is the centrality of design decisions about matching the domain of goods over which a mechanism operates to the domain over which agents have preferences. When the match is imperfect (as is almost inevitable), the market game induced by the mechanism is analytically intractable, and the literature provides an incomplete characterization of rational bidding policies. A review of the literature suggests that much of our existing knowledge comes from computational simulations, including controlled studies of abstract market designs (e.g., simultaneous ascending auctions), and research tournaments comparing agent strategies in a variety of market scenarios. An empirical game-theoretic methodology combines the advantages of simulation, agent-based modeling, and statistical and game-theoretic analysis.http://deepblue.lib.umich.edu/bitstream/2027.42/49510/1/ace_galleys.pd

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Modèles et algorithmes pour les enchères combinatoires

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal