This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more
Optimization in dynamic environments is a challenging but important task since many real-world optimization problems are changing over time. Evolutionary computation and swarm intelligence are good tools to address optimization problems in dynamic environments due to their inspiration from natural self-organized systems and biological evolution, which have always been subject to changing environments. Evolutionary optimization … Read more
We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market … Read more
We analyze the relationship between the noise level of a function and the accuracy and reliability of derivatives and difference estimates. We derive and empirically validate measures of quality for both derivatives and difference estimates. Using these measures, we quantify the accuracy of derivatives and differences in terms of the noise level of the function. … Read more
We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear production games. We also show that our techniques … Read more
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to … Read more
For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers’ risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate … Read more
We completely characterize deterministic strategy-proof and group strategy-proof mechanisms on single-sinked public policy domain. The single-sinked domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents’ preferences have a single most loathful point (the sink) in the interval, and the preferences … Read more
Recently there has been intensive interest on approximation of the NP-hard submodular maximization problem due to their theoretical and practical significance. In this work, we extend this line of research by focusing on the simultaneous approximation of multiple submodular function maximization. We address existence and nonexistence results for both deterministic and randomized approximation when the … Read more
We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We illustrate the results on an optimal stopping … Read more