Decision Optimization

Finding optimal decisions in large, complex, sequential, and uncertain domains.

Decision analysis and optimization is concerned with making optimal choices so as to optimize key performance measures, for example minimize energy, cost, pollution, or maximize reliability, revenue, comfort, etc., usually using predictive models obtained from collected data. A lot of the decision problems that we are addressing involve significant uncertainty, and we are researching methods for stochastic optimization to handle that uncertainty from a probability and decision theory perspective. For example, the optimal scheduling of thermal power generators depends strongly on the uncertainty in power demand and output of uncontrollable renewable power sources. Similarly, the optimal operation of air conditioners in a building over a period of one day or longer depends strongly on the ambient temperature that cannot be known with full certainty over the entire period. Furthermore, these decision problems involve entire sequences of decisions, due to the significant temporal coupling existing in most systems and processes of interest. For this reason, our research has focused on algorithms for optimal sequential decision making under uncertainty. We have proposed optimization solvers based on representation formalisms such as factored Markov decision processes and computational schemes such as dynamic programming and value function approximation. Other problems that can be addressed by this approach include predictive car navigation, group elevator scheduling, and run-curve optimization for trains.

Even when the optimization problem of interest is not sequential or uncertain, it is very often non-convex, with a significant loss of optimality if the global optimum is not reached. Examples of such problems include optimal power flow in electrical networks, thermal comfort optimization in buildings, and energy optimization in electrified railroads. In order to overcome the loss of optimality, we have been researching methods for global optimization based on branch-and-bound and interior point optimization, employing various forms of duality. It is our hope that the synergies between continuous and combinatorial optimization can be leveraged to address even harder industrial decision optimization problems in the future.