Sequential Sampling-based Stochastic Optimization Algorithms

Abstract:  Optimization problems arising in many real settings -- such as power systems operations, supply chain management, finance etc. --  involve decision making in an uncertain environment. Stochastic optimization/programming has provided a systematic approach to handle these decision problems since the 1960s. The emergence of data-intensive applications and improved data assimilation techniques in recent years has called for a wave of innovations in stochastic optimization. These innovations are expected to be scalable for real-scale systems and to address the evolving nature of decision environment. In order to meet such expectations,  a more effective integration of decision and data sciences is necessary. With this in mind, this talk will begin with a brief overview of the field of stochastic optimization by identifying classical problems, mathematical programming models and algorithms. Subsequently, we will contrast these classical methods with our sequential sampling-based stochastic optimization approaches. These approaches will be presented in the context of stochastic optimization problems arising in power systems operations. These problems, and corresponding algorithmic developments, span both the two-stage as well as the multistage stochastic optimization. The sequential sampling approaches allow for engineering problems to use statistical models in service of constrained engineering optimization. Specifically, these algorithms do not rely on a-priori characterization of uncertainty through scenarios or distributions, and hence, can be used directly with data streams generated using state-of-the-art simulators. Results obtained from our computational experiments on real scale systems will also be presented.