(371i) An Efficient Approach to Solving Stochastic Optimal Control Problems with Application to Sustainability Assessment of a Complex Integrated Model
This paper intends to contribute in this area in two ways. First, we have developed a novel approach to address stochastic optimal control problems based on the Better Optimization of Nonlinear Uncertain Systems (BONUS) algorithm (Diwekar, 2015). This method avoids the need for excessive model evaluations through a reweighting scheme using kernel density estimation and relies on sampling to estimate the probabilistic objective function. A batch reactor for biodiesel production is used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles are similar to those obtained by the Stochastic Maximum Principle (SMP) technique. Also, by searching on the whole decision space through sampling, the BONUS approach avoids local optima commonly found by the SMP technique.
As a second contribution, we have reformulated an integrated compartmental model for sustainability analysis (Kotecha et al., 2013) as a stochastic optimal control problem by considering the uncertain behavior of some model parameters (mortality and birth rate; wages). The resulting problem has then been solved through our efficient approach based on BONUS. The aim is to maximize the sustainability of the system, analyzing it in a scenario of instability and using ecological indicators as a measure of sustainability. The results show the complexity of ecosystem behavior and the big impacts that human activities have over the ecological components, as well as the difficulty to mitigate them. Results can also help decision makers to identify critical policy guidelines that allow such integrated systems to be driven into a more sustainable framework.
Keywords: Sustainability theory, stochastic optimal control, BONUS
Diwekar, U.; David, A., BONUS Algorithm for Large Scale Stochastic Nonlinear Programming Problems, Springer Briefs in Optimization, 2015.
Kotecha, P.; Diwekar, U.; Cabezas, H., Model-based approach to study the impact of biofuels on the sustainability of an ecological system, Clean Technologies and Environmental Policy, 15, 21â33, 2013.