Addressing state space multicollinearity in solving an ozone pollution dynamic control problem - Ariyajunya, Bancha; Chen, Ying; Chen, Victoria C.P.; Kim, Seoung Bum; Rosenberger, Jay (European journal of operational research, 2021)
•State space multicollinearity in approximate dynamic programming is described.•The negative impact of ignoring state space multicollinearity is illustrated.•One approach to address multicollinearity seeks low variance inflation factors.•A second approach to address multicollinearity conducts orthogonalization.•Comparisons are demonstrated using an Atlanta ozone pollution control problem. High ground-level ozone concentrations constitute a serious air quality problem in many metropolitan regions. In this paper, we study a stochastic dynamic programming (SDP) formulation of the Atlanta metropolitan ozone pollution problem that seeks to reduce ozone via reductions of nitrogen oxides. The initial SDP formulation involves a 524-dimensional continuous state space, including ozone concentrations that are highly correlated. In prior work, a design and analysis of computer experiments (DACE) based approximate dynamic programming (ADP) solution method was able to conduct dimensionality reduction and value function approximation to enable a computationally-tractable numerical solution. However, this prior work did not address state space multicollinearity. In statistical modeling, high multicollinearity is well-known to adversely affect the generalizability of the constructed model. This issue is relevant whenever an empirical model is trained on data, but is largely ignored in the ADP literature. We propose approaches for addressing the multicollinearity in the Atlanta case study and demonstrate that if high multicollinearity is ignored, the resulting empirical models provide misleading information within the ADP algorithm. Because many SDP applications involve multicollinear continuous state spaces, the lessons learned in our research can guide the development of ADP approaches for a wide variety of SDP problems.