A MINLP Model for Global Optimization of Plug-In Hybrid Vehicle Design and Allocation to Minimize Life Cycle Greenhouse Gas Emissions

Plug-in hybrid electric vehicles (PHEVs) have potential to reduce greenhouse gas (GHG) emissions in the U.S. light-duty vehicle fleet. GHG emissions from PHEVs and other vehicles depend on both vehicle design and driver behavior. We pose a twice-differentiable, factorable mixed-integer nonlinear programming model utilizing vehicle physics simulation, battery degradation data, and U.S. driving data to determine optimal vehicle design and allocation for minimizing lifecycle greenhouse gas (GHG) emissions. The resulting nonconvex optimization problem is solved using a convexification-based branch-and-reduce algorithm, which achieves global solutions. In contrast, a randomized multistart approach with local search algorithms finds global solutions in 59% of trials for the two-vehicle case and 18% of trials for the three-vehicle case. Results indicate that minimum GHG emissions is achieved with a mix of PHEVs sized for around 35 miles of electric travel. Larger battery packs allow longer travel on electric power, but additional battery production and weight result in higher GHG emissions, unless significant grid decarbonization is achieved. PHEVs offer a nearly 50% reduction in life cycle GHG emissions relative to equivalent conventional vehicles and about 5% improvement over ordinary hybrid electric vehicles. Optimal allocation of different vehicles to different drivers turns out to be of second order importance for minimizing net life cycle GHGs.