This work presents a comprehensive computational study of diesel - natural gas (NG) dual fuel engine. A complete computational model is developed for the operation of a diesel - NG dual fuel engine modified from an AVL 5402 single cylinder diesel test engine. The model is based on the KIVA-3V program and includes customized sub-models. The model is validated against test cell measurements of both pure diesel and dual fuel operation. The effects of NG on ignition and combustion in dual fuel operation are analyzed in detail. Zero-dimensional computations with a diesel surrogate reaction mechanism are conducted to discover the effects of NG on ignition and combustion and to reveal the fundamental chemical mechanisms behind such effects. Backed by the detailed theoretical analysis, the engine operation parameters are optimized with genetic algorithm (GA) for the dual fuel operation of the modified AVL 5402 test engine.