Dual-fuel reactivity controlled compression ignition (RCCI) combustion has shown high thermal efficiency and superior controllability with low NOx and soot emissions. However, as in other low temperature combustion (LTC) strategies, the combustion control using low exhaust gas recirculation (EGR) or a high compression ratio at high load conditions has been a challenge. The objective of this work was to examine the efficacy of using dual direct injectors for combustion phasing control of high load RCCI combustion. The present computational work demonstrates that 21 bar gross indicated mean effective pressure (IMEP) RCCI is achievable using dual direct injection. The simulations were done using the KIVA3V-Release 2 code with a discrete multicomponent fuel evaporation model, coupled with sparse analytical Jacobian solver for describing the chemistry of the two fuels (iso-octane and n-heptane). In order to identify an optimum injection strategy a nondominated sorting genetic algorithm II (NSGA II), which is a multiobjective genetic algorithm, was used. The goal of the optimization was to find injection timings and mass splits among the multiple injections that simultaneously minimize the six objectives: soot, nitrogen oxide (NOx), carbon monoxide (CO), unburned hydrocarbon (UHC), indicated specific fuel consumption (ISFC), and ringing intensity. The simulations were performed for a 2.44 liter, heavy-duty engine with a 15:1 compression ratio. The speed was 1800 rev/min and the intake valve closure (IVC) conditions were maintained at 3.42 bar, 90 °C, and 46% EGR. The resulting optimum condition has 12.6 bar/deg peak pressure rise rate, 158 bar maximum pressure, and 48.7% gross indicated thermal efficiency. The NOx, CO, and soot emissions are very low.