Operating chips at high energy efficiency is one of the major challenges for modern large-scale supercomputers. Low-voltage operation of transistors increases the energy efficiency but leads to frequency and power variation across cores on the same chip. Finding energy-optimal configurations for such chips is a hard problem. In this work, we study how integer linear programming techniques can be used to obtain energy-efficient configurations of chips that have heterogeneous cores. Our proposed methodologies give optimal configurations as compared with competent but sub-optimal heuristics while having negligible timing overhead. The proposed ParSearch method gives up to 13.2% and 7% savings in energy while causing only 2% increase in execution time of two HPC applications: miniMD and Jacobi, respectively. Our results show that integer linear programming can be a very powerful online method to obtain energy-optimal configurations.