Population annealing is a Monte Carlo algorithm that marries features from simulated annealing and parallel tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of population annealing Monte Carlo by computing ground states of the three-dimensional Ising spin glass with Gaussian disorder, whilst comparing to simulated annealing and parallel tempering Monte Carlo. Our results suggest that population annealing Monte Carlo is significantly more effiicient than simulated annealing but comparable to parallel tempering Monte Carlo for finding spin-glass ground states.