In this paper a new population update rule for population based ant colony optimization (PACO) is proposed. PACO is a well known alternative to the standard ant colony optimization algorithm. The new update rule allows to weight different parts of the solutions. PACO with the new update rule is evaluated for the example of the single machine total weighted tardiness problem (SMTWTP). This is an $\mathcal{NP}$-hard optimization problem where the aim is to schedule jobs on a single machine such that their total weighted tardiness is minimized. PACO with the new population update rule is evaluated with several benchmark instances from the OR-Library. Moreover, the impact of the weights of the jobs on the solutions in the population and on the convergence of the algorithm are analyzed experimentally. The results show that PACO with the new update rule has on average better solution quality than PACO with the standard update rule.