We propose a multi-objective generalisation for the well known Counting Ones problem, called the Multi-objective Counting Ones (MOCO) function. It is shown that the problem has four qualitative different regions. We have constructed a convergence time model for the Simple Evolutionary Multi-objective Optimiser (SEMO) algorithm. The analysis gives insight in the convergence behaviour in each region of the MOCO problem. The model predicts a l~2 ln l running time, which is confirmed by the experimental runs.
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