This paper proposed a Markov chain-based local optima network (LON), representing search transitions of an evolutionary algorithm (EA). LON is a graph constructed by local optima as nodes and search transitions of an optimization algorithm as edges. This paper focused on a mutation-based (1+1)-EA as the target optimization algorithm and constructed its LON, which could estimate the success ratio to find the optimal solution and the time to reach it based on the Markov chain model. We generated the proposed LONs on NK-landscape problems with twenty variables and the different number of co-variables from two to five and discussed the relations among the success ratio, the convergence time, and quantitative features observed from the generated LONs. The results revealed that the optimal solution’s funnel ratio in the variable space greatly impacts the success ratio. Also, we showed that the estimation accuracy of the success ratio and the convergence time of the (1+1)-EA by the proposed LON increase as the number of objective function evaluations increases. The coefficient of determination of the success ratio prediction exceeded 0.9 when the number of objective function evaluations got more than one thousand.
