This paper studies a multi-objective maintenance optimization embedded within the imperfect preventive maintenance (PM) for one single-unit system subject to the dependent competing risks of degradation wear and random shocks. We consider two kinds of random shocks in the system: 1) fatal shocks that will cause the system to fail immediately, and 2) nonfatal shocks that will increase the system degradation level by a certain cumulative shock amount. Also, an improvement factor in the form of quasi-renewal sequences is introduced to modulate the imperfect maintenance by raising the degradation critical threshold proportionally. Finally, the two decision variables for maintenance scheduling, the number of PMs to replacement, and the initial PM interval, are determined by simultaneously maximizing the system asymptotic availability, and minimizing the system cost rate using the fast elitist non-dominated Sorting Genetic Algorithm (NSGA-II). Sensitivity analysis for two parameters, including imperfect PM degree, and quasi-renewal coefficient of imperfect PM interval, is performed to provide insight into the behavior of the proposed maintenance policies. The comparison results show that the optimization solution is consistent between one-objective and multi-objective optimization, and the Pareto frontier for the maintenance optimization problem can provide alternative solutions according to customer preference and resource constraints.