# Optimization of Inspection Period in Natural Stone Claddings
## 1 Introduction
In the multi-objective optimization procedure, the following conflicting objectives are considered: (i) minimization of the service life cycle costs in terms of maintenance; (ii) maximization of the efficiency index of the maintenance plan; (iii) maximization of the service life; (iv) minimization of the total number of replacements over the time horizon. In the literature, there are several works that deal with optimal maintenance planning. For instance, some studies have focused on the schedule of maintenance activities: in bridges, in highway transportation networks [27; 28; 29; 30]; on water distribution systems [31; 32]; on power plants [33; 34]; on other civil infrastructures [35; 36; 37]. Concerning the optimal planning of inspection in civil infrastructures, [PERSON] et al. [38] implemented a multi-objective genetic algorithm (MOGA) to prioritize inspection works in a large real-life sewer network. A trade-off between the risk of failures and the cost of inspections is used to identify the sewers that should be first inspected. This methodology identifies the set of sewers where the propensity and the consequences of failures are higher. Later, still in a sewer distribution system, [PERSON] et al. [39] presented a work where a multi-objective optimization approach was used to optimize inspections in sewer pipelines. In this model, resource allocation is considered by minimizing the time and cost spent on inspections and maximizing the number of pipelines inspected. A more mathematical perspective about the optimization of inspection intervals was given by [PERSON] and [PERSON] [40]. The authors investigated the use of different evolutionary algorithms (EA) to optimize the inspection intervals of safety systems in nuclear power plants. In this paper, the problem is both treated as single-objective and multi-objective optimization. In the multi-objective optimization approach, the availability of the facility, the cost of the inspection, and the exposure time of the maintenance operators are the different conflicting objective functions. Finally, [PERSON] and [PERSON] [8] applied the multi-objective probabilistic optimization process (MOPOP) for optimum inspection and repair scheduling of fatigue-sensitive structures. This methodology considers two alternatives to determine the best single optimum inspection plan. In decision-making before MOPOP, the weight factors are used to convert the multiple objectives into a single objective, and, consequently, a single optimum solution for inspection planning is obtained. On the other hand, in decision-making after MOPOP, the essential objectives are identified and used to select the best Pareto optimal solution. According to the ISO 15686-1 standard [41], maintenance can be defined as the \"combination of all technical and associated administrative actions during the service life to retain a building, or its parts, in a state in which it can perform its required functions\", where inspection is one of those actions. As can be seen from the studies above, when the aim is to optimize the planning of inspections in civil infrastructures, the literature is scarce and becomes even scarcer when the planning of inspections in building components is considered since, for many years, the maintenance of building components has not been a major concern for stakeholders [42]. However, the results of these studies show that there are advantages in using multi-objective optimization procedures to optimize inspection intervals. It is a flexible and rational approach, and the results are useful for decision-makers since the most effective and efficient sequences of inspections are identified based on the restrictions imposed, allowing achieving significant cost-saving when compared with the current inspection practices. Furthermore, the genetic algorithms are revealed to be accurate for the optimization of inspection periods, helping to plan inspections that monitor the actual behavior of the elements, in particular for those where there is no in-service data.