## 2 Background
### Types of Optimization  
Optimization can be generally classified into two types, as follows: Single-objective optimization (SOO) and multi-objective optimization (MOO) [9]. Their relationship and targeted solutions are shown in Figure 3.  
SOO optimizes only one optimization objective subject to optimization constraints. It aims at the optimal solution that produces the best value on the objective and satisfies all the constraints. MOO optimizes multiple optimization objectives subject to optimization constraints. It aims at Pareto solutions, each producing the best objective values that cannot be improved without worsening the value of another objective. Additionally, all the Pareto solutions satisfy all the constraints. A MOO problem often has more than one existing Pareto solution. Some MOO methods can identify a set of Pareto solutions, while others only identify one Pareto solution, based on the decision makers' preference. Figure 4 presents the application number of SOO and MOO on this subject. According to this figure, SOO was applied first and dominated in this field before the 2010s. Often a main management goal is defined as optimization objective and other goals and requirements are converted to optimization constraints. The commonly used SOO model is to minimize the M&R cost subject to the acceptable worst condition [26; 27; 28] or to improve the condition/condition-based benefit, subject to an annual budget [29; 30; 31]. By reviewing the articles, this paper finds out that, today, a considerable amount of articles still use SOO for their DM in IAM, while its orientation is moving to the hard DM problems, including huge networks [32; 33], life-cycle analysis [34; 35; 36], complex non-linear models [37; 38; 39], and cross-assets [40; 41]. Figure 3: Types of optimization methods and their targeted solutions. With the development of IAM, DM tends to consider multiple goals. When managing infrastructure, some management goals are commensurable and concordant, e.g., improving the network condition and increasing the level of service, and are often integrated into one objective and solved by SOO algorithms [42; 43; 44]. In this case, only one solution is obtained according to the integrated objective. However, often the management goals are incommensurable or conflicting, e.g., improving network condition and reducing management cost [45]. In this case the objectives cannot be simply integrated and this DM is formulated as a MOO problem and each incommensurable or conflicting goal is defined as an individual objective. MOO can describe practical problems in a more rational manner and leads to more informed decisions [7]. Hence, as shown in Figure 4, the application of MOO is increasing. A MOO problem often has a set of existing Pareto solutions. However, not all of the optimization methods can obtain all the existing Pareto solutions. Figure 5 illustrates the percentage of the reviewed articles targeting at one Pareto solution or a set of Pareto solutions when adopting MOO in DM in IAM. Among the 337 reviewed articles that adopted MOO in their DM in IAM, 59% of them only produced one solution. These types of solutions require the input from decision makers, i.e., the preference on objectives, weighting of outcomes, expert experience, or practical consideration, and then, one solution is generated to match the decision makers' input. When decision makers have sufficient knowledge to give the input, obtaining one solution can largely simplify the solving procedure and speed up the optimization process. In recent years, the attempt at a set of Pareto solutions is growing, according to the reviewed articles. This is mainly because the Pareto solution set not only offers the best solutions but also indicates the achievable best objective values, alternative trade-offs of objectives, and objective relationships, which can be used to clarify the problems at hand, balance the objectives, and lead to an informed decision [46; 47; 48].