## 2 Background
### Applied Optimization Methods
#### 3.4.1 Deterministic Methods  
The most popular deterministic methods are the priority-based methods, with an application percentage of 11%. They measure the priority of management options by exploring measurement criteria, weighting the criteria, and scoring the options accordingly. The highest-priority option is finally selected. These methods can be applied to SOO [21; 55] and MOO, especially when optimizing several management criteria or objectives [56; 57; 58]. These methods can help in specifying the relationship of management outcomes in terms of measurement criteria. However, these methods require expert adjustment to make the rules of priority before or during optimization procedure and only produce one solution, based on the priority. They are recommended when sufficient knowledge is obtained to support the expert adjustment and to build the priority system. When the problems are complicated, a proper priority system may not be easily built. Another popular group of deterministic methods in this paper is the so-called numerical methods. A total of 9% of the reviewed articles apply these types of methods in their DM. They build mathematical models and then compute the optimal solution following specific algorithms. They  
Figure 6: Optimization methods applied by the reviewed articles. have been applied to help with IAM since 1975 [12]. Different algorithms are proposed and applied, including linear programming [59; 60; 61], dynamic programming [62; 63], dual programming [64], and branch and bound [65]. Additionally, with the help of powerful computers, numerical methods can efficiently solve decision making problems and obtain the optimal solution or Pareto solutions. They also can be incorporated in management software tools [66; 67]. According to the reviewed articles, numerical methods are mainly applied to SOO or used as a solver for MOO. These methods often follow strict requirements and algorithms, which may result in a limited application scope. Hence, they are recommended for large-sized DM problems, especially when the outcome relationships are simple. Enumeration based methods are one of the earliest and the most effective optimization methods when assisting IAM. They enumerate the possible options and select the best one(s). They can handle various DM problems, including complicated ones. Enumeration based methods can easily handle both SOO and MOO and guarantee to obtain the optimal solution (SOO) [68; 69; 70] or all the existing Pareto solutions (MOO) [71; 72; 73]. Compared to other deterministic methods the conventional enumeration-based methods, e.g., decision trees, are time consuming. Hence, they are recommended for problems with small networks and complicated problems where outcome relationships cannot be accurately described as mathematical formulae. The acceleration is necessary when analyzing large networks. A total of 20 of the reviewed articles adopted transformation-based methods in their IAM. These methods transform a MOO problem into a SOO sub-problem or a set of SOO sub-problems and then solve the sub-problem(s) individually. Hence, they are widely applied to handle MOO problems for DM. The most commonly used transformation based method is the weighted sum method, which weighted sums all the objectives into one using a weighting system [74; 75; 76]. Transformation based methods can obtain a Pareto solution or a set of Pareto solutions. With the help of powerful computers, they can quickly analyze large problems, i.e., life-cycle analysis of large networks. However, these methods may not obtain the entire set of existing Pareto solutions. Additionally, these methods cannot directly solve an optimization problem but, rather, transform it into a sub-problem(s) and a solver is needed to solve the sub-problem(s). They are highly recommended for MOO, with a powerful solver, especially for hard DM, e.g., large-sized networks, life-cycle analysis, and complicated DM problems. Similarly, simulation-based methods also contributed 6% of the applications among the reviewed articles.