## 6 Recent Applications of Fuzzy Simheuristics  
In this section, some recent applications of fuzzy simheuristics in L&T are reviewed. [PERSON] et al. (2019) were the first to propose the combination of fuzzy techniques, simulation, and metaheuristic optimization algorithms to solve large-scale optimization problems that have both probabilistic and non-probabilistic uncertainty elements. They used a fuzzy inference system (FIS) to compute the collected reward by taking the electric vehicle battery levels and weather conditions as input variables. The authors established nine fuzzy rules to calculate the reward and transformed it to a crisp value using the center-of-gravity method. Their methodology was applied to solve the team orienteering problem with fuzzy and stochastic elements. The results obtained by these researchers when solving a set of classical instances are summarized in the box-plots displayed in Figure 4. In the TOP, the goal is to maximize the total reward collected by the fleet of vehicles during their trips. Notice that the highest rewards (both the individual ones for each instance as well as the average ones across instances) are achieved for the deterministic scenario. Here, a standard metaheuristic algorithm can provide efficient solutions, OBD-D (best deterministic solutions in a deterministic scenario) with an average reward of 358.1. When the former routing plans generated by the metaheuristic are applied in a stochastic scenario, OBD-S, their performance is worse (average reward of 313.6) than the best solutions provided by a simheuristic algorithm (OB-S, with an average reward of 331.5). Of course, the average and individual rewards decrease as the level of uncertainty increases. This can be observed when considering a stochastic-fuzzy scenario, where a fuzzy simheuristic provides solutions OB-SF with an average value of 263.7, and also when considering a pure fuzzy scenario, where a fuzzy approach generates solutions OB-F with an average value of 217.2. [PERSON] et al. (2019) presented a fuzzy simheuristic approach for the vehicle routing problem. The FIS considers fuzzy variables, such as customer demand and remaining vehicle capacity, represented by triangular fuzzy numbers, to calculate the preference strength to travel to a customer. The fuzzy output is an index that determines if the next node will be visited or if the vehicle should return to the depot. The results obtained by these researchers when solving a set of classical instances are summarized in the box-plots displayed in Figure 5. In the VRP, the goal is to minimize the total cost incurred by the fleet  
Figure 4: Results for the TOP using a fuzzy simheuristic. of vehicles during their trips. Notice that the lowest costs (both the individual ones for each instance as well as the average ones across instances) are achieved for the deterministic scenario. Here, a standard metaheuristic algorithm can provide efficient solutions, OBD-D, with an average cost of 945.8. When the former routing plans generated by the metaheuristic are applied in a stochastic scenario, solutions OBD-S, their performance is worse (average reward of 1049.3) than the best solutions provided by a simheuristic algorithm (OB-S, with an average cost of 978.6). As expected, the average and individual costs increase with the level of uncertainty. This can be observed when considering a stochastic-fuzzy scenario, where a fuzzy simheuristic provides solutions OB-SF with an average value of 1266.3, and also when considering a pure fuzzy scenario, where a fuzzy approach generates solutions OB-F with an average value of 1549.2. Moreover, [PERSON] et al. [10] used a similar fuzzy simheuristics methodology to address the location routing problem. The results obtained when solving a set of classical instances are summarized in the box-plots displayed in Figure 6. In the LRP, the goal is to minimize the total cost due to the opening of facilities plus the routing of the vehicles.