## 5 Computational Results and Discussion  
This section presents and describes the computational experiments for the validation of the proposed racing + CBR approach. Benchmark instances of job-shop scheduling problems extracted from OR-Library ([[http://people.brunel.ac.uk/~mastjib/jeb/info.html](http://people.brunel.ac.uk/~mastjib/jeb/info.html)]([http://people.brunel.ac.uk/~mastjib/jeb/info.html](http://people.brunel.ac.uk/~mastjib/jeb/info.html)), accessed on 7 February 2021) have been used. The reader shall note that the proposed hybrid approach is compared separately with each of the techniques used, racing and CBR, but racing + CBR is also compared with previously published results (a previous approach: [9]). The implementation was performed via Java programming language, using a H2 database and Hibernate framework as the database access layer. The computer used for the computational study was an HP Z400 with the following key features: Intel Xeon W3565 3.20 GHz processor, 6 GB DDR3 RAM memory, Samsung HD103 SJ 1 TB 7200 rpm hard drive and Microsoft Windows 7 operating system. Both of the outcomes are consistent with the goal of reducing the completion time (\(C_{max}\)). Every instance was run five times, with the average of the results determined. The ratio between the optimum value and the average value of \(C_{max}\) was used to normalize the values (Equation (17)) to estimate the deviation value obtained from the value of the optimal solution cited in the literature. \[\text{ratio}=1-\frac{\text{OptC}_{\text{max}}}{\text{C}_{\text{max}}} \tag{17}\]  
where \(\text{OptC}_{\text{max}}\) is the optimum completion time and \(\text{C}_{\text{max}}\) is the obtained completion time. Rather than comparing the values directly, the deviations of the average values of C\({}_{\max}\) from the optimum value are compared, which is especially useful when dealing with different C\({}_{\max}\) values. Considering, for instance, two scenarios where the optimum values are 60 and 90, respectively, if we get 65 for the first instance and 98 for the second, we can infer that the value obtained for the second instance is closer to the optimum, since the ratio is 0.103 for the first and it is 0.082 for the second. The CBR casebase was initialized based on the parameters obtained by the racing module. These parameters are shown in Tables 1-6 and correspond to the outputs from the racing module. In this hybrid approach, 150 initial cases were inserted, corresponding to the tuning of six metaheuristics in 25 instances. The analysis of the CBR module was carried out using the initial casebase filled by racing, with the system being run in test instances. The descriptive analysis of the ratio of the average \(C_{max}\) for all approaches, including racing + CBR, is presented in Table 7. By examining the chart in Figure 6, analyzing the median and dispersion of data, it is possible to draw conclusions about the benefits of the racing + CBR method. When comparing the results of the racing + CBR approach to the results of the racing module, one can see a slight improvement in the results, especially in the dispersion, indicating that the addition of the CBR module can keep the results more consistent. In Table 7, it is possible to conclude for a lower average and standard deviation than the racing module, and lower maximum and minimum values, which is crucial given that the scheduling problem is a minimization problem. When comparing the findings of the hybrid approach to those of CBR, the difference is not as important, indicating that combining the two modules could be beneficial. In Table 7, the minimum and maximum values have improved, as has the average, but the standard deviation has increased marginally, though the difference is not important. Finally, the results of the racing + CBR are compared with the previous published results [9]. At this point, clear improvements are shown, which indicates a statistically significant advantage in using learning algorithms in the tuning of metaheuristic parameters in optimization problems.