## 4 Experimental Studies  
A series of experiments have been designed to assess the effectiveness and understandability of the suggested methodology across various scenarios. The following parameters were used in our experimental setup to create simulation environments:  
* The job-shop simulated in our model consisted of 10 machines;
* Jobs came to the shop dynamically over time, following the Poisson distribution;
* A warm-up time period of 500 jobs was required to reach a stable state, and the data of the following 2000 jobs were applied;
* Each job had 1-10 operations in its operating sequence;
* The mean processing time of each operation was drawn from a uniform distribution with a range of 25 to 100;
* Jobs were given weights 1, 2, or 4, with probability 0.2, 0.6, and 0.2;
* Job due dates were calculated based on the Total Work Content method, with various tightness factors. The machine failures were generated based on the data presented in [54; 55], wherein the interbreakdown times and machine repair times adhered to an exponential distribution. All machines exhibited identical values for both the mean time to repair (MTTR) and the mean time between failures (MTBF). The failure level (F) represented the percentage of time that the machine was expected to break down throughout the simulation run. The machine breakdown configurations investigated in this paper were \(\mathrm{MTTR}=\{2\overline{\mathrm{p}},\,\overline{5\mathrm{p}},\,\mathrm{and}\, 10\overline{\mathrm{p}}\}\) where \(\overline{\mathrm{p}}\) indicated the mean total processing time of a job and F = [5%,10%, and 15%]. According to earlier research, the tightness factor and machine usage were the crucial variables utilized to establish load circumstances, which have a major impact on rule performance [56; 57]. Both low and heavy load cases were considered in this paper to evaluate the effectiveness of the developed dispatching rules. In the job-shop simulation, two to three values were designated for \(\alpha\) and \(\mu\), with a range of 2 to 8 and 80% to 99%, respectively. During the training phase, each scenario in a training set was processed once, using the simulator. In order to obtain accurate results from the simulation, 20 simulated replications were run to test the created rules. Table 2 details the parameters of the simulation scenarios represented by the tuple \(\langle\alpha,\,\mu,\,f\rangle\). Several preliminary experiments were carried out to determine the optimal parameter settings. Research has indicated that the performance of GEP is enhanced by increasing the length of the gene head. The efficacy of Gene Expression Programming (GEP) may experience a decline in cases where the size of the gene head exceeds a certain threshold. Therefore, it was essential to choose a suitable parameter, striking a balance between efficacy and complexity. The efficacy of GEP was also significantly impacted by various factors, such as population size, mutation, recombination, and transportation rates, as well as the number of individuals in the population. In order to determine the values of these parameters, we referred to prior research from [58; 59] as well as a preliminary experiment. Multiple values were specified for each parameter. Subsequently, the GEP was utilized to ascertain an evolutionary principle for each set of parameter combinations. Ultimately, the optimal parameter combination was determined based on an evaluation of the fitness function values. Table 3 provides the parameter settings of the proposed algorithm. \begin{table}
\begin{tabular}{l l l l} \hline
**Parameter** & **Description** & **Training** & **Test** \\ \hline \(\alpha\) & Due dates tightness factor & 3, 5, 7 & 2, 4, 8 \\ \(\mu\) & Shop utilization level & 85, 90, 95 & 80, 90, 99 \\ \(f\) & Machine failure & 5, 10 & 5, 10, 15 \\ Scenarios \(\times\) replications & & 18\(\times\)1 & 27\(\times\)20 \\ Objectives functions: MS, MWT, MFT & & \\ \hline \end{tabular}
\end{table} 
Table 2: Scenarios used in simulations for training and testing.