## 6 An Illustrative Example
Figure 10 shows the convergence of the solving process in terms of the number of candidates that fulfill all the strict design requirements formulated as inequality constraints in Equation (5) with data in Table 2. At the start of the heuristic algorithm execution, all individuals in the population are un-feasible. However, in about 100 iterations, all the candidate solutions fulfill the constraints. This characteristic means that all the individuals  
Figure 8: Pareto front in terms of the three objective functions for a feasible solution for the example in Figure 7.  
in the population now satisfy the strict design requirements that ensure that the solutions can be built and develop the requested task. Once the heuristic algorithm has found feasible solutions, the solvers focus on finding solutions that improve the objective function values but at the same time ensures that the constraints are fulfilled. This task means that to find solutions that improve soft design requirements associated with user expectations. Figure 11 shows the computed convergence of the solving process for the criteria associated with the task performance and overshoot criterion in Table 2. At the beginning of the algorithm execution, the objective function's values are not registered since those values can be higher or lower for non-feasible solutions. The algorithm function manager starts making decisions only after the individuals in the population are feasible. Therefore, the decreasing behavior of the objective functions corresponds to the feasible solutions presented in Figure 7.0 This figure illustrates that once feasible individuals in the population appear, it is possible to find configurations that improve overshoot criterion with fewer iterations than the first objective function. Figure 12 shows the convergence of the objective function associated with energy consumption. This figure shows that the search space is huge for this criterion since its evaluation can produce high values compared to the last registered values at the end of  
Figure 7.1 Computed convergence of the solving process in terms of the number of candidate solutions that fulfill strict-design requirements for the first 200 algorithm iterations (\(G\leq 0\) in Table 2). Figure 7.2 Computed convergence of the solving process in terms of the Grashof constraint and mass center position (\(g_{4}\) and \(g_{7}\) in Table 2). the algorithm execution. It might represent an issue for the numerical solver that can be improved. Another essential aspect that can be analyzed is the convergence of the design parameters as the solving process takes place. Figure 13 shows the computed convergence in terms of the input link size parameter and its mass, similar to Figure 7.3 The value of this parameter changes rapidly from one iteration to another while there are no feasible individuals. However, when feasible individuals appear in the population, the frequency change of this value is reduced. This figure illustrates how the algorithm explores the parameter space in search of feasible configurations and the improvement of objective functions in those different stages. Figure 14 shows the obtained behavior of the selected solution to be analyzed using the computed dynamic model. This figure shows the behavior of the input link angular velocity \(x_{2}=\dot{\theta}_{2}\) where it can be seen the performance of the system. There are still notable variations in comparison with the target velocity, and this characteristic also shows the high non-linearity of the study case. Nevertheless, the obtained response satisfy strict design requirements and an optimal trade-off with soft design requirements for the selected solution.