*Engineering Problems - Uncertainties, Constraints and Optimization Techniques*


#### **Table 2.**

*Continuous variables for aircraft design problem.*


#### **Table 3.**

*Discrete technologies for aircraft design problem.*

The problem also has four constraints that appear in **Table 4**. The constraints ensure that the design solution meets the desired field length criteria, has sufficient ground clearance, and sets a maximum limit on the amount of allowable fuel carrying space in the fuselage.

The aircraft design optimization problem considers two different pairs of competing objectives. The first pair involves simultaneous minimization of the aircraft fuel weight (index of CO2 emissions) and the total operating cost of the aircraft, and the second pair involves minimizing the NO*<sup>X</sup>* emissions and the total operating cost of the aircraft. The GA population has been limited to 48 individuals while setting the upper limit for the number of generations to 50 as before. The maximum


number of function evaluations for the SQP minimization (using MATLAB's fmincon) have been limited to the default value of 100 times the total number of continuous variables for this study. For certain combinations of discrete technology selection choices, the gradient-based approach may not find a feasible solution. In such cases, as mentioned in the methodology section, those designs are assigned high penalty for elimination in the subsequent generations.

#### *4.3.3 Results for aircraft design problem*
