According to the design exploration result, it is found that the most solutions show better performance than that of the best solution obtained by previous study, and it is also suggests that the promising designs has large sweep back and, the sharp fuselage-nose.
The best solution obtained by proposed GA is shown in Table 8 and its variable values in Table 9.
Let ( Pb_i^t = [{pb_{i,1}^t,pb_{i,2}^t, ldots,pb_{i,2n}^t }] ) be the best solution which particle i has obtained by iteration t, and let ( P_g^t = [{p_{g,1}^t,p_{g,2}^t, ldots,p_{g,2n}^t }] ) be the best solution obtained by iteration t.
We adopt the solution error measure ((f(x) - f(x*))), where f(x) is the best solution obtained by algorithms in one run and (f(x*)) is well-known global optimum of each benchmark function, which is recorded after 1.2e05, 6.0e05, and 3.0e06 function evaluations (FEs) for CEC'2010 and 5.0e03*D function evaluations (FEs) for CEC'2008, respectively.
For easier test instances 1 and 2 (where the number of potential locations is set to 16 and 51 respectively) the solution obtained by CPLEX within 10 hours is slightly (less than 0.26%) better then the best solution obtained by VNS within one minute.
The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods.
The optimal results obtained by the CSA algorithm are much better than the best solutions obtained by the existed methods.
For Case study 1 the results obtained lie within the range of best solutions obtained by other authors.
The comparisons show that the results obtained by KH can be better than the best solutions obtained by the existing methods in these three case studies.
The table also reports the percentage of error of the best solutions obtained by Fekete et al. [8].
Also, Fig. 3 compares the best solutions obtained by the proposed GA and enumerative method in different sizes.
