Developing a Differential Evolution with Adaptive Evaluation Function to Treat Real Optimization Problems with Black-box Constraints

In recent years, much attention has been paid to the development of evolutionary computation algorithms that can perform well not only on benchmark problems but also on real optimization problems. Wind Turbine Design optimization Problem (WTDOP) is a real optimization problem in Evolutionary Computation Competition in Japan. WTDOP has 22 constraints and they are described as black-box constraint functions. From previous studies, it was found that WTDOP has a multi-modal landscape fitness function. Hori et al. performed optimization by established a new evaluation function which includes objective function value and a penalty value of constraint violations and by using iDEaSm which is an evolutionary computation algorithm. However there were two issues. One is a fixed penalty which was added to the objective value of solution. Another is that the variety of solutions is not ensured. In order to overcome such issues, in this paper, two improvements are proposed and examined. One of the improvements is the adaptive evaluation function. By changing the penalty depending on the search depth, it is possible to search the boundary between the infeasible and feasible regions without eliminating the infeasible solutions in the early or middle stage of the search. Another is an additional mutation of solution candidates. The additional mutations ensure diversity stochastically and allow the search to continue after the initial convergence. From the comparison between proposed and previous algorithms, our proposed algorithm could find better solutions. Therefore, our proposed algorithm may have better possibility to solve other real optimization problems.