Research On The Optimization Problems Based On Differential Evolution Algorithm

The optimization calculation, with its computational complexity, is always a researchhotspot nowadays. In particular, most of the traditional classic solutions solving the complexproblems of large scales are based on gradient and always easy to fall into local optimalsolutions. In1990s, American scholars Storn and Price researched differential evolutionalgorithm(DE). Since its performance of solving complex global optimization problems isprominent and its evolution process is simple, it draws many scholars’ attention. DE has beensucceeded in many application fields, but it also has some shortcomings: the lack of localsearch ability, the sensitivity of parameter settings, the difficult selection of mutation strategyand so on. Aiming at the shortcomings, scholars proposed improved DE, and also achievedgood results, which proved that this algorithm has high efficiency and good practicality.This thesis improves the basic DE to solve the constrained optimization problems andmulti-objective optimization problems. For the constrained optimization problems, theconstraint handling strategy is improved, the constraint handling technique and precision oftermination are combined, which avoid premature convergence effectively. Then the mutationoperator is improved, elitism strategy is used to generate better mutation individuals, in orderto reduce the sensitivity of setting parameters and decrease the difficulty of choosing themutation strategy. It makes the results more effectively drop out of the fixed bound andconverge to the optimal direction faster. Through numeral experiments, it can be seen that theimproved DE has better global searching ability and faster search speed, which proves theimproved DE has some practicability.For multi-objective optimization, fast non-dominated sorting, crowding-distance andtournament selection are introduced into DE, in order to maintain the diversity of Paretooptimal solutions. It can be seen through numeral experiments, the new DE is correct andeffective, it can obtain the effective, uniform distribution, approximately complete and optimalPareto optimal solution sets.