An Evolutionary Algorithm For Multiobjective Bilevel Optimization Problem

Multi-level programming is describing the mathematical model of decision problems. In this model, decision-makers, whose position in the decision-making is different, can be divided into the upper level decision-maker (UDM) with a higher decision-making power (Leader) and the lower level decision-maker (LDM) (Follower). We can often see bi-level programming in multi-level programming, it is important research in multi-level programming, multi-objective bi-level programming problem is the most complex type in bi-level programming problem, especially when the multi-function of LDM and UDM has more than one. By making the low level optimization problem convert into the constraint of upper level, then convert the multi-objective bi-level programming problem into multi-objective single level programming problem already existed.EA(evolutionary algorithm) in the past 20 years made great development. Because it bases on the evolutionary process of population, especially fitting for multi-objective programming problems, we can find many similar optimization solutions in evolutionary process one time. So far, there are many MOEAs already raised, NSGA-II has take effect on many problems and be confirmed quite effective.Based on extensive and thorough reading of the literature both at home and abroad, this thesis makes an in-depth theoretical study on the fundamental theories and methods of Genetic Algorithms and we apply GA to design a valid algorithm for bi-level programming problems with some integer decision variables in the upper level. The gist is as follows:i. A systematic and detailed introduction of the general procedure, fundamental theories and methods of Genetic Algorithms.ii. A brief introduction of bi-level programming problems' concepts, an analysis of the BLPP's research status, and some algorithms for BLPP.iii. An algorithm based on ordinary EAs for BLPP , finding one group and two groups weight-sums in the low-level, two different algorithms to take effect, utilizing existing constraint handling strategy and selection mechanism.iv. The effectiveness of the suggested methods is demonstrated by performing some numerical experiments on some problem instances and comparing the results to each other.