Study Of Multi-objective Optimization Method Based On Evolutionary Algorithm

There are many multi-objective optimization problems in practice, this kind of problems have many objectives to be optimized simultaneously and normally they conflicting with each other. Thus, we cannot find one solution that optimize all the objectives to be optimum, all we can do is to find a set of solutions that make a good trade-off between all the objectives. In the case of traditional mathematical programming techniques, in order to find several solutions we have to perform a series of separate runs. Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of possible solutions (the so-called population). This allows us to find several members of the Pareto optimal set in a single run of the algorithm. Additionally, evolutionary algorithms are less susceptible to the shape or continuity of the Pareto front (e.g., they can easily deal with discontinuous or concave Pareto fronts). The key technique of multi-objective optimization evolutionary algorithms are studied in this dissertation, and the main research work is as follows:1) In order to decide which individual is better, the pareto dominance is used, because it is too strict, a lot of solutions will be generated between them we can't decide which one is better, which will lead the algorithm to stagnate. In order to preserve the diversity of the population, a lot of measures have been used, because they aren't compliant with pareto dominance, which will lead the pareto front to deteriorate. For the phenomenon of stagnation and deterioration appear, the idea of hypervolume dominance is used to improve the well-known algorithm NSGA-Ⅱ, the selection strategy based on pareto dominance is replaced by the selection strategy based on hypervolume dominance, it is compliant with the selection strategy based on pareto dominance, and additional method isn't needed to preserve the diversity of the population. As the simulation results show, the solution set obtained by the improved algorithm HYPE-NSGA-Ⅱhas greatly improved in terms of distribution and convergence.2) When the evolutionary multi-objective optimization algorithm, which will not incorporate the preference information of decision maker into it, is used to solve problems, follow problems always exist: (1)most of the computing time is wasted on searching the areas where the decision maker is not interested in. (2)After the running of the algorithm, too many solutions is presented to the decision maker, which increase the decision burden of the decision maker. For the above problems, based on the improved algorithm HYPE-NSGA-Ⅱ, the preference information is incorporated into it. Preference information is given in the form of reference point, the expected value of every objective function is included in the reference point. The concrete method is to combinate the fitness evaluation function and function which contains the preference information. As the simulation results show, after the decision maker's preference information is incorporated, a lot of solutions which near to the reference point are obtained, it is not noly decrease the computing time of the algorithm, but also decrease the decision burden of the decision maker.