Research On Evolutionary Algorithm For Many-objective Optimization Problems

Multi-objective optimization problems are everywhere in scientific research and engineering applications,which are embodied in automatic control,portfolio and decision-making,workshop scheduling and so on.Although the manyobjective optimization problems are widely used in many fields,the existing many-objective optimization algorithms also expose more disadvantages with the gradual increase of the number of objectives.For example,the number of non-dominated solutions increases rapidly in the evolution process of the algorithm,which can not better judge the dominant relationship of the solution.Thus,it is difficult for the algorithm to select the appropriate individual to enter the next generation.Finally,the algorithm converges to the local optimal solution or even fails to converge.Aiming at the many-objective optimization problem,this thesis mainly studies the following points:(1)In some manyobjective optimization problems,the optimal solution may be located in a discrete regions or region.We want to find a strategy to change the traditional dominant relationship and expand the dominant region of the solution.(2)The traditional optimization algorithm costs a lot in solving the many-objective optimization problem.The problem needs tens of thousands of real function evaluations to get better convergence results.We want to find a mechanism to reduce the number of function evaluations.In view of these,the main work of this thesis is arranged as follows.(1)A many-objective evolutionary algorithm based on extended region dominance and improved niche technology is proposed with the continuous increase of target dimension,lots of non-dominated solutions will be generated in the process of algorithm evolution.For a feasible solution,there may be some feasible solutions that are slightly better in some targets but significantly worse in most targets.For these solutions,they should be dominated by that solution.But the traditional Pareto dominance relationship cannot solve this problem.At the same time,the optimal solutions of some problems are in discrete regions,and the traditional Pareto dominance relationship can not find these solutions.Therefore,a new nonlinear extended dominance relation is proposed,which not only expands the dominance,but also finds the optimal solution in a discrete region.Firstly,the function value of every objectives is normalized in order to remove the negative effects caused by order of magnitude differences.After that,we modify the normalized objective function values of individuals in the population with the newly proposed extended dominance relationship.Finally,combined with the improved niche technology to make up for the problem that the diversity of solution sets is decreased by large convergence pressure.In this thesis,the new nonlinear extended dominance relation and niche technology are applied to NSGA-Ⅲ algorithm.Compared with the mainstream many-objective evolutionary algorithm,the results show that the algorithm plays a good performance in convergence and diversity.(2)A surrogate-assisted evolutionary algorithm is proposed.The traditional many-objective optimization algorithm needs tens of thousands of real function evaluation times to achieve the effect of convergence when solving the optimization problem,and this method is difficult to accept from the cost of engineering optimization.Therefore,a surrogate-assisted evolutionary algorithm is proposed.Firstly,the model is trained by the initial population.Secondly,new individuals are generated through the agent model.Finally,the excellent individuals are selected to enter the next generation population by the selection strategy for area.Therefore,the times of real evaluation are carried out.In the process of evolution,the traditional selection strategies often only favor the individuals with good diversity or convergence of solutions,while the newly proposed area selection strategy can combine diversity and convergence to select excellent individuals into the next generation.In this thesis,the proposed selection strategy is applied to a evolutionary algorithm surrogateassisted by Bayesian optimization method.Besides,we improve its acquisition function,and introduce the distance between individuals and ideal points in the target space.Compared with the mainstream many-objective evolution algorithm,the results show that the algorithm plays a good performance in convergence and diversity.