The Research And Application Of Multi-objective Evolutionary Based On Decomposition

In real life,people are the pursuit of maximum benefit and minimization cost,so multi-objective optimization problems are prevalent.The difficulty of multi-objective optimization problem is that it needs to deal with multiple multi-targets which are conflicting and mutually constrained.The final solution set is not unique solution,but a series of approximate Pareto optimal solution sets.Pareto optimal solutions are a good choice for decision makers.Since the evolutionary algorithm can provide multiple Pareto optimal solutions through one time running and is not affected by the mathematical properties of the objective function,so as to it is becoming a hotspot in recent years to study the multi-objective optimization problem by using the evolutionary algorithm.In 2007,Professor Zhang Qingfu combines the traditional mathematical Programming and evolutionary algorithm,and then put forward multi-objective evolutionary based on decomposition algorithm(MOEA/D),the algorithm decompose the complex MOP into a number of single objective problems and optimizes them simultaneously by pre-setting weight vector.It owes strong search ability,efficient fitness,evolution,good convergence merits in solving multi-objective optimization problems so as to attract more attention and much research.However,when solving the multi-objective optimization problem with relatively large target or complex Pareto optimal solution,there is a problem that the convergence rate is slow and the quality of solution is low in the condition of the same times of evolution.Therefore,researches on improving MOEA/D and modified decomposition based multi-objective evolutionary algorithms are of great theoretical significance and potential practical value.In this paper,we focus on the shortcomings of the fixed neighborhood structure and the size of the unified neighborhood in the process of evolution,and then propose two improvement strategies,and integrate into the MOEA/D,so two improved decomposition multi-objective evolutionary algorithm are proposed.In the interest of the effectiveness of the strategies,the relevant simulation experiments are carried out.The main research works in this dissertation consist of the following aspects:1.In order to make full use of a series of information of guiding value brought by the new solution of parental reproduction,a dynamic neighborhood updating strategy is proposed and applied in MOEA/D,which proposes a multi-objective Evolutionary algorithm(MOEA/D-UN).The new neighborhood structure is formed by selecting the appropriate individual for each individual's next generation hybrid and substituting by comparing the aggregation function values of the individual individuals with all the individual weight vectors.Which enhances the convergence ability of the algorithm and improves the convergence rate of the algorithm,which provides a solution to the difficult multi-objective optimization problem.And the performance test is carried out on the standard test function,such as ZDT series,DTLZ series and MOP series test questions.The common IGD and HV indicator are used to evaluate the performance of these algorithm,and with the original MOEA/D,the enhanced convergence algorithm MOEA/D-GR,the results show that the convergence rate of the improved algorithm is obviously improved.2.In order to solve the problem that different sub problems use the same size of neighborhood for optimization,which slow down the rate of algorithm for searching the global optimal solution.This paper try to propose a dynamic neighborhood setting strategy that sets a unique neighborhood for each subproblem.First of all,anglicize the reason of not equally treating them;and then,propose the strategy of which decreasing the neighborhood size of the boundary sub problem and the nearest,but the others neighborhood size is increasing,according to the distance between the sub problems and boundary,at last,the strategy is adopted in the MOEA/D,proposing a new algorithm.Furthermore,the special arguments of proposed algorithm are analyzed.The performance of the new algorithm is evaluated in the classic problems such as ZDT,DTLZ,WFG and analyzing the property of the algorithm by Inverted generational distance and Hypervolume indicator,the results show that the convergence performance of the algorithm achieve greatly improvement,on the contrary of MOEA/D.The validity of the strategy of different sub-problem neighborhood should be verified.Which lays the foundation for the improvement of the performance of the algorithm.3.In order to detect the influence of two main parameters proposed in the algorithm on the performance of the algorithm,a series of simulation experiments are carried out by setting a series of parameters.The results show that,for different test problems,the change of parameters has little effect on the performance of the algorithm.But to improve the performance of the algorithm,different subproblems can try to find the appropriate parameters.For the sub-problem of distinguishing near the boundary,the threshold is set to pi/18 and the effect is better,as for the PF is similar to the ZDT6,the angle threshold setting should be slightly larger.4.The MOEA/D-DNS is used for the integrated design of the pattern synthesis of array antennas.Using this algorithm,the linear array antenna with the main beam power and the sidelobe is suppressed.The experimental results show that the proposed algorithm is consistent with the expected value.At the same time,the convergence speed of the algorithm is faster and the solution quality is high.