Research On Multi-objective Optimization Algorithm Based On Diversity Enhancement

Unlike the single objective optimization problem which have only one optimal solution,a set of trade-off optimal solutions exist in a MOP.There are 2 aspects to evaluate the solution set called convergency and diversity.Convergency means the distance between obtained solutions to the true optimal solutions and the closer distance means better convergency;diversity means the differences of all the obtained solutions and the larger differences means better diversity.In this paper following research has been done about diversity of the solution set:1.According to the advantages and disadvantages of diversity indicators,a diversity indicator based on reference vectors(DIR)have been proposed.At first,a set of uniformly distributed reference vectors are generated.The coverage of each solution in the objective space is evaluated by the number of representative reference vectors it is associated with and the diversity is determined by the standard deviation of the coverage for all the solutions.The smaller value of DIR,the better the diversity of a solution set is.Both the artificial solution sets and the real solution sets generated by different manyobjective algorithms are used to verify DIR as an effective diversity indicator.Based on this indicator,we propose a algorithm called d-NSGA-II which can deal with many objective optimization problems well.Comparing with other state-of-the-art many objective optimization algorithms on two popular test suites,d-NSGA-II can get relatively better results.In addition,d-NSGA-II performs better on two realworld optimization problems(i.e.crash-worthiness design of vehicles and car side-impact problem).2.The diversity maintenance of combinatorial multi-objective optimization is more difficult.In this thesis,a grid weighted sum dominance(gws-dominance)is proposed to maintain the diversity of populations.In the grid system,at most one representative solution is maintained in each grid.The selection of solutions in different grids is according to strong grid dominance and the solutions in the same grid are selected according to the grid weight sum values.Gws-dominance is integrated into PLS for combinatorial multi-objective optimization problems with multiple.In the experimental studies,the GWS-PLS is compared with the classical PLS,three decomposition-based local search approaches(MOEA/D-LS(WS,TCH and PBI)),a grid based algorithm(?-MOEA)and a state-of-the-art hybrid approach(MOMAD)on two sets of benchmark combinatorial MOPs.The experimental results show that the GWS-PLS significantly outperforms the compared algorithms and remains effective on combinatorial optimization problems with more than 3 objectives.