Research On Decomposition Methods In Evolutionary Multi-objective Optimization Algorithms

The decomposition-based evolutionary multi-objective optimization algorithm(MOEA/D)uses the divide-and-conquer idea to achieve better performance for solving multi-objective optimization problems.However,its performance is highly dependent on the decomposition method on the one hand,and it also has some defects and shortages in the performance for solving many-objective optimization problems on the other.This dissertation starts with the improvement of the decomposition method,and then makes a further exploration on improving the performance for solving many-objective optimization problems,aiming to further improve the convergence,diversity and robustness of the algorithm.The major work and contribution in this dissertation include:(1)When the Pareto Front(PF)is upper convex,the inverted penalty-based boundary intersection(IPBI)decomposition method could not work well.Theoretical analysis have been conducted to explain the reasons causing these shortcomings,giving rise to an enhanced MOEA/D with robust IPBI decomposition method(R-IPBI).Despite the IPBI decomposition method is effective on improving the spread of solutions obtained by MOEA/D compared to the ideal point based decomposition method,it still has several shortcomings:MOEA/D with IPBI decomposition method(MOEA/D-IPBI)often fails to obtain any solution within certain PF regions.Furthermore,it may produce and retain unwanted dominated solutions outside the PF for some problems.The dissertation propose two improvement strategies,i.e.,the adaptive reference point setting strategy and the adaptive subproblem replacement strategy,to overcome the two shortcomings of the IPBI decomposition method respectively.Experimental studies on WFG benchmark problems and the real-world reservoir flood control operation(RFCO)problems suggest that the two improvement strategies are very effective in overcoming the two shortcomings of the IPBI decomposition method.As a result,the proposed R-IPBI algorithm is shown to be able to outperform the original MOEA/D-IPBI reliably.(2)To address the problem of diversity loss and lack of convergence caused by population size limitation in many-objective optimization of the MOEA/D,a novel decomposition method based on user-preference is proposed.Generally speaking,the number of possible solutions for a good approximation of the complete PF increases exponentially with the number of objectives.So it would be more desirable to focus the search on a smaller and more specific PF region in the objective space.The dissertation first proposes a novel decomposition method making use of a series of new reference points derived from a reference point specified by the decision maker(DM)in the preference model.Based on this decomposition method,the dissertation then develops a user-preference-based EMO algorithm,namely R-MOEA/D,targeting only solutions in a small region of the PF defined by the preference information supplied by the DM.This is particularly advantageous for solving many-objective optimization problems.One key merit of R-MOEA/D is that it does not rely on an estimation of the ideal point,which may impact significantly the performances of state-of-the-art decomposition based EMO algorithms.Our experimental results on multiobjective and many-objective benchmark problems have shown that R-MOEA/D provides a more direct and efficient search towards the preferred PF region,resulting in competitive performances.In an interactive setting when the DM changes the reference point during optimization,R-MOEA/D has a faster response speed and performance than the compared algorithms,showing its robustness and adaptability to changes of the preference model.Furthermore,the effectiveness of R-MOEA/D is verified on a real-world problem of reservoir flood control operations.