Multi-objective test problems, linkages, and evolutionary methodologies
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Journal of Global Optimization
Multiobjective immune algorithm with nondominated neighbor-based selection
Evolutionary Computation
A dominance tree and its application in evolutionary multi-objective optimization
Information Sciences: an International Journal
Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II
IEEE Transactions on Evolutionary Computation
C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization
Information Sciences: an International Journal
Information Sciences: an International Journal
Differential evolution in constrained numerical optimization: An empirical study
Information Sciences: an International Journal
On convergence of the multi-objective particle swarm optimizers
Information Sciences: an International Journal
Multi-objective optimization with artificial weed colonies
Information Sciences: an International Journal
Information Sciences: an International Journal
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
Handling multiple objectives with particle swarm optimization
IEEE Transactions on Evolutionary Computation
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition
IEEE Transactions on Evolutionary Computation
RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm
IEEE Transactions on Evolutionary Computation
Information Sciences: an International Journal
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This paper presents an algorithm, named the uniform design multiobjective differential algorithm based on decomposition (UMODE/D), for optimizing multiobjective problems. The algorithm is a modification to the new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE proposed by Li and Zhang (2009) [20]. Its distinguishing features include: (1) The uniform design method is applied to generate the aggregation coefficient vectors so that the decomposed scalar optimization subproblems are uniformly distributed, and therefore the algorithm could explore uniformly the region of interest from the initial iteration; (2) The simplified quadratic approximation with three best points is employed to improve the local search ability and the accuracy of the minimum scalar aggregation function value. UMODE/D is compared with the original MOEA/D-DE and NSGA-II by solving a wide set of problems with complicated Pareto set shapes in this paper. Experimental results indicate that UMODE/D significantly outperforms MOEA/D-DE and NSGA-II on these test problems. Two sets of experiments are carried out to illustrate the efficiency of the uniform design method and the simplified quadratic approximation separately. In addition, UMODE/D is tested on CEC 2009 problems and combinatorial knapsack problems. Experimental results show that the proposed algorithm performs better than the further improved MOEA/D for almost all the CEC 2009 problems, and the results obtained are very competitive when comparing UMODE/D with some other algorithms on these multiobjective knapsack problems.