MOEA/D:  Multiobjective Evolutionary Algorithms Based on Decomposition

• Q.  Zhang,  H. Li,  MOEA/D: A Multi-objective Evolutionary Algorithm Based on Decomposition. IEEE Trans. on Evolutionary Computation, vol.11, no. 6, pp7 12-731  2007  ( an early version of this paper appeared as Technical Report CSM-450,  Department of Computer Science, University of Essex, 2006).

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and NSGA-II. Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been showed that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.

C++Code:  continuous MOP and knapsack problem

Matlab Code.

Java Code (written by Wudong Liu).

• H.  Li and Q. Zhang, Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II,    IEEE Trans on Evolutionary Computation, 2008. Accepted (An early version has appeared as Working  Report CES-476,  Dept of CES, University of Essex,  paper (pdf) and C++ code )

• H. Li, Q. Zhang, "A Multiobjective Differential Evolution Based on Decomposition for Multiobjective Optimization with Variable Linkages", Reykjavik 10-13 September, 2006.

• P. C. Chang, S. H. Chen and Q. Zhang,   MOEA/D for Flowshop Scheduling Problems, CEC'08, accepted

• W. Liu, Q. Zhang, E. Tsang and B Virginas, Tchebycheff Approximation in Gaussian Process Model Composition for Multi-objective Expensive Black Box Optimisation, CEC'08, accepted.

• W. Peng, Q. Zhang and H. Li, Comparison Between NSGA-II and MOEA/D on the  Multiobjective Travelling Salesman Problem,  Working  Report CES-478,  Dept of CES, University of Essex, Dec/2007 (an e-copy can be obtained at request).

_____________________________________________________________________

last updated March, 2006, Q. Zhang