1. MOEA/D-AMS: Improving MOEA/D by an Adaptive Mating Selection Mechanism Reporter:Steven Date:2011/8/9

2. Abstract  MOEA/D  Controlled Subproblem Selection  Adaptive mating selection mechanism

3. Main idea of MOEA/D

4. Step1: Initialization Subplem i: (3,2) λ : ( 0.3,0.6) Subplem: (2,3) λ : ( 0.8,0.2) Subplem: (1,4) λ : (0.7,0.1) Subplem: (4,2.5) λ : (0.5,0.2) Subplem: (6,2.5) λ : ( 0.9,0.4) Subplem: (0.5,5) λ : ( 0.6,0.3) Population: 6 Neighborhood: :3 Neighborhood of Subproblem i : (2,3) (4,2.5) (1,4) (6,2.5) (0.5,5) (6.5,5)

5. Step2: Update y‘ Mutation y DE Operator Update of Z* Subplem i: (3,2) λ : ( 0.3,0.6) Subplem: (1,4) λ : (0.7,0.1) Subplem: (4,2.5) λ : (0.5,0.2) (6.5,7) (3.5,4.5) λ : ( 0.5,0.6) P(1,4) P(3,2) P(4,2.5) gte(y’) = 1.5

6. Controlled Subproblem Selection (CSS)  However,even distribution of computational effort to the subproblems might not always be good since the difficulty of the subproblems could be different.

7.  MOEA/D-DE, update step is executed for N times in each generation, where N is the population size.  We perform update steps only for individuals whose corresponding subproblems are still unsolved. We regard a subproblem as solved if its solution is not improved for α consecutive generations.  Besides, the β individuals with the largest crowding distance are always enabled. The intention is to keep searching in the unexplored regions.

8. Mating Pool Adjustment (MPA)  In author’s observations, however, individuals close on the objective space might be far way from one another on the decision space.  Individuals with which are allowed to mate are selected according to the Euclidean distance between individuals on the decision space instead of the distance between weight vectors of their subproblems on the objective space.  We start the adjustment of mating pool after γ ⋅ Gen generations, where Gen is the maximum generation number.  To save time, we do the adjustment every ε generations.

9. EXPERIMENTS AND RESULTS

11. Effect of Controlled Subproblem Selection

12. Effect of Mating Pool Adjustment

14. CONCLUSION AND FUTURE WORK  The CSS saves computational effort of solved subproblems and assigns it to unsolved subproblems so that the computational effort is utilized effectively.  The MPA mates individuals with those who are close on the decision space so that small change of gene values can be achieved, which is required at the late stage of evolutionary process.  Comparing with two versions of MOEA/D, the proposed MOEA/D-AMS provides better solution quality in terms of IGD.