Processes 2021 , 9 , 274
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Algorithm 1 MOEA/DTL 1. Initialize the population scale and the number of subproblems. 2. Initialize the maximum number of iterations ( Mt ). 3. Initialize a set of N weight vectors with uniform distribution ( λ 1 , λ 2 , . . . , λ N ). 4. Initialize the number of neighbors for every weight vector ( T ). 5. Set the external population EP = Φ . 6. for each i = 1 to N do 7. The nearest T weight vectors of the i -th weight vector is calculated according to Euclidean distances. 8. Set B ( i )= λ i 1 , λ i 2 , . . . , λ i T ,where B ( i ) is the neighbors of λ i with T weight vectors. 9. endfor 10. Generate x 1 , x 2 , . . . , x N by a specific method. 11. FV i = F x i is set by the decomposition approach. 12. Set z =( z 1 , z 2 , . . . , z n ) T ,where z j = min 1 ≤ i ≤ N f j x i , f j x i is the j -th objective of solution x i . 13. while true do 14. for i = 1 to N do 15. Teaching phase: 16. if x i is not the best individual among its T neighbors 17. An individual from its T neighbors is randomly set as teacher Th witha probability Ps , or an individual is randomly selected from EP as teacher Th witha probability 1- Ps . 18. else 19. An individual is randomly selected from EP as Th . 20. end if 21. A new individual y is generated by a crossover operation from x i and Th . 22. Mutation operation is applied to y with probability Pm to generate a new individual y . 23. for each j ∈ [ 1, . . . , m ] do 24. Set z j = min z j , f j ( y ) . If g te y λ i , z ≤ g te x i λ i , z , set x i = y and FV i = F ( y ) . 25. endfor 26. Learning phase: 27. for each j ∈ B ( i ) do 28. if x j is not the best individual in the T neighbors of x i 29. A new individual y is first generated by crossover operation from x i and x j . 30. A new individual y is generated by applying the mutation operation to y with probability Pm . 31. else 32. Continue to the next iteration. 33. end if 34. for each j ∈ [ 1, . . . , m ] do 35. set z j = min z j , f j ( y ) . 36. if g te y λ i , z ≤ g te x i λ i , z 37. Set x i = y and FV i = F ( y ) . 38. end if 39. endfor 40. endfor 41. endfor 42. Update EP : a new non-dominated set is selected from EP and the new population as the new EP , and get rid of the duplicate solution. If the size of EP is smaller than the setting value, some randomly generated individuals ( EP ) are added to EP until the size of EP is equal to the setting value. 43. for each i = 1 to size ( EP ) do 44. An individual x i is randomly selected from EP − EP , and an individual x j is ran- bdomly selected from EP − EP with a probability Pc , or an individual x j is selected from EP with a probability 1 − Pc . 45. Anew y is generated by crossover operation from x i and x j .
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