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**Genetic algorithm for minimizing the total weighted completion time scheduling problem with learning and release times.**
*(English)*
Zbl 1205.90139

Summary: This paper considers a single-machine problem with the sum-of-processing time based learning effect and release times. The objective is to minimize the total weighted completion times. First, a branch-and-bound algorithm incorporating with several dominance properties and two lower bounds are developed for the optimal solution. Then a genetic heuristic-based algorithm is proposed for a near-optimal solution. Finally, a computational experiment is conducted to evaluate the performances of the proposed algorithms. The results show that the branch-and-bound algorithm can solve instances up to 15 jobs, and the average error percentage of the genetic heuristic algorithm is less than 0.105%.

### MSC:

90B35 | Deterministic scheduling theory in operations research |

90C59 | Approximation methods and heuristics in mathematical programming |

### Keywords:

genetic heuristic algorithm; scheduling; sum-of-processing time based learning effect; release time
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\textit{C.-C. Wu} et al., Comput. Oper. Res. 38, No. 7, 1025--1034 (2011; Zbl 1205.90139)

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