本論文利用基因演算法搜索單機排程問題的最佳解，並擇優保留最長共同子序列配合隨機交配來改良它，使得演算法可以在較短的迭代次數內就達到停止條件。

In this paper we propose an improved algorithm to search optimal solutions to the single machine total weighted tardiness scheduling problem. We propose using longest common sequence to combine with the random key method. Numerical simulation shows that the scheme we proposed could improve the search efficiency of genetic algorithm in this problem for some cases.

1 Introduction 1
2 Preliminaries 3
2.1 Single Machine Total Weighted Tardiness Scheduling Problem 3
2.2 Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Binary Representation . . . . . . . . . . . . . . . . . . 4
2.2.2 Decoding Heuristic . . . . . . . . . . . . . . . . . . . . 5
3 Design of Genetic Algorithm 10
3.1 Original Genetic Algorithm . . . . . . . . . . . . . . . . . . . 10
3.1.1 Initial Population . . . . . . . . . . . . . . . . . . . . . 10
3.1.2 Fitness and Scaling . . . . . . . . . . . . . . . . . . . . 12
3.1.3 Reproduction . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.4 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.5 Mutation . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Longest Common Subsequences . . . . . . . . . . . . . . . . . 16
4 Numerical Results 19
4.1 Test Data Construction . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Conclusions 22
Bibliography 23

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