DNA computing在最近幾年常被應用在解NP-complete問題如SAT問題、銷售員問題(the traveling salesman problem)等的方法上。之前發表的一些方法，本質上幾乎都是暴力法(brute force method)：先產生所有可能的解答，再從中逐一檢查並找出最好的解。DNA computing的概念是一開始製造代表所有的解答的DNA序列，再利用一些分子生物學的實驗技術淘汰掉不適合的解，剩下來的DNA序列所代表的就是欲解之問題的最佳解。對傳統的DNA computing觀念而言，其好處是較容易實作，壞處是在淘汰掉不適合的解的這個過程中，可能會誤將好的解答也淘汰掉，造成好的解之相對濃度比不好的解答來的低。在這篇論文中，我們將螞蟻系統(ant colony optimization algorithms)的觀念應用到傳統的DNA computing概念中。在新的方法中，整個過程會一再重複，就算在某回合誤將好的解答淘汰，剩下的解答在下回合也會重組並可能形成更好的解答，若干回合後好的解答的濃度自然會大幅提升，亦較容易剩下的DNA序列中取出正確解答。

Previous research on DNA computing has shown that DNA algorithms are useful to solve some combinatorial problems, such as the Hamiltonian path problem and the traveling salesman problem. The basic concept implicit in previous DNA algorithms is the brute force method. That is, all possible solutions are created initially, then inappropriate solutions are eliminated, and finally the remaining solutions are correct or the best ones.

However, correct solutions may be destroyed while the procedure is executed. In order to avoid such an error, we recommend combining the conventional concepts of DNA computing with a heuristic optimization method and apply the new approach to design strategies. In this thesis, we present a DNA algorithm based on ant colony optimization (ACO) for solving the traveling salesman problem (TSP). Our method manipulates DNA strands of candidate solutions initially. Even if the correct solutions are destroyed during the process of filtering out, the remaining solutions can be reconstructed and correct solutions can be reformed. After filtering out inappropriate solutions, we employ control of melting temperature to amplify the surviving DNA strings proportionally. The product is used as the input and the iteration is performed repeatedly. Accordingly, the concentration of correct solutions will be increased.

Our results agree with that obtained by conventional ant colony optimization algorithms and are better than that obtained by genetic algorithms. The same idea can be applied to design methods for solving other combinatorial problems with DNA computing.

Chapter 1. Introduction

Chapter 2. Preliminaries
2.1 Biochemical Operations
2.2 The Method for Solving the Hamiltonian Path Problem by Adleman
2.3 Applying Concentration Control to the Method for Solving the Shortest Path Problem
2.4 Using Solid Phase DNA Algorithm to Solve HPP
2.5 Applying Temperature-Gradient Method on the DNA Algorithm to Solve TSP

Chapter 3. Ant Colony Optimization Algorithms
3.1 The Concept of ACO
3.2 The Application of ACO on TSP

Chapter 4. The DNA Algorithm for Solving TSP
4.1 The Concept and the Procedure of the DNA Algorithm
4.1.1 The Concept of the Algorithm
4.1.2 The Procedure of the DNA Algorithm
4.2 Simulation and Analysis of the Algorithm
4.2.1 Result and Analysis of the Simulation
4.2.2 Discussion

Chapter 5. Conclusion

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