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The general form of 0-1 programming problem based on DNA computing

The general form of 0-1 programming problem based on DNA computing. ZhiXiang Y, Fengyue Z, Jin X., Biosystems. 2003 Jun;70(1):73-8. Summarized by Wha-Jin Lee. Introduction(1/2). Adleman showed that DNA can be used to solve the directed Hamiltonian path problem.

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The general form of 0-1 programming problem based on DNA computing

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  1. The general form of 0-1 programming problem based on DNA computing ZhiXiang Y, Fengyue Z, Jin X., Biosystems. 2003 Jun;70(1):73-8. Summarized by Wha-Jin Lee

  2. Introduction(1/2) • Adleman showed that DNA can be used to solve the directed Hamiltonian path problem. • Lipton proposed DNA experiment to solve the SAT problem. • Ouyang et al. presented a solution to the maximal clique problem. • Parallelism allows DNA computers to solve larger, harder problems such as NP-complete problems.

  3. Introduction(2/2) • We present the general form of the 0-1 programming problem was solved by fluorescence labeling techniques based on surface chemistry. • 0-1 programming problem is an important in operation research and has very widespread application • But the model of 0-1 programming problem based on DNA computing has never been studied. • Problems • A great amount of DNA in decoding • DNA computing is inaccurate

  4. 0-1 programming problem • The general form of 0-1 programming problem :

  5. Example of 0–1 programming problem • simple 0–1 programming problem example

  6. Method - decoding • The first group represented variable x, y, z. • The second group represented variable (x = 1 if and only of = 0, such as y, z) • The third group represented the complementary strand of the first group • The fouth group represented the complementary strand of the second group.

  7. Example 2) x+z<=1 3) y+z<=1 1) x+y-z>=1 Optimal solution : (1,0,0)

  8. Method • Step 1. Generate all possible combinations of variable 0 or 1 in the given problem. • Step 2. Reject infeasible solutions according to constraint inequalities (reserved feasible solution). • Step 3. Generate remaining solutions. • Step 4. Repeat Steps 2 and 3. We can remove all infeasible solutions and obtain feasible solutions of the problem; then proceed Step 5. • Step 5. By comparing to value of object function corresponding to every feasible solution, we can obtain an optimum solution.

  9. Result • In order to solve a practical issue, there are still some problems that need further study in biologic technology. • We adopt fluorescence marking technique and laser focus technique, and determine the solution by analyzing fluorescence, the method of which has some significant advantages such as low cost, low error, short operating time, reusable surface and imple experimental steps.

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