Replaceable Encoding for Basic Variable of Traffic Network Transportation Optimization Problem

A linear programming problem is solved for the first time based on DNA computing model, which has important significance for research on DNA computing. According to feature of the mathematical model of traffic network transportation optimization problem (TNTOP), three groups of replaceable encoding for each basic variable are designed in the algorithm as follows: basic variable group; variable value group and c value group, which stores the information of basic variable and its value and has many groups replaceable foreign DNA corresponding to the basic variable. In the algorithm of TNTOP based on replaceable encoding for basic variable, combination operation which is used can assign or re-assign values to variables, which is composed of group insert experiment, gel electrophoresis experiment and group deleting experiment. The combination operation can test the constraint conditions and extract all optimal solutions of TNTOP. Detection experiment designed based on electrophoresis experiment can detect mixture containing many kinds of closed circle DNA sequence, and can detect out all closed circle DNA sequences or one closed circle DNA sequence of the mixture according to requirement of the algorithm. The correctness and the complexity of the DNA algorithm are proved, and a simulation example is given to explain feasibility of the DNA algorithm.