Abstract
A DNA (DeoxyriboNucleic Acid) algorithm is proposed to solve the job shop scheduling problem. An encoding scheme for the problem is developed and DNA computing operations are proposed for the algorithm. After an initial solution is constructed, all possible solutions are generated. DNA computing operations are then used to find an optimal schedule. The DNA algorithm is proved to have an O(n2) complexity and the length of the final strand of the optimal schedule is within appropriate range. Experiment with 58 benchmark instances show that the proposed DNA algorithm outperforms other comparative heuristics.
Highlights
It is well known that the traditional silicon-based computers use serial algorithms, so that their computing speed cannot qualitatively leap
It is well known that optimal solutions of most of the celebrated computationally intractable problems can only be found by an exhaustive search through all possible solutions
An appropriate encoding strategy is developed first to generate all possible solutions in parallel using DNA computing
Summary
It is well known that the traditional silicon-based computers use serial algorithms, so that their computing speed cannot qualitatively leap. It is well known that optimal solutions of most of the celebrated computationally intractable problems can only be found by an exhaustive search through all possible solutions. The insurmountable difficulty lies in the fact that such an exhaustive search is too vast to carry out using currently available computing technology, so that numerous intractable problems cannot be solved effectively. Some visionary remarks were made about new ways of solving such problems through possible miniaturizations. Adleman’s experiment [2] solved the Hamiltonian Path Problem for a given directed graph, and demonstrated the strong parallel computing power of DNA computing. Lipton’s DNA-based solution of the satisfiability problem [3] used some of Adleman’s basic operations.
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