A DNA algorithm for the job shop scheduling problem based on the Adleman-Lipton model

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.

A Parallel DNA Algorithm for Solving the Quota Traveling Salesman Problem Based on Biocomputing Model

“…Currently, DNA computing algorithms for different complex problems are being proposed, for example, Wu et al [ 48 ] and Tian et al [ 31 ] used DNA computing to solve the family traveling salesperson problem and job shop scheduling problem respectively, achieving great efficiency gains in terms of algorithmic computational complexity. In addition, DNA computing has been increasingly applied to different scenarios, such as image recognition [ 53 ], artificial neural network design [ 54 ] and quantum computing [ 55 ].…”

“…In 2019, Wang et al [ 30 ] designed a bio-inspired computing model to solve the capacitated vehicle routing problem. In 2020, Tian et al [ 31 ] showed a DNA algorithm with O ( n 2 ) time complexity for the job shop scheduling problem. For the generalised traveling salesman problem (GTSP), Ren et al [ 32 ] used DNA biological chains to represent different vertices, point groups and weights, and found the optimal solution of the problem using a series of different DNA sequence biochemical reactions.…”