Solving the 0–1 multi-objective knapsack problem using self-assembly of DNA tiles

Recently, many researchers have demonstrated that computation by DNA tile self-assembly may be scalable and it is considered as a promising technique in nanotechnology. In this paper, we show how the tile self-assembly process can be used for solving the 0–1 multi-objective knapsack problem by mainly constructing four small systems which are nondeterministic guess system, multiplication system, addition system and comparing system, by which we can probabilistically get the feasible solution of the problem. Our model can successfully perform the 0–1 multi-objective knapsack problem in polynomial time with optimal Θ(1) distinct tile types, parallely and at very low cost.