Solving two-dimensional HP model by firefly algorithm and simplified energy function

In order to solve the HP model of the protein folding problem, we investigated traditional energy function and pointed out that its discrete property cannot give direction of the next step to the searching point, causing a challenge to optimization algorithms. Therefore, we introduced the simplified energy function into a turn traditional discrete energy function to continuous one. The simplified energy function totals the distance between all pairs of hydrophobic amino acids. To optimize the simplified energy function, we introduced the latest swarm intelligence algorithm, the firefly algorithm (FA). FA is a hot nature-inspired technique and has been used for solving nonlinear multimodal optimization problems in dynamic environment. We also proposed the code scheme strategy to apply FA to the simplified HP model with the clash test strategy. The experiment took 14 sequences of different chain lengths from 18 to 100 as the dataset and compared the FA with standard genetic algorithm and immune genetic algorithm. Each algorithm ran 20 times. The averaged energy convergence results show that FA achieves the lowest values. It concludes that it is effective to solve 2D HP model by the firefly algorithm and the simplified energy function.