An Artificial Intelligence Algorithm for Multi-dimensional Knapsack Problem Based on Small World Phenomenon

The genetic algorithm (GA) always loses diversity in the set of the candidate solutions and prematurely converges, when itpsilas used to solve the complex combinatorial optimization problems, such as 0-1 multi-dimensional knapsack problems. In order to overcome these shortcomings of GA, we propose an optimization algorithm for 0-1 multi-dimensional knapsack problems, called the binary-coding small world algorithm (BSWA), based on searching mechanisms in social networks. The BSWA emphasizes local rather (as mutation in GA) than global search (as crossover in GA) to find the solutions for optimization problems. Compared with the corresponding GA, the BSWA is capable of preserving diversity, avoiding premature convergence, and it converges faster. These properties suggest that the BSWA is a useful method for solving complicated optimization problems. The simulation studies show that the best known solutions of 72.73% of the 55 standard 0-1 knapsack problems can be found by the BSWA in each of the 50 independent runs and the final solutions found by the BSWA for the other problems are very close to the best known ones.