Solving Unbounded Knapsack Problem Using an Adaptive Genetic Algorithm with Elitism Strategy

With the popularity of sensor networks, solving the knapsack problem has become important in selecting the best combination of sensor nodes. Many methods have been proposed to solve the Knapsack problem, but few of them have used the genetic algorithm, especially in unbounded Knapsack problems. In this paper, we use the genetic algorithm to solve the unbounded Knapsack problem. We combine an elite strategy and a self adapting system into the genetic algorithm. Using the elite strategy overcomes the problem of the slow convergence rate of the general genetic algorithm. The elite strategy retains good chromosomes and ensures that they are not eliminated through the mechanism of crossover and mutation, ensuring that the features of the offspring chromosomes are at least as good as their parents. The system automatically adapts the number of the initial population of chromosomes and the number of runs to be executed in the genetic algorithm. It will obtain the best value from the chromosomes of each run executed, and retain the values in an elite group. The optimal value is then taken from the elite group and adopted as the real solution. Experimental results have shown that our method rapidly discovers the best solution of the problem.