In mathematics and computer science an optimization problem, the problem is finding the best solution among all possible solutions. Given the importance of the knapsack in computer sciences, different algorithms are used to solve it. Knapsack problem is a combinational problem of selectivity and the purpose of solving the most benefit by taking the capacity is the tolerable knapsack. Since the knapsack is a problem of constrained maximization. In this study, a mathematical model in the form of a function unlimited minimization and designed for it, hen this model on Particle Swarm Optimization , Firefly Algorithm and Artificial Bee Colony has been implemented in MATLAB software environment, The results show that the artificial bee colony algorithm, the model is better than the other two algorithms .The advantage of this model is the objective function , because minimization and unlimited models , to implement with many  Bio-Inspired algorithms.