Backtracking Ant Colony Algorithm for the 0ߝ1 Knapsack Problem

The 0ߝ1 Knapsack Problem is of a class of typical combinational optimization problems and is NP-hard. It has important practical significance to study it. Based on the characteristics of the 0ߝ1 Knapsack Problem, we design a binary coding directed graph which makes the Ant Colony algorithm suitable for the Knapsack Problem. In addition, we also adopt the concept of backtracking from the Nested Partition(NP) algorithm and apply it to the Ant Colony Optimization(ACO) for strengthening the Ant Colony algorithm of local search ability to solve the 0ߝ1 Knapsack Problem. Numerical tests on typical instances show the efficiency and advantage of the algorithm.