多维背包问题的一个蚁群优化算法

An Improved Ant Algorithm for Multidimensional Knapsack Problem

蚁群优化(ACO)是一种通用的启发式方法,已被用来求解很多离散优化问题.近年来,已提出几个ACO算法求解多维背包问题(MKP).这些算法虽然能获得较好的解但也耗用太多的CPU时间.为了降低用ACO求解MKP的复杂性,文章基于一种已提出但未实现过的MKP的信息素表示定义了新的选择概率的规则和相应的基于背包项的一种序的启发式信息,从而提出了一种计算复杂性较低、求解性能较好的改进型蚁群算法.实验结果表明,无论串行执行还是虚拟并行执行,在计算相同任务时,新算法耗用时间少且解的价值更高.不仅如此,在实验中,文中的新算法获得了ORLIB中测试算例5.250-22的两个"新"解.

Ant Colony Optimization （ACO） is a metaheuristic. And it has been applied to many hard discrete optimization problems. Recently, some researchers have proposed several different ACO algorithms to solve the multidimensional knapsack problem （MKP）, which is an NP-hard combinatorial optimization problem. Although these algorithms could obtain good solutions of MKP, they consume too more CPU time. For the sake of decreasing the time complexity of the existing ACO algorithms, a new improved ACO algorithm is proposed for MKP in this paper. First, a pheromone representation, which was defined by Blum C. in his paper ＂the hyper-cube framework for ant colony optimization＂ as an example, models binary decision variables assigned to all items and their values. Based on this pheromone model, a new rule choosing the objective item is defined. In this way, the time complexity of the proposed ACO algorithm can be decreased. However, incorporating the heuristic information into the solution construction of the artificial ants is difficult. A new heuristic information of MKP based on some order of all items is described. Experimental results show that in the case of the same computing task~, the new one uses less CPU time and obtains better solutions compared with other ACO algorithms whether the serial or parallel implementation. Also, the new algorithm has obtained two new solutions of test 5. 250-22.