基于猴群算法求解0-1背包问题
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摘要
0-1背包问题是一个经典的NP完全问题,该问题在实际生活中具有广泛的应用.针对现有算法在求解0-1背包问题时精度不高的缺点,提出了一种诱导因子猴群算法.所给诱导因子猴群算法的基本思想是,在基本猴群算法的爬过程中引入诱导因子,诱导其向上爬行,从而可以逃逸局部最优解,找到全局最优解.在仿真试验中,与已有方法进行比较,结果说明利用所给诱导因子猴群算法求解0-1背包问题是有效的.
The 0-1 knapsack problem is a classical NP complete problem, which has a wide range of applications in real life. In view of the existing algorithms with the shortcoming of low precision in solving 0-1 knapsack problem, an inducing factor monkey algorithm is proposed to solve the problem. The basic idea of the proposed inducing factor monkey algorithm is that an inducing factor is adopted in the climbing process of the basic monkey algorithm to induce it to crawl upward, which can escape from local optimal solution and find the global optimal solution. In the simulation,compared with the existing methods, the results show that the proposed inducing factor monkey algorithm for solving 0-1 knapsack problem is valid.
The 0-1 knapsack problem is a classical NP complete problem, which has a wide range of applications in real life. In view of the existing algorithms with the shortcoming of low precision in solving 0-1 knapsack problem, an inducing factor monkey algorithm is proposed to solve the problem. The basic idea of the proposed inducing factor monkey algorithm is that an inducing factor is adopted in the climbing process of the basic monkey algorithm to induce it to crawl upward, which can escape from local optimal solution and find the global optimal solution. In the simulation,compared with the existing methods, the results show that the proposed inducing factor monkey algorithm for solving 0-1 knapsack problem is valid.
引文
1Merkle R,Hellman M.Hiding information and signatures in trapdoor knapsacks.IEEE Transactions on Information Theory,1978,24(5):525–530.[doi:10.1109/TIT.1978.1055927]
2 赵学武,刘向娇,王兴,等.求解0-1背包问题的遗传算法.南阳师范学院学报,2014,13(6):21–25.
3Srinivasan V,Varghese G.Fast address lookups using controlled prefix expansion.ACM Transactions on Computer Systems,1999,17(1):1–40.[doi:10.1145/296502.296503]
4 李鸣山,郑海虹.0-1背包问题的多重分枝-限界算法.武汉测绘科技大学学报,1995,20(1):83–87.
5宁爱兵,马良.0/1背包问题快速降价法及其应用.系统工程理论方法应用,2005,14(4):372–375.
6 王粉兰,孙小玲.不可分离凸背包问题的拉格朗日分解和区域分割方法.运筹学学报,2004,8(4):45–53.
7王乐,王世卿,张静乐.基于Matlab的0-1背包问题的动态规划方法求解.计算机技术与发展,2006,16(4):88–89,92.
8 荆源.背包问题的差分进化算法.才智,2011,(7):92–93.
9赵传信,季一木.粒子群优化算法在0/1背包问题的应用.微机发展,2005,15(10):23–25.[doi:10.3969/j.issn.1673-629 X.2005.10.009]
10 乐天.遗传算法求解0/1背包问题的综述.浙江海洋学院学报(自然科学版),2013,32(1):71–74.
11Zhao RQ,Tang WS.Monkey algorithm for global numerical optimization.Journal of Uncertain Systems,2008,2(3):164–176.
12李晓,倪富陶,孙维刚,等.基于猴群算法的连续刚构桥传感器优化布置研究.公路,2016,61(3):65–69.
13 张佳佳,张亚平,孙济洲.基于猴群算法的入侵检测技术.计算机工程,2011,37(14):131–133.[doi:10.3778/j.issn.1002-8331.2011.14.037]
14赵涛,夏雨,宗玛利.基于猴群算法的加气站项目进度研究.价值工程,2010,29(8):90–92.
15 申彩英,高韬.基于猴群算法的混合动力汽车能量管理策略.计算机工程与应用,2014,50(14):9–13,120.[doi:10 .3778/j.issn.1002-8331.1308-0015]
16Ituarte-Villarreal CM,Lopez N,Espiritu JF.Using the monkey algorithm for hybrid power systems optimization.Procedia Computer Science,2012,(12):344–349.[doi:10.1016/j.procs.2012.09.082]
17 Hodashinsky IA,Samsonov SS.Design of fuzzy rule based classifier using the monkey algorithm.Mathematical Methods and Algorithms of Business Informatics,2017,1 (39):61–67.
2 赵学武,刘向娇,王兴,等.求解0-1背包问题的遗传算法.南阳师范学院学报,2014,13(6):21–25.
3Srinivasan V,Varghese G.Fast address lookups using controlled prefix expansion.ACM Transactions on Computer Systems,1999,17(1):1–40.[doi:10.1145/296502.296503]
4 李鸣山,郑海虹.0-1背包问题的多重分枝-限界算法.武汉测绘科技大学学报,1995,20(1):83–87.
5宁爱兵,马良.0/1背包问题快速降价法及其应用.系统工程理论方法应用,2005,14(4):372–375.
6 王粉兰,孙小玲.不可分离凸背包问题的拉格朗日分解和区域分割方法.运筹学学报,2004,8(4):45–53.
7王乐,王世卿,张静乐.基于Matlab的0-1背包问题的动态规划方法求解.计算机技术与发展,2006,16(4):88–89,92.
8 荆源.背包问题的差分进化算法.才智,2011,(7):92–93.
9赵传信,季一木.粒子群优化算法在0/1背包问题的应用.微机发展,2005,15(10):23–25.[doi:10.3969/j.issn.1673-629 X.2005.10.009]
10 乐天.遗传算法求解0/1背包问题的综述.浙江海洋学院学报(自然科学版),2013,32(1):71–74.
11Zhao RQ,Tang WS.Monkey algorithm for global numerical optimization.Journal of Uncertain Systems,2008,2(3):164–176.
12李晓,倪富陶,孙维刚,等.基于猴群算法的连续刚构桥传感器优化布置研究.公路,2016,61(3):65–69.
13 张佳佳,张亚平,孙济洲.基于猴群算法的入侵检测技术.计算机工程,2011,37(14):131–133.[doi:10.3778/j.issn.1002-8331.2011.14.037]
14赵涛,夏雨,宗玛利.基于猴群算法的加气站项目进度研究.价值工程,2010,29(8):90–92.
15 申彩英,高韬.基于猴群算法的混合动力汽车能量管理策略.计算机工程与应用,2014,50(14):9–13,120.[doi:10 .3778/j.issn.1002-8331.1308-0015]
16Ituarte-Villarreal CM,Lopez N,Espiritu JF.Using the monkey algorithm for hybrid power systems optimization.Procedia Computer Science,2012,(12):344–349.[doi:10.1016/j.procs.2012.09.082]
17 Hodashinsky IA,Samsonov SS.Design of fuzzy rule based classifier using the monkey algorithm.Mathematical Methods and Algorithms of Business Informatics,2017,1 (39):61–67.