区间自适应遗传算法优化无约束非线性规划问题
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摘要
针对无约束非线性规划传统优化方法存在的问题,将区间自适应遗传算法引入无约束非线性规划优化中,算法可以利用当前进化信息,自适应移动搜索区间,找到全局最优解,故可缩短搜索区间长度,提高编码精度,降低算法计算量,解决了传统遗传算法处理优化问题时,给定区间必须包含最优解这一问题,这也是本算法有别于其他优化算法的独特优势,为某些最优解所在区间难以估计的无约束非线性规划问题的优化提供了一条有效可行的途径.系统阐述了区间自适应遗传算法的原理,给出了算法优化无约束非线性规划问题的步骤,以MatlabR2016b仿真方式对算法进行了实例测试,结果表明,方法是一种计算稳定、正确、有效、可靠实用的无约束非线性规划优化方法.
To solve the problems existing in the traditional unconstrained nonlinear programming optimization method, this paper introduces interval adaptive genetic algorithm into optimizing unconstrained nonlinear programming problems. The algorithm can use the current evolution information to adaptively move the search interval, find the global optimal solution. So it can shorten the search interval length, improve the coding accuracy, reduce the amount of calculation, and it solve the problem in traditional genetic algorithm dealing with optimization problems that the given interval must contain the optimal solution. This is also the unique advantage of this algorithm compared to other optimization algorithms. It provides an effective and feasible way for some unconstrained nonlinear programming problems that the interval where the optimal solution lies in is difficult to estimate. In this paper, the principle of interval adaptive genetic algorithm is expounded systematically, and the steps of the algorithm to optimize the unconstrained nonlinear programming problem are given. The algorithm is tested by Matlab simulation. The results show that the method is a computationally stable,accurate, efficient, reliable and practical optimization method for the unconstrained nonlinear programming.
To solve the problems existing in the traditional unconstrained nonlinear programming optimization method, this paper introduces interval adaptive genetic algorithm into optimizing unconstrained nonlinear programming problems. The algorithm can use the current evolution information to adaptively move the search interval, find the global optimal solution. So it can shorten the search interval length, improve the coding accuracy, reduce the amount of calculation, and it solve the problem in traditional genetic algorithm dealing with optimization problems that the given interval must contain the optimal solution. This is also the unique advantage of this algorithm compared to other optimization algorithms. It provides an effective and feasible way for some unconstrained nonlinear programming problems that the interval where the optimal solution lies in is difficult to estimate. In this paper, the principle of interval adaptive genetic algorithm is expounded systematically, and the steps of the algorithm to optimize the unconstrained nonlinear programming problem are given. The algorithm is tested by Matlab simulation. The results show that the method is a computationally stable,accurate, efficient, reliable and practical optimization method for the unconstrained nonlinear programming.
引文
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[19]纪震,廖惠连.粒子群算法及应用[M].北京:科学出版社,2009
[20]朱会霞,郝志云,王福林.二进制遗传算法编码长度的计算方法[J].辽宁工业大学学报(自然科学版),2016(02):138-140.
[2] He Y, Gao S, Liao N, Liu H. A nonlinear goal-programming-based DE and ANN approach to grade optimization in iron mining[J]. Neural Computing&Applications, 2016, 27(7):20651-2081.
[3] Nit a C, Vandewalle S, Meyers J. On the efficiency of gradient based optimization algorithms for DNS-based optimal control in a turbulent channel flow. Computers&Fluids, 2016, 125:11-24.
[4]陈力,万嵩林,徐雪炀.水面舰艇编队防空和信息化战争评估模型[J].数学的实践与认识,2016, 46(14):95-103.
[5]李宜芮,刘进忙,王刚.基于非线性规划协同进化遗传算法的防空导弹火力优化分配研究[J].测控技术,2017, 36(08):82-85.
[6]张中强,宋学锋.基于非线性规划的社会系统协调发展优化模型及其应用[J].数学的实践与认识,2010,40(19):76-84.
[7]应玖茜,魏权龄.规划及其理论[M].北京:中国人民大学出版社,1994.
[8]石礼堂,陈伟.非线性无约束优化问题的滤子填充函数算法[J].运筹学学报,2017, 21(01):55-64.
[9]韩晓龙,李上,杨全业.基于遗传算法的战略供应链集成研究[J].计算机工程与应用,2018, 54(02):214-221.
[10]吴睿.无约束非线性优化问题的算法比较[J].衡水学院学报,2011(04):19-21.
[11]戴虹,刘新为.线性与非线性规划算法与理论[J].运筹学学报,2014, 18(01):69-92.
[12]谢海玲.无约束非线性规划的最优性条件[A].中国运筹学会不确定系统分会.第十二届中国青年信息与管理学者大会论文集[C].中国运筹学会不确定系统分会,2010:3.
[13]叶峰,邵之江,梁昔明,钱积新.四种无约束优化算法的比较研究[J].数学的实践与认识,2004, 34(05):108-112.
[14]曾刘拴.求解无约束优化问题的混合信赖域方法[D].重庆大学,2014.
[15]张静.无约束非线性规划的共轭梯度法研究综述[J].北京联合大学学报(自然科学版),2008(02):72-76.
[16]徐晓光,王开荣.一类具有充分下降性的共轭梯度算法[J/OL].华东师范大学学报(自然科学版),2017(02):44-51+60.
[17]玄登影,王福林,高敏慧,马海志.一种改进适应度函数的遗传算法[J].数学的实践与认识,2015, 45(16):232-238.
[18]汪定伟,王俊伟,王洪峰,张瑞友,郭哲.智能优化方法[M].北京:高等教育出版社,2007.
[19]纪震,廖惠连.粒子群算法及应用[M].北京:科学出版社,2009
[20]朱会霞,郝志云,王福林.二进制遗传算法编码长度的计算方法[J].辽宁工业大学学报(自然科学版),2016(02):138-140.