基于约束保持法的矢量拟态物理学约束优化算法研究
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摘要
生产实践中存在很多难以优化的约束优化问题,智能进化算法与传统约束处理方法相结合成为解决这类问题的有效方法。拟态物理学优化算法是一种最近提出的启发式算法。矢量拟态物理学算法是在拟态物理学优化算法的基础上引入了矢量模型,增强了种群多样性,个体在引斥力规则作用下向目标函数最优值所在的区域移动。矢量拟态物理学算法具有良好的全局搜索能力,并且不受约束条件函数本身特点的影响,算法原理简单,适合与传统约束处理方法结合处理约束优化问题。
本文采用矢量拟态物理学优化算法与约束保持法相结合来求解约束优化问题。约束保持法是一种传统约束处理方法,它要求所有个体在任何时刻都在可行域内,这就要求个体在初始情况下均为可行解。首先分别采用随机方法和矢量拟态物理学优化算法来产生可行个体,仿真实验表明在产生初始可行解时矢量拟态物理学优化算法优于随机方法;然后针对越界个体引入收缩系数,使得越界个体在不改变其速度方向的前提下收缩回问题空间。利用违反约束量函数来判断个体是否在可行域内,分别采用斐波那契法、黄金分割法、二分法等一维搜索方法将不可行个体拉回可行域,再利用矢量拟态物理学优化算法搜索目标问题的最优解;仿真实验表明这三种方法中,混合黄金分割法的矢量拟态物理学优化算法的搜索精度最优,搜索性能最稳定,混合二分法的矢量拟态物理学优化算法和混合斐波那契法的矢量拟态物理学优化算法次之。混合多维搜索约束保持法的矢量拟态物理学优化算法求解约束优化问题时,将不可行个体拉回可行域的过程转化为求解以收缩矩阵η为变量的违反约束量函数的最优值问题,其搜索过程相当于在超多方体内进行搜索。对比一维搜索方法在超曲面内搜索,多维搜索方法搜索到可行个体的概率比一维搜索方法要大,并且增加了种群多样性。仿真结果表明混合多维搜索的矢量拟态物理学算法比混合一维搜索的矢量拟态物理学算法具有更好的搜索性能和稳定性。
There are many constraint optimization problems which are difficult to optimize in the production, combining intelligence evolutionary algorithm with the traditional constraint processing method become the effective method to solve this kind of problem. APO algorithm is a new proposed heuristic algorithm. VM-APO algorithm introduces vector model based on the artificial physics optimization algorithm, enhance the diversity of population, and the individual move to the area in which the optimal value of objective function under the regular action of gravitation and repulsion. The VM-APO algorithm which is not affected by the characteristics of constrained function itself has good global search capability, and the theory of the algorithm is simple. It’s suited to combine the VM-APO algorithm with traditional constraint processing method to solve the constraint optimization problems.
A new method which is combined the VM-APO algorithm with constraint-preserving method is adopted to solve the constrained optimization problem in this text. Constraint-preserving method which is a kind of traditional constraint processing method requires all individual in the feasible region at all times, so it requires that the individuals must be feasible solutions in the initial case. First random method and VM-APO algorithm are used respectively to produce all feasible individuals. Simulation experiment shows that VM-APO algorithm is better than random method when the initial feasible solutions to produce. Then shrinkage coefficient is introduced aiming at cross-border individual, which is shrinked back to the problem space without changing the direction of speed. The violation degree function is used to determine whether every individual is in the feasible region or not, and the Gold Cutting Method, the Dichotomy Method and Fibonacci method are used respectively to pull the unfeasible individuals back to the feasible region. Finally the VM -APO algorithm is adopted to search the optimal value of objective function. The Simulation results show that the search performance and stability of VM-APO-GDM algorithm is the best and the most stable, this is followed by VM-APO-FM and VM-APO-DM algorithm. When the VM-APO algorithm with mixed multidimensional search is used to solve constraint optimization problems, the process of pulling infeasible individual back to the feasible region is turned into solving optimal value problem of the violation degree function in terms of contraction matrixη. Contrasting multi-dimensional search method with one-dimension search method on searching feasible individual in hypersurface, the probability of former is greater than the latter, and the diversity of population is increased. The simulation results indicate that the VM-APO-MDCPM algorithm is better than VM-APO-ODCPM algorithm in search performance and stability.
本文采用矢量拟态物理学优化算法与约束保持法相结合来求解约束优化问题。约束保持法是一种传统约束处理方法,它要求所有个体在任何时刻都在可行域内,这就要求个体在初始情况下均为可行解。首先分别采用随机方法和矢量拟态物理学优化算法来产生可行个体,仿真实验表明在产生初始可行解时矢量拟态物理学优化算法优于随机方法;然后针对越界个体引入收缩系数,使得越界个体在不改变其速度方向的前提下收缩回问题空间。利用违反约束量函数来判断个体是否在可行域内,分别采用斐波那契法、黄金分割法、二分法等一维搜索方法将不可行个体拉回可行域,再利用矢量拟态物理学优化算法搜索目标问题的最优解;仿真实验表明这三种方法中,混合黄金分割法的矢量拟态物理学优化算法的搜索精度最优,搜索性能最稳定,混合二分法的矢量拟态物理学优化算法和混合斐波那契法的矢量拟态物理学优化算法次之。混合多维搜索约束保持法的矢量拟态物理学优化算法求解约束优化问题时,将不可行个体拉回可行域的过程转化为求解以收缩矩阵η为变量的违反约束量函数的最优值问题,其搜索过程相当于在超多方体内进行搜索。对比一维搜索方法在超曲面内搜索,多维搜索方法搜索到可行个体的概率比一维搜索方法要大,并且增加了种群多样性。仿真结果表明混合多维搜索的矢量拟态物理学算法比混合一维搜索的矢量拟态物理学算法具有更好的搜索性能和稳定性。
There are many constraint optimization problems which are difficult to optimize in the production, combining intelligence evolutionary algorithm with the traditional constraint processing method become the effective method to solve this kind of problem. APO algorithm is a new proposed heuristic algorithm. VM-APO algorithm introduces vector model based on the artificial physics optimization algorithm, enhance the diversity of population, and the individual move to the area in which the optimal value of objective function under the regular action of gravitation and repulsion. The VM-APO algorithm which is not affected by the characteristics of constrained function itself has good global search capability, and the theory of the algorithm is simple. It’s suited to combine the VM-APO algorithm with traditional constraint processing method to solve the constraint optimization problems.
A new method which is combined the VM-APO algorithm with constraint-preserving method is adopted to solve the constrained optimization problem in this text. Constraint-preserving method which is a kind of traditional constraint processing method requires all individual in the feasible region at all times, so it requires that the individuals must be feasible solutions in the initial case. First random method and VM-APO algorithm are used respectively to produce all feasible individuals. Simulation experiment shows that VM-APO algorithm is better than random method when the initial feasible solutions to produce. Then shrinkage coefficient is introduced aiming at cross-border individual, which is shrinked back to the problem space without changing the direction of speed. The violation degree function is used to determine whether every individual is in the feasible region or not, and the Gold Cutting Method, the Dichotomy Method and Fibonacci method are used respectively to pull the unfeasible individuals back to the feasible region. Finally the VM -APO algorithm is adopted to search the optimal value of objective function. The Simulation results show that the search performance and stability of VM-APO-GDM algorithm is the best and the most stable, this is followed by VM-APO-FM and VM-APO-DM algorithm. When the VM-APO algorithm with mixed multidimensional search is used to solve constraint optimization problems, the process of pulling infeasible individual back to the feasible region is turned into solving optimal value problem of the violation degree function in terms of contraction matrixη. Contrasting multi-dimensional search method with one-dimension search method on searching feasible individual in hypersurface, the probability of former is greater than the latter, and the diversity of population is increased. The simulation results indicate that the VM-APO-MDCPM algorithm is better than VM-APO-ODCPM algorithm in search performance and stability.
引文
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[19]闫建国.一种基于多样性保持的遗传算法及其仿真[J].计算机仿真,2010,27(4):206-209.
[20] D. Beasley, D.R. Bull, R.R. Martin. An overview of genetic algorithms: Part 2, Research topics[J]. Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum Associates,1993, 15(2): 170-181.
[21] Rocha A, Fernandes E. A modified electromagnetism-like algorithm based on a pattern search method[C]. European Computing Conference. Springer-Verlag,2009:1035-1042.
[22] Rocha A., Fernandes E. Feasibility and dominance rules in the electromagnetism-like algorithm for constrained global optimization[C]. (ICCSA 2008). 2008:768-783.
[23]郭鹏.基于类电磁机制算法的函数优化研究[D].西安,西安电子科技大学.2009.
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