摘要
目前由于实际系统优化问题的规模越来越大,约束条件不断增多,非线性严重,致使系统优化难度越来越大,因此,粒子群及其改进算法成为相关学科的研究热点。国内外很多学者对其进行了研究,并在很多方面得到了应用。
由于在粒子群模型中,粒子群一旦找到一个极值很快就收敛,容易陷入局部最优,粒子群模型描述的系统没有一定要找到全局最优的机制,求得的最优粒子只是适应度较好的粒子,因此需要对粒子群算法进行改进。其中一个改进方法是引入了混沌的思想,基于混沌搜索的优化方法利用混沌运动的遍历性特点,即混沌运动能够在一定范围内按其自身的“规律”不重复地遍历所有状态,将混沌状态引入到优化变量中,然后利用混沌变量进行搜索。
本文分析了混沌粒子群算法解的精度难以保证的原因,混沌粒子群算法虽然能使粒子在自变量的全部空间中进行搜索,但后期搜索尺度过大,极值精度难以保证。因此本文提出了分区间的混沌粒子群优化算法,它能使粒子群在选定的自变量区间内进行搜索,缩小了搜索空间的范围,使找到的解更接近全局最优解。
本文用分区间的混沌粒子群优化方法对Benchmark函数优化问题进行了求解。并在相同条件下,与粒子群改进算法、混沌粒子群算法的结果进行了比较,证明了分区间的混沌粒子群优化算法在优化效果和稳定性方面都优于以上算法,是一种更为有效的方法。
在此基础上,用分区间的混沌粒子群算法对流程工业中典型优化问题进行了仿真计算,解决流程工业中的典型非线性规划问题,在运行时间和优化效果方面取得了很好的结果。该算法具有很强的通用性,且无需问题的特殊信息,因此其可成功应用在流程工业中。
Now the scale of optimization problem of real system becomes bigger and bigger, constraint conditions increase continuously and non-linear phenomenon becomes severe, and it's more and more difficult to optimize the system. So the particle swarm optimization algorithm and its improved algorithms have become the hotspots of recent research. Many scholars have done research on it, and have got successful applications in many aspects.
In the particle swarm optimization (PSO) model, once the swarm found an optimum, it converges very fast, and is easy to get trapped in local optimum. The system which the PSO model describes doesn't have the mechanism of definitely finding the global optimum, the best particle it finds is just the particle with better fitness value, so PSO algorithm needs improving. One of the methods to improve it is to introduce in the chaos method. The optimization method based on chaotic search uses the ergodicity of the chaos movement, that is, the chaos movement can spread all the status without repeat by its own "rules" in a certain range. It introduces chaos status into optimized variables and then uses chaos variable to search.
This thesis analyses the reason why the high precision of solution of chaotic particle swarm optimization(CPSO) algorithm is hard to achieve. Though chaotic particle swarm optimization algorithm lets particles search in the whole variable space, the search scale in final time is too large and the high precision of solution is hard to achieve. This thesis proposes a particle swarm optimization algorithm based on divided-interval chaotic search, it lets the particles search in the selected interval, reduces the scope of the search space, and makes the solution more approximate to the global optimum.
The particle swarm optimization algorithm based on divided-interval chaotic search is used to solve Benchmark function optimization problems. Then the method is compared with improved PSO algorithm and CPSO algorithm in the same conditions, which certifies that the particle swarm optimization algorithm based on divided-interval chaotic search has advantage over the above algorithms in the aspects of optimization results and stability, and is a more effective algorithm.
On this base, the particle swarm optimization algorithm based on divided-interval chaotic search is used to simulate typical optimization problem in process industry. It solves a typical non-linear program problem in process industry, and has good results in running time and optimization effects. The algorithm has good commonality, and doesn't need special information, so it can be used in process industry successfully.
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