求解约束优化问题的差分进化算法

发布时间：2018-05-26 03:59

本文选题：约束优化问题 + 差分进化　；参考：《西安电子科技大学》2012年硕士论文

【摘要】：约束优化问题是实际中经常用到的一类数学规划问题．近年来，约束优化问题的求解已成为进化计算研究的一个重要方向．差分进化算法因其原理简单、受控参数少、鲁棒性强等特点，引起了越来越多学者的关注，但是其本质上是一种无约束的优化算法，在求解约束优化问题时需要引入约束处理技术．从约束差分进化算法=约束处理技术+差分进化算法的研究框架出发，从两方面来考虑约束优化差分进化算法的性能具有理论意义和应用前景．本文首先对差分进化算法的研究背景和发展现状做了简要的描述，并就其原理、改进策略、较其他进化算法的优点和应用做了详细说明；然后对基于进化算法的约束处理技术进行分类，并对每类方法的研究现状做了综述；最后将复合差分进化算法与两种不同的约束处理技术相结合，提出了两种改进的约束复合差分进化算法．第一种改进算法基于惩罚函数法，利用自适应惩罚函数的约束处理技术，引入距离作为适应值函数，根据种群的可行率计算个体的距离，对每个个体施行两种惩罚，分别基于目标函数和约束违反程度；同时结合复合差分进化算法，保留后代种群中的较优个体．这样既保留了种群的多样性，又使得种群可以在寻找可行解和寻找最优解之间进行调节．数值实验结果表明，新算法与同类算法相比，，具有较好的全局寻优能力和自适应性．第二种改进算法基于多目标法，将原问题转化为包含原目标函数和约束违反程度两个目标的多目标优化问题，运用多目标优化方法进行求解．该方法由两部分组成：种群进化模型和不可行解替换机制．种群进化模型中复合差分进化算法作为搜索引擎进化种群，利用Pareto支配比较个体，选择其中性能较好的个体；不可行解替换机制用于改善种群中个体的质量和可行率，进而引导种群向可行域逼近．数值实验结果表明，新算法的结果具有较高的计算精度和全局搜索能力．
[Abstract]:Constrained optimization problem is a kind of mathematical programming problem that is often used in practice. In recent years, the solution of constrained optimization problems has become an important research direction in evolutionary computing. Differential evolution algorithm has attracted more and more attention of scholars because of its simple principle, few controlled parameters and strong robustness, but it is essentially an unconstrained optimization algorithm. It is necessary to introduce constraint processing technology in solving constrained optimization problems. Based on the research framework of constrained differential evolution algorithm = constraint processing technology, the performance of constrained optimization differential evolution algorithm is considered from two aspects, which has theoretical significance and application prospect. In this paper, the research background and development status of differential evolutionary algorithm are briefly described, and its principle, improvement strategy, advantages and applications of other evolutionary algorithms are explained in detail. Then, the constraint processing technology based on evolutionary algorithm is classified, and the research status of each kind of method is summarized. Finally, the composite differential evolution algorithm is combined with two different constraint processing techniques. Two improved constrained composite differential evolution algorithms are proposed. The first improved algorithm is based on the penalty function method, using the constraint processing technique of the adaptive penalty function, introducing distance as the fitness function, calculating the individual distance according to the feasible rate of the population, and carrying out two kinds of punishment for each individual. Based on the objective function and the degree of constraint violation, combined with the composite differential evolution algorithm, the optimal individuals in the offspring population are retained. This not only preserves the diversity of the population, but also allows the population to adjust between finding the feasible solution and finding the optimal solution. The numerical results show that the new algorithm has better global optimization ability and adaptability than similar algorithms. The second improved algorithm is based on the multi-objective method. The original problem is transformed into a multi-objective optimization problem with two objectives including the original objective function and the degree of constraint violation, and the multi-objective optimization method is used to solve the problem. The method consists of two parts: population evolution model and infeasible solution replacement mechanism. In the population evolution model, composite differential evolution algorithm is used as search engine evolution population. Pareto is used to control and compare the individuals, and the better performance individuals are selected, and the infeasible solution replacement mechanism is used to improve the quality and feasibility rate of the individuals in the population. Then it leads the population to approach the feasible region. The numerical results show that the new algorithm has high computational accuracy and global search ability.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TP18;O224

【引证文献】