多目标差分进化混合算法研究及其在磨矿分级中的应用
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摘要
在自然学科和社会学科领域中存在很多多目标优化问题,传统的多目标优化方法对复杂优化问题难以有效求解。基于Pareto概念的多目标进化算法由于具有高效的搜索能力,己成为当今研究热点。差分进化算法作为一种新兴的进化计算技术,具有全局搜索能力强、收敛速度快、简单易行等优点,已在优化领域得到了广泛的关注。
本文对差分进化算法进行深入探索和研究,并与局部搜索算法进行有机融合,旨在针对多目标优化问题设计高效的差分进化混合算法,并应用求解磨矿分级过程多目标优化问题。
论文通过对多目标优化方法和差分进化算法进行分析研究,针对目前一般多目标差分进化算法中存在的退化现象和“早熟”问题,提出一种多目标差分进化混合算法。通过改进的选择操作合并父代和子代所有个体,进行Pareto非劣排序,加强各个体间的信息交流和充分比较,防止退化；并对个体的排序指标进行改进以克服搜索不均匀的问题；同时融入了单纯形局部搜索,以期能够丰富优化过程的搜索行为,达到脱离局部最优、提高搜索效率的目的。
进一步对约束多目标优化问题的约束处理机制进行研究,提出了基于多种群差分进化的约束多目标混合优化算法,对某些具有优良特性的不可行解采取保留和随机优化策略,避免了惩罚函数的构造,同时避免了一些有意义的不可行解被删除或忽略。通过测试函数仿真表明,提出的算法能够快速有效地收敛于真实Pareto前沿,获得高质量的解集,具有较好的分布性。
最后,将基于多种群差分进化的约束多目标混合优化算法用于求解磨矿分级过程产品产量和质量的多目标优化问题,采用TOPSIS决策获得优化磨矿分级过程的最优方案,达到提高生产效率的目的,获得最大经济效益。
Multi-objective optimization problems exist widely in natural and social sciences. The traditional optimization methods can not solve the complex problems effectively. Multi-objective evolutionary algorithms based on Pareto theory have become a hot issue for its highly efficient searching capability. Differential evolution algorithm is a newly arisen evolutionary computation technique. Due to its feasible and simple structure, strong global search ability and fast convergence speed, DE has attracted wide attention in the optimum area.
Based on the intensive research of DE algtorithm and hybrid strategy with local search algorithm, the objective of this paper is to design a fast and efficient hybrid DE algorithm for solving multi-objective optimization problems, which is then applied to solve the MOPs in the grinding and classification process.
In order to overcome the problems such as degradation and local optimum exist in common multi-objective DE algorithms, a novel hybrid DE algorithm for MOPs is proposed. It strengthens the exchanges of information among individuals and prevents degradation using a modified selecting method, which sorts all individuals including the parents and offspring based on the Pareto non-dominated theory. Meanwhile, the ranking index of individuals is improved to overcome the problem of uneven search. In addition, the simplex local search method is mixed in the evolution algorithm to enrich the searching behavior in the optimization process, get out from the local optimum and improve searching efficiency.
Moreover, based on further research on the constraints processing mechanism of constrained multi-objective optimization problems, a hybrid DE algorithm with multi-population is designed for CMOPs. Some infeasible solutions with better performance are allowed to save and participate optimization randomly in the evolution. The advantage of the proposed algorithm is the avoidance of difficulties such as constructing penalty function and deleting meaningful infeasible solutions directly. Simulation results on benchmarks indicate that the proposed algorithm can converge quickly and effectively to the true Pareto front with better distribution.
Finally, the proposed algorithm is applied to solve multi-objective optimization model of product output and quality in grinding and classification process. Based on TOPSIS, the satisfactory solution is obtained by using decision-making method on multiple attribute, achieving the goals of improving the production efficiency and maximum economic benefits.
本文对差分进化算法进行深入探索和研究,并与局部搜索算法进行有机融合,旨在针对多目标优化问题设计高效的差分进化混合算法,并应用求解磨矿分级过程多目标优化问题。
论文通过对多目标优化方法和差分进化算法进行分析研究,针对目前一般多目标差分进化算法中存在的退化现象和“早熟”问题,提出一种多目标差分进化混合算法。通过改进的选择操作合并父代和子代所有个体,进行Pareto非劣排序,加强各个体间的信息交流和充分比较,防止退化；并对个体的排序指标进行改进以克服搜索不均匀的问题；同时融入了单纯形局部搜索,以期能够丰富优化过程的搜索行为,达到脱离局部最优、提高搜索效率的目的。
进一步对约束多目标优化问题的约束处理机制进行研究,提出了基于多种群差分进化的约束多目标混合优化算法,对某些具有优良特性的不可行解采取保留和随机优化策略,避免了惩罚函数的构造,同时避免了一些有意义的不可行解被删除或忽略。通过测试函数仿真表明,提出的算法能够快速有效地收敛于真实Pareto前沿,获得高质量的解集,具有较好的分布性。
最后,将基于多种群差分进化的约束多目标混合优化算法用于求解磨矿分级过程产品产量和质量的多目标优化问题,采用TOPSIS决策获得优化磨矿分级过程的最优方案,达到提高生产效率的目的,获得最大经济效益。
Multi-objective optimization problems exist widely in natural and social sciences. The traditional optimization methods can not solve the complex problems effectively. Multi-objective evolutionary algorithms based on Pareto theory have become a hot issue for its highly efficient searching capability. Differential evolution algorithm is a newly arisen evolutionary computation technique. Due to its feasible and simple structure, strong global search ability and fast convergence speed, DE has attracted wide attention in the optimum area.
Based on the intensive research of DE algtorithm and hybrid strategy with local search algorithm, the objective of this paper is to design a fast and efficient hybrid DE algorithm for solving multi-objective optimization problems, which is then applied to solve the MOPs in the grinding and classification process.
In order to overcome the problems such as degradation and local optimum exist in common multi-objective DE algorithms, a novel hybrid DE algorithm for MOPs is proposed. It strengthens the exchanges of information among individuals and prevents degradation using a modified selecting method, which sorts all individuals including the parents and offspring based on the Pareto non-dominated theory. Meanwhile, the ranking index of individuals is improved to overcome the problem of uneven search. In addition, the simplex local search method is mixed in the evolution algorithm to enrich the searching behavior in the optimization process, get out from the local optimum and improve searching efficiency.
Moreover, based on further research on the constraints processing mechanism of constrained multi-objective optimization problems, a hybrid DE algorithm with multi-population is designed for CMOPs. Some infeasible solutions with better performance are allowed to save and participate optimization randomly in the evolution. The advantage of the proposed algorithm is the avoidance of difficulties such as constructing penalty function and deleting meaningful infeasible solutions directly. Simulation results on benchmarks indicate that the proposed algorithm can converge quickly and effectively to the true Pareto front with better distribution.
Finally, the proposed algorithm is applied to solve multi-objective optimization model of product output and quality in grinding and classification process. Based on TOPSIS, the satisfactory solution is obtained by using decision-making method on multiple attribute, achieving the goals of improving the production efficiency and maximum economic benefits.
引文
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