基于进化算法的多目标优化方法研究
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摘要
多目标优化方法具有很强的工程应用背景。近年来,基于进化算法求解多目标优化问题已成为国际学术界的一个研究热点。本文研究了多目标优化进化算法的关键技术和算法的应用问题,主要内容如下:
(1)提出了一种引入偏好信息的多目标优化进化算法。给出了一种将目标间的相对重要程度进行量化的偏好处理方法,分析了该方法中的参数对偏好处理结果的影响。基于模糊逻辑构造了一种“强度优于”排序关系,替代常规的Pareto支配关系判断候选解间的优劣,分析了两种排序关系间的联系。根据“强度优于”关系设计了一种新型的适应度评价方法。通过图形用户界面在多目标优化进化算法中交互式地引入决策者的偏好信息,使算法搜索到期望区域内的解。对算法的计算复杂度进行了分析。使用所提算法求解具有5个优化目标的柔性机械手控制系统的参数优化问题,仿真结果表明所提算法能够有效地处理高维多目标优化问题,并能够减轻决策者的决策负担。
(2)提出了一种保持群体多样性的多目标优化进化算法。基于信息熵的概念给出了一种适用于多目标空间的群体多样性测度。该测度将群体当前的进化状态与算法的运行机制相关联,探索位于稀疏区域内的精英个体附近的新个体,对精英个体的保留数目加以控制,依据群体多样性测度的优劣自适应地调整算法新一代群体的组成方式,并在“利用精英个体”和“探索新区域个体”两种模式之间进行转换,以防止算法因对当前精英个体的过度依赖而产生停滞或早熟现象。对算法的计算复杂度进行了分析。在多模态测试函数和机械设计问题中的仿真结果表明,所提算法具有较优的收敛性能和分布特性。
(3)针对可以分解的多目标优化问题,提出了一种多目标优化合作型协同进化算法。使用n个子群体分别进化问题的n个决策变量,结合多目标优化问题的特点,设计了一种能够提高候选解多样性的子群体间合作方式。对算法的计算复杂度进行了分析。在一组标准测试函数中的仿真结果表明,所提算法具有较高的求解效率。针对难以分解的多目标优化问题,提出了一种子群体个数动态变化的合作型多目标优化协同进化算法。给出了一种在多目标优化条件下的进化算法群体停滞判别准则,设计了多目标优化协同进化算法中子群体新增和灭绝的条件以及算法的终止准则。对算法的计算复杂度进行了分析,在一组标准测试函数中的仿真结果表明,所提算法能够在保证算法收敛性能与多样性的同时,尽可能多地节约计算资源。
(4)研究了多目标优化进化算法的应用问题。建立了机械手运动学逆解问题的多目标优化模型,针对该问题的特点,在本论文提出的保持群体多样性的多目标优化进化算法中,采用了一种能够保证约束条件始终满足的个体生成方式,并基于改进后的算法求解具有3个优化目标的冗余机械手运动学逆解问题。建立了单机器人路径规划问题的多目标优化模型,针对该问题的特点,在本论文提出的保持群体多样性的多目标优化进化算法中,引入了基于问题先验知识的启发式群体初始化方法和智能进化算子,使所提算法能够同时优化问题的多个性能指标。建立了多机器人路径规划问题的多目标优化模型,给出了一种多机器人间的协调策略,使用本论文提出的多目标优化合作型协同进化算法规划多机器人的运动路径。
Multi-objective optimization approaches have been widely used in the field of engineering applications. Many researchers have been attracted by the research on solving multi-objective optimization problems based on evolutionary algorithms. The key technique issues and applications of multi-objective optimization evolutionary algorithms are studied in this dissertation, and the main research work is concluded as follows:
(1) A multi-objective optimization evolutionary algorithm incorporating preference information is proposed. A preference handling method to quantify the relative importance between pairs of objectives is proposed, and the influence of the parameters on the results of the preference handling is discussed. A new outranking relation called "strength superior" is constructed based on fuzzy logic to compare candidate solutions instead of the commonly used Pareto dominance relation. The relationship between these two outranking relations is analyzed theoretically. A novel strategy of fitness evaluation is designed based on the "strength superior" relation. The preference information of the decision maker is incorporated into the algorithm interactively vie the graphical user interface in order to guide the algorithm to find the solutions located in the desired regions. The computational complexity of the algorithm is analyzed. The proposed algorithm is applied to a parameter optimization problem in the control system for a manipulator with 5 objectives. Simulation results indicate that the proposed algorithm can deal with high dimensional multi-objective optimization problems effectively, and it can reduce the burden of the decision maker.
(2) A multi-objective optimization evolutionary algorithm keeping diversity of the population is proposed. A metric based on entropy to measure the diversity of the population in the case of multi-objective space is proposed. The evolving state of current population is associated with the running mechanism of the algorithm by the diversity metric. It explores new individuals in the vicinity of elitist individuals located in the sparse region, controls the number of elitist individuals, adjusts the formation of the population in the new generation adaptively according to the diversity metric, and converts between the two searching modes which are exploitation of elitist individuals and exploration of new individuals so as to prevent the algorithm from stagation or premature. The computational complexity of the algorithm is analyzed. Simulation results in a complex multi-modal function and a mechanical design problem indicate that the proposed algorithm has good performance of convergence and distribution.
(3) For the decomposable problem, a cooperative co-evolutionary algorithm for multi-objective optimization is proposed. n subpopulations are set to evolve n decision variables of the problem respectively. Considering the characteristics of multi-objective optimization problems, a novel form of collaboration among subpopulations which can increase the diversity of the candidate solutions is designed. The computational complexity of the algorithm is analyzed. Simulation results in a suite of standard test functions indicate that the proposed algorithm has high searching efficiency. For the undecomposable problem, a multi-objective optimization co-evolutionary algorithm with dynamically varying number of subpopulations is proposed. A new criterion judging the stagnation of the population in evolutionary algorithms in the existence of multiple objectives is presented, and the conditions of adding and deleting subpopulations and the stopping criterion of the algorithm are induced. The computational complexity of the algorithm is analyzed. Simulation results in a suite of standard test functions indicate that the proposed algorithm can save computational resources as many as possible while ensuring the performance of convergence and diversity of the algorithm.
(4) The applications of multi-objective optimization evolutionary algorithms are studied. The multi-objective optimization model of the inverse kinematics problem of the redundant manipulator is constructed. For the characteristic of this problem, a new way to produce individuals which can ensure the satisfaction of the constraints is adopted in the proposed multi-objective optimization evolutionary algorithm keeping diversity of the population. The improved algorithm is employed to solve the inverse kinematics problem of the redundant manipulator with 3 objectives. The multi-objective optimization model of the single robot path planning problem is constructed. For the characteristics of this problem, the heuristic method based on domain knowledge is employed in the initialization, and three intelligent evolutionary operators are adopted in the proposed multi-objective optimization evolutionary algorithm keeping diversity of the population, which make the algorithm optimize multiple objectives of the problem simultaneously. The multi-objective optimization model of the multi-robot path planning problem is constructed. A coordinated strategy among robots is presented. The paths of multiple robots are planned based on the proposed cooperative co-evolutionary algorithm for multi-objective optimization.
(1)提出了一种引入偏好信息的多目标优化进化算法。给出了一种将目标间的相对重要程度进行量化的偏好处理方法,分析了该方法中的参数对偏好处理结果的影响。基于模糊逻辑构造了一种“强度优于”排序关系,替代常规的Pareto支配关系判断候选解间的优劣,分析了两种排序关系间的联系。根据“强度优于”关系设计了一种新型的适应度评价方法。通过图形用户界面在多目标优化进化算法中交互式地引入决策者的偏好信息,使算法搜索到期望区域内的解。对算法的计算复杂度进行了分析。使用所提算法求解具有5个优化目标的柔性机械手控制系统的参数优化问题,仿真结果表明所提算法能够有效地处理高维多目标优化问题,并能够减轻决策者的决策负担。
(2)提出了一种保持群体多样性的多目标优化进化算法。基于信息熵的概念给出了一种适用于多目标空间的群体多样性测度。该测度将群体当前的进化状态与算法的运行机制相关联,探索位于稀疏区域内的精英个体附近的新个体,对精英个体的保留数目加以控制,依据群体多样性测度的优劣自适应地调整算法新一代群体的组成方式,并在“利用精英个体”和“探索新区域个体”两种模式之间进行转换,以防止算法因对当前精英个体的过度依赖而产生停滞或早熟现象。对算法的计算复杂度进行了分析。在多模态测试函数和机械设计问题中的仿真结果表明,所提算法具有较优的收敛性能和分布特性。
(3)针对可以分解的多目标优化问题,提出了一种多目标优化合作型协同进化算法。使用n个子群体分别进化问题的n个决策变量,结合多目标优化问题的特点,设计了一种能够提高候选解多样性的子群体间合作方式。对算法的计算复杂度进行了分析。在一组标准测试函数中的仿真结果表明,所提算法具有较高的求解效率。针对难以分解的多目标优化问题,提出了一种子群体个数动态变化的合作型多目标优化协同进化算法。给出了一种在多目标优化条件下的进化算法群体停滞判别准则,设计了多目标优化协同进化算法中子群体新增和灭绝的条件以及算法的终止准则。对算法的计算复杂度进行了分析,在一组标准测试函数中的仿真结果表明,所提算法能够在保证算法收敛性能与多样性的同时,尽可能多地节约计算资源。
(4)研究了多目标优化进化算法的应用问题。建立了机械手运动学逆解问题的多目标优化模型,针对该问题的特点,在本论文提出的保持群体多样性的多目标优化进化算法中,采用了一种能够保证约束条件始终满足的个体生成方式,并基于改进后的算法求解具有3个优化目标的冗余机械手运动学逆解问题。建立了单机器人路径规划问题的多目标优化模型,针对该问题的特点,在本论文提出的保持群体多样性的多目标优化进化算法中,引入了基于问题先验知识的启发式群体初始化方法和智能进化算子,使所提算法能够同时优化问题的多个性能指标。建立了多机器人路径规划问题的多目标优化模型,给出了一种多机器人间的协调策略,使用本论文提出的多目标优化合作型协同进化算法规划多机器人的运动路径。
Multi-objective optimization approaches have been widely used in the field of engineering applications. Many researchers have been attracted by the research on solving multi-objective optimization problems based on evolutionary algorithms. The key technique issues and applications of multi-objective optimization evolutionary algorithms are studied in this dissertation, and the main research work is concluded as follows:
(1) A multi-objective optimization evolutionary algorithm incorporating preference information is proposed. A preference handling method to quantify the relative importance between pairs of objectives is proposed, and the influence of the parameters on the results of the preference handling is discussed. A new outranking relation called "strength superior" is constructed based on fuzzy logic to compare candidate solutions instead of the commonly used Pareto dominance relation. The relationship between these two outranking relations is analyzed theoretically. A novel strategy of fitness evaluation is designed based on the "strength superior" relation. The preference information of the decision maker is incorporated into the algorithm interactively vie the graphical user interface in order to guide the algorithm to find the solutions located in the desired regions. The computational complexity of the algorithm is analyzed. The proposed algorithm is applied to a parameter optimization problem in the control system for a manipulator with 5 objectives. Simulation results indicate that the proposed algorithm can deal with high dimensional multi-objective optimization problems effectively, and it can reduce the burden of the decision maker.
(2) A multi-objective optimization evolutionary algorithm keeping diversity of the population is proposed. A metric based on entropy to measure the diversity of the population in the case of multi-objective space is proposed. The evolving state of current population is associated with the running mechanism of the algorithm by the diversity metric. It explores new individuals in the vicinity of elitist individuals located in the sparse region, controls the number of elitist individuals, adjusts the formation of the population in the new generation adaptively according to the diversity metric, and converts between the two searching modes which are exploitation of elitist individuals and exploration of new individuals so as to prevent the algorithm from stagation or premature. The computational complexity of the algorithm is analyzed. Simulation results in a complex multi-modal function and a mechanical design problem indicate that the proposed algorithm has good performance of convergence and distribution.
(3) For the decomposable problem, a cooperative co-evolutionary algorithm for multi-objective optimization is proposed. n subpopulations are set to evolve n decision variables of the problem respectively. Considering the characteristics of multi-objective optimization problems, a novel form of collaboration among subpopulations which can increase the diversity of the candidate solutions is designed. The computational complexity of the algorithm is analyzed. Simulation results in a suite of standard test functions indicate that the proposed algorithm has high searching efficiency. For the undecomposable problem, a multi-objective optimization co-evolutionary algorithm with dynamically varying number of subpopulations is proposed. A new criterion judging the stagnation of the population in evolutionary algorithms in the existence of multiple objectives is presented, and the conditions of adding and deleting subpopulations and the stopping criterion of the algorithm are induced. The computational complexity of the algorithm is analyzed. Simulation results in a suite of standard test functions indicate that the proposed algorithm can save computational resources as many as possible while ensuring the performance of convergence and diversity of the algorithm.
(4) The applications of multi-objective optimization evolutionary algorithms are studied. The multi-objective optimization model of the inverse kinematics problem of the redundant manipulator is constructed. For the characteristic of this problem, a new way to produce individuals which can ensure the satisfaction of the constraints is adopted in the proposed multi-objective optimization evolutionary algorithm keeping diversity of the population. The improved algorithm is employed to solve the inverse kinematics problem of the redundant manipulator with 3 objectives. The multi-objective optimization model of the single robot path planning problem is constructed. For the characteristics of this problem, the heuristic method based on domain knowledge is employed in the initialization, and three intelligent evolutionary operators are adopted in the proposed multi-objective optimization evolutionary algorithm keeping diversity of the population, which make the algorithm optimize multiple objectives of the problem simultaneously. The multi-objective optimization model of the multi-robot path planning problem is constructed. A coordinated strategy among robots is presented. The paths of multiple robots are planned based on the proposed cooperative co-evolutionary algorithm for multi-objective optimization.
引文
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