面向装备保障的多准则决策相关方法和技术研究
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摘要
许多装备保障决策问题都具有大规模、多目标、多约束等特点,传统的依赖决策者阅历、知识和偏好的经验型决策已经不能满足装备保障“适时、适地、适量”的需求,必须研究如何对规模庞大、结构复杂、目标多元的装备保障决策问题科学定量决策的问题。本文按照先优化后决策的思路,对装备保障多准则决策相关的方法和技术进行了研究,其主要研究内容与创新点如下：
(1)对MOP测试函数和性能评价方法进行了综述分析,给出了几组典型的约束、非约束多目标测试函数,并总结了几种衡量算法收敛性、分散性等性能的定量性能指标评价方法,为本文提出的新算法的性能分析及与其它同类算法的性能对比分析提供了依据。
(2)对多目标粒子群相关的几个重要问题,如外部档案、密度测量方法、全局向导和个体向导选择等进行了分析综述,为多目标粒子群算法的改进提供了基础。
(3)对约束多目标处理方法进行了综述,在对约束多目标搜索空间特点及其处理难点分析的基础上,提出了改进的约束多目标粒子群算法(CMOPSO)。以一种动态ε不可行度许可约束支配关系作为主要的约束处理方法,提高了约束多目标粒子群算法的边缘搜索能力和跨越非联通可行区域的能力；设计了一种新的计算简便的密集距离度量方法用于外部档案维护,提高了算法的效率；在分析外部档案中的解与群中各粒子关系的基础上,提出了新的全局向导选取策略,使算法获得了更好的收敛性和多样性。对一组典型或复杂的约束、非约束多目标函数进行了计算机仿真,图形及定量性能指标度量结果验证了该算法的可行性和有效性。
(4)基于粒子群算法搜索机理的分析及多目标粒子群算法自身的特点设计了模糊多目标粒子群算法,即模糊学习子群多目标粒子群算法(FLSMOPSO)。对CMOPSO作了进一步改进,在粒子进化过程中,通过模糊学习可使每个粒子在进化过程中产生线性递减的p个粒子形成子群而不是只产生一个粒子,然后从p个粒子中选择模糊满意解作为每个粒子的新位置。本文提出的改进的模糊多目标粒子群算法可迅速缩小搜索区域,加快算法收敛速度,并维持较好的多样性。对一组典型或复杂的约束、非约束多目标函数进行了试验仿真,并与典型的模糊多目标粒子群算法及本文构建的约束多目标粒子群算法进行了对比分析,结果表明FLSMOPSO算法可得到分布性、均匀性及逼近性都较好的Pareto最优解。
(5)对基于Vague集的决策方法进行了分析综述,提出了基于Vague集的多阶段模糊多属性决策方法。通过反复引入偏好进行决策方案收缩和选优,可从数量众多的决策方案中获取用户最满意解,有效解决了现有Vague集排序方法中同一排序值对应不同的Vague值而致使排序函数失效的问题,也能解决因一次转换而使不同方案拥有同样的Vague值,从而导致任何排序方法都失效的问题。
(6)对约束多目标维修任务分配和灾难应急救援定位运输问题这两种典型的复杂装备保障决策问题进行了分析建模,前者的特点是多目标多约束且决策方案众多,而后者属于多约束／多目标／多阶段数学规划问题,运用传统方法很难求解。分别运用本文提出的两种改进的多目标粒子群算法进行了仿真实验,均能快速得到Pareto最优解集。针对产生数量众多的Pareto非劣解而无法得出唯一决策方案的情况,可再基于本文提出的基于Vague集的多阶段模糊多属性决策方法优选出最令决策者满意的决策方案。仿真实验表明,本文提出的优化和决策算法能有效解决装备保障科学定量决策的问题,为装备保障决策由手工盲目决策向自动智能科学定量决策提供了好的解决方法。
Many equipment supporting decision-making problems have features of large scale, multiple objectives, and multiple constraints and so on. The traditional empirical decision making methods which depend on policymakers' experience, knowledge and preferences cannot satisfy the demands of making equipment supporting achieving the aim of "supporting at suitable time, on right place, and with appropriate manners". Therefore, it's necessary to learn how to make scientific quantitative decisions for complex, large scale and multi-objective equipment supporting decision problems. According to the ideas of making decisions after optimization, the methods and techniques of multiple criteria decision making for equipment supporting are studied in this paper, and the main research contents and innovation points are as follows:
(1)MOP test functions and performance evaluation methods are reviewed and analyzed, several groups of typical constrained and unconstrained MOP test functions are given, and quantitative performance evaluation methods for measuring the diversity and convergence of the algorithm are introduced, which provides a basis for the performance analysis of the proposed algorithm in this paper and its comparative performance analysis to other similar algorithms.
(2)Some important operators such as external archive, density measuring method, global guide and personal guide selecting strategies are surveyed, which provide guides for the improvement of multi-objective particle swarm algorithm.
(3)Constrained multi-objective processing methods are summarized. On the basis of the analysis of the characteristics of the multi-objective search space and the difficulties of the constrained multi-objective processing, an improved constrained multi-objective particle swarm algorithm (CMOPSO) is put forward. A dynamicεunfeasible degree allowable constraint dominance relation as the main constraint processing method is brought forward in this algorithm, which improves the algorithm's edge search ability and its ability of crossing unconnected feasible regions; A simple density measuring method is put forward for external archive maintenance, which improves the efficiency of the algorithm; On the analysis of the relation of the particles in the swarm and the solutions of the external archive, a new global guide selection strategy is put forward, which brings a better convergence and diversity to the algorithm. The computer simulation and measurement comparison results verified the feasibility and the rationality of the algorithm.
(4)Based on the analysis of the search mechanism of PSO and the characteristics of MOPSO, a fuzzy gathered multi-objective particle swarm algorithm called fuzzy learning subswarm multi-objective particle swarm optimization (FLSMOPSO) is put forward in this paper. The method of fuzzy learning is used to improve the CMOPSO. In the evolutionary process, each particle in the swarm can have linear regressive p particles to form a subwarm rather than a single particle. Then, a fuzzy satisfied solution particle should be selected as the new position of the particle. The improved fuzzy multi-objective particle swarm algorithm put forward in this paper can rapidly narrow the search area and speed up the convergence rate. At the same time, it can maintain the diversity of evolution population. Comparative analysis to the typical FMOPSO algorithm and the CMOPSO algorithm above show that the FLSMOPSO algorithm proposed in this paper can find a sufficient number of widely and evenly distributed Pareto optimal solutions, which are both good in uniformity and the approximation of the Pareto front.
(5)Based on the survey of the decision methods based on Vague set, a new Vague set based multi-stage fuzzy multiple attribute decision making method is proposed. Through the two stages of non-inferior solution set shrinkage and optimum choice, it can automatically fetch the most satisfied solution from numerous non-inferior solution set for policymakers, effectively solve the problems existing in Vague set based multiple attribute decision making methods that multiple different Vague set have the same Vague value so they cannot be compared with each other.
(6)Two typical complicated equip supporting problems of multi-objective maintenance tasks distribution and disaster emergency rescue positioning and transportation are analyzed and modeled. The former problem has the characteristics of multiple constraints, multiple objectives and a large number of optimal decision-making plans, while the latter problem is a multi-constraint/multi-objective/multi-stage mathematical programming problem, which can not be solved by traditional methods. Simulation experiments are done using the improved multi-objective particle swarm algorithms proposed in this paper respectively, Pareto non-inferior solution set can be soon obtainted. Under certain conditions where there are a large number of non-inferior solutions, a Vague set based multi-stage fuzzy multiple attribute decision making method is used to get the most satisfied solution for policymakers. Simulation experiments show that the proposed optimization and decision-making algorithms proposed in this paper can effectively solve the problem of making scientifically quantitative decision for equipment supporting, which provides a good way to transform complex equipment supporting decision-making problems from experimentally qualitative to scientifically quantitative.
(1)对MOP测试函数和性能评价方法进行了综述分析,给出了几组典型的约束、非约束多目标测试函数,并总结了几种衡量算法收敛性、分散性等性能的定量性能指标评价方法,为本文提出的新算法的性能分析及与其它同类算法的性能对比分析提供了依据。
(2)对多目标粒子群相关的几个重要问题,如外部档案、密度测量方法、全局向导和个体向导选择等进行了分析综述,为多目标粒子群算法的改进提供了基础。
(3)对约束多目标处理方法进行了综述,在对约束多目标搜索空间特点及其处理难点分析的基础上,提出了改进的约束多目标粒子群算法(CMOPSO)。以一种动态ε不可行度许可约束支配关系作为主要的约束处理方法,提高了约束多目标粒子群算法的边缘搜索能力和跨越非联通可行区域的能力；设计了一种新的计算简便的密集距离度量方法用于外部档案维护,提高了算法的效率；在分析外部档案中的解与群中各粒子关系的基础上,提出了新的全局向导选取策略,使算法获得了更好的收敛性和多样性。对一组典型或复杂的约束、非约束多目标函数进行了计算机仿真,图形及定量性能指标度量结果验证了该算法的可行性和有效性。
(4)基于粒子群算法搜索机理的分析及多目标粒子群算法自身的特点设计了模糊多目标粒子群算法,即模糊学习子群多目标粒子群算法(FLSMOPSO)。对CMOPSO作了进一步改进,在粒子进化过程中,通过模糊学习可使每个粒子在进化过程中产生线性递减的p个粒子形成子群而不是只产生一个粒子,然后从p个粒子中选择模糊满意解作为每个粒子的新位置。本文提出的改进的模糊多目标粒子群算法可迅速缩小搜索区域,加快算法收敛速度,并维持较好的多样性。对一组典型或复杂的约束、非约束多目标函数进行了试验仿真,并与典型的模糊多目标粒子群算法及本文构建的约束多目标粒子群算法进行了对比分析,结果表明FLSMOPSO算法可得到分布性、均匀性及逼近性都较好的Pareto最优解。
(5)对基于Vague集的决策方法进行了分析综述,提出了基于Vague集的多阶段模糊多属性决策方法。通过反复引入偏好进行决策方案收缩和选优,可从数量众多的决策方案中获取用户最满意解,有效解决了现有Vague集排序方法中同一排序值对应不同的Vague值而致使排序函数失效的问题,也能解决因一次转换而使不同方案拥有同样的Vague值,从而导致任何排序方法都失效的问题。
(6)对约束多目标维修任务分配和灾难应急救援定位运输问题这两种典型的复杂装备保障决策问题进行了分析建模,前者的特点是多目标多约束且决策方案众多,而后者属于多约束／多目标／多阶段数学规划问题,运用传统方法很难求解。分别运用本文提出的两种改进的多目标粒子群算法进行了仿真实验,均能快速得到Pareto最优解集。针对产生数量众多的Pareto非劣解而无法得出唯一决策方案的情况,可再基于本文提出的基于Vague集的多阶段模糊多属性决策方法优选出最令决策者满意的决策方案。仿真实验表明,本文提出的优化和决策算法能有效解决装备保障科学定量决策的问题,为装备保障决策由手工盲目决策向自动智能科学定量决策提供了好的解决方法。
Many equipment supporting decision-making problems have features of large scale, multiple objectives, and multiple constraints and so on. The traditional empirical decision making methods which depend on policymakers' experience, knowledge and preferences cannot satisfy the demands of making equipment supporting achieving the aim of "supporting at suitable time, on right place, and with appropriate manners". Therefore, it's necessary to learn how to make scientific quantitative decisions for complex, large scale and multi-objective equipment supporting decision problems. According to the ideas of making decisions after optimization, the methods and techniques of multiple criteria decision making for equipment supporting are studied in this paper, and the main research contents and innovation points are as follows:
(1)MOP test functions and performance evaluation methods are reviewed and analyzed, several groups of typical constrained and unconstrained MOP test functions are given, and quantitative performance evaluation methods for measuring the diversity and convergence of the algorithm are introduced, which provides a basis for the performance analysis of the proposed algorithm in this paper and its comparative performance analysis to other similar algorithms.
(2)Some important operators such as external archive, density measuring method, global guide and personal guide selecting strategies are surveyed, which provide guides for the improvement of multi-objective particle swarm algorithm.
(3)Constrained multi-objective processing methods are summarized. On the basis of the analysis of the characteristics of the multi-objective search space and the difficulties of the constrained multi-objective processing, an improved constrained multi-objective particle swarm algorithm (CMOPSO) is put forward. A dynamicεunfeasible degree allowable constraint dominance relation as the main constraint processing method is brought forward in this algorithm, which improves the algorithm's edge search ability and its ability of crossing unconnected feasible regions; A simple density measuring method is put forward for external archive maintenance, which improves the efficiency of the algorithm; On the analysis of the relation of the particles in the swarm and the solutions of the external archive, a new global guide selection strategy is put forward, which brings a better convergence and diversity to the algorithm. The computer simulation and measurement comparison results verified the feasibility and the rationality of the algorithm.
(4)Based on the analysis of the search mechanism of PSO and the characteristics of MOPSO, a fuzzy gathered multi-objective particle swarm algorithm called fuzzy learning subswarm multi-objective particle swarm optimization (FLSMOPSO) is put forward in this paper. The method of fuzzy learning is used to improve the CMOPSO. In the evolutionary process, each particle in the swarm can have linear regressive p particles to form a subwarm rather than a single particle. Then, a fuzzy satisfied solution particle should be selected as the new position of the particle. The improved fuzzy multi-objective particle swarm algorithm put forward in this paper can rapidly narrow the search area and speed up the convergence rate. At the same time, it can maintain the diversity of evolution population. Comparative analysis to the typical FMOPSO algorithm and the CMOPSO algorithm above show that the FLSMOPSO algorithm proposed in this paper can find a sufficient number of widely and evenly distributed Pareto optimal solutions, which are both good in uniformity and the approximation of the Pareto front.
(5)Based on the survey of the decision methods based on Vague set, a new Vague set based multi-stage fuzzy multiple attribute decision making method is proposed. Through the two stages of non-inferior solution set shrinkage and optimum choice, it can automatically fetch the most satisfied solution from numerous non-inferior solution set for policymakers, effectively solve the problems existing in Vague set based multiple attribute decision making methods that multiple different Vague set have the same Vague value so they cannot be compared with each other.
(6)Two typical complicated equip supporting problems of multi-objective maintenance tasks distribution and disaster emergency rescue positioning and transportation are analyzed and modeled. The former problem has the characteristics of multiple constraints, multiple objectives and a large number of optimal decision-making plans, while the latter problem is a multi-constraint/multi-objective/multi-stage mathematical programming problem, which can not be solved by traditional methods. Simulation experiments are done using the improved multi-objective particle swarm algorithms proposed in this paper respectively, Pareto non-inferior solution set can be soon obtainted. Under certain conditions where there are a large number of non-inferior solutions, a Vague set based multi-stage fuzzy multiple attribute decision making method is used to get the most satisfied solution for policymakers. Simulation experiments show that the proposed optimization and decision-making algorithms proposed in this paper can effectively solve the problem of making scientifically quantitative decision for equipment supporting, which provides a good way to transform complex equipment supporting decision-making problems from experimentally qualitative to scientifically quantitative.
引文
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