混合不确定多目标优化模型及其仿生智能求解方法研究

Hybrid uncertain multi-objective optimization problems are key problems demanding prompt solutions in the areas of science and engineering. This project aims to study the model and solution method of this kind of problems based on multi-objective optimization theory and uncertainty theories, such as probability theory, type-2 fuzzy sets theory and probability-possibility transformation theory. Firstly, we provide the description, aggregation and propagation methods for different types of uncertainties, develop a reasonable hybrid uncertain multi-objective optimization model, and analyze the influences of uncertainties on the optimization results, which mainly address the difficulties inherent in the complexity, fuzziness and randomness of the decision environment and the model input parameters. Secondly, considering the hybrid uncertain multi-objective optimization problem, we design a bio-inspired intelligent solution algorithm, which mainly addresses the problems of low convergence speed and obtaining unevenly distributed Pareto fronts of traditional algorithms. Finally, considering the multi-objectivity of multi-objective problem, we develop an interactive multi-objective optimization experimental verification system, which mainly addresses the problem of representing and applying of decision makers’ preferences reasonably, and take the unmanned aerial vehicle path planning problem as an example to test the effectiveness of the designed model and its solution method in solving practical optimization problems. Through this project, the theory and methologies of uncertain multi-objective optimization could be further developed and improved, which has great application potential and development prospects in a variety of areas such as intelligent transportation and so on.

混合不确定多目标优化问题是科学和工程领域亟待解决的关键问题。本项目通过综合运用多目标优化理论及概率理论、二型模糊集理论、概率-可能性分布变换理论等不确定性理论，对该类问题的模型和求解方法进行研究：（1）给出不同类型的不确定信息的描述、集结和传播方法，建立合理的混合不确定多目标优化模型，分析不确定信息对优化结果的影响，解决决策环境及模型输入参数的复杂性、模糊性和随机性等问题；（2）针对混和不确定多目标优化问题，设计仿生智能求解算法，解决传统算法的收敛速度慢、所得Pareto前沿分布不均等的问题；（3）针对多目标优化问题的多目标性，建立交互式多目标优化试验验证系统，解决偏好信息的合理表达及运用问题，并以无人飞行器航迹规划为例检验所设计模型和求解方法在实际优化问题中的应用效果。通过对本项目的研究，进一步发展和完善不确定多目标优化理论与方法体系，在智能交通等诸多领域具有巨大的应用潜力及发展前景。

由于主客观因素的影响， 多目标优化问题往往伴随着大量的不确定信息。在不确定环境下做出合理的、优化的决策已成为一个有着强烈需求的实际问题。在许多工程实际中，随机、模糊不确定性并不是单一存在的，而是同时出现的。因此，研究混合不确定多目标优化问题更具有现实意义和科学价值，同时也更具挑战性。尽管混合不确定多目标优化问题有很强的实际背景，但目前研究尚不成熟，与之相关的理论、模型与算法仍需要进一步研究。. 本项目基于多目标优化理论及概率理论、二型模糊集理论、概率-可能性分布变换理论等不确定性理论对混合不确定多目标优化模型及其求解方法进行研究，主要研究内容包括以下几个方面：（1）在对不确定信息的描述、集结、传播方法等进行系统研究的基础上，建立了合理的混合不确定多目标优化模型，分析了不确定信息对优化结果的影响，解决了决策环境及模型输入参数的复杂性、模糊性和随机性等问题；（2）针对混合不确定多目标优化问题，设计了高效的仿生智能求解算法，克服了传统多目标优化方法在收敛性以及保持解的多样性等方面的不足，具有更好的收敛性、稳定性及全局搜索能力；(3)针对多目标优化问题的多目标性，设计了高效的多目标优化试验验证系统,解决了偏好信息的合理表达及运用问题并以无人飞行器航迹规划为例验证了所设计的模型和求解方法的有效性和科学性。. 本项目的研究成果可进一步丰富和完善不确定多目标优化理论与方法体系，在交通运输、模式识别、大数据、机器学习、智慧物流、金融管理等诸多领域具有广阔的应用前景。