基于粒子群优化算法的不确定性多目标优化问题研究及其应用

Dynamic multi-objective optimization problems (DMOPs) usually involve objective functions, constraints which change with time. This kind of problem is a main branch of uncertain optimization. Most of the existing algorithms can not track varying Pareto fronts effectively and do not consider how to deal with the constraints in dynamic environments. In order to address these limitations, firstly, we should consider the relationship between the Pareto optimal solutions from the last time and that of the current time. Based on this, a prediction model will be proposed to predict the position of the Pareto optimal solutions at the current time; secondly,in order to handle the dynamically changed constraints, a new particle swarm algorithm will be proposed based on the diversity design. The personal best position and global best position of a particle will be perturbed based on the diversity design. Noisy multi-objective optimization problem is another main branch of uncertain optimization. To date, most common method to deal with noise is re-sampling. This kind of method is effective, but costly. Thus, it is hard to be used in practice. To address this issue, a local model in the context of noisy particle swarm multi-objective optimization will be proposed. We expect it to filter noise effectively and increase the robustness of the particle swarm algorithm. More important, we expect it to decrease the computational cost. Finally, the above mentioned dynamic particle swarm multi-objective optimization algorithm will be applied to solve the grid task scheduling problems.

动态多目标优化问题是指其目标函数和约束条件不仅与决策变量有关，而且与时间(环境)有关的一类优化问题，是不确定优化领域的难点和热点问题。现有算法的大部分并不能快速而准确的追踪到随时间动态变化的Pareto最优解，而且没有考虑到如何处理动态变化的约束条件。本项目以粒子群算法为搜索引擎，首先研究上一时刻(环境)所获得的Pareto最优解与下一时刻(环境)Pareto最优解之间的关系，建立预测模型，通过该模型近似下一时刻最优解的位置；为了处理随时间(环境)动态变化的约束条件，给出基于多样性设计的粒子个体极值和全局极值扰动的新方法。另外，噪声多目标优化问题是不确定优化领域的另一难点问题，现有大部分算法的计算量都非常巨大，为了克服此缺陷，本项目拟通过建立一个局部优化模型来过滤噪音，减少算法的计算量。最后将上述的动态多目标粒子群算法应用到网格安全任务调度问题中去，体现了动态多目标优化的应用价值。

对于动态多目标粒子群算法，关键点有2个：第一：如何良好的追踪环境变换，产生一组分布均与、散布广泛，并随时间动态变化的Pareto 最优解。第二：如何处理随环境动态变换的约束条件。. 第一, 理论分析表明当环境随时间缓慢平缓变化时，上一时刻Pareto最优解和下一时刻Pareto最优解距离不会太远；因此，本项目设计了“基于超矩形搜索”的预测技术来估计下一时刻最优解的位置。数值试验表明，该预测模型能快速准确的找到下一时刻的Pareto最优解。 . 第二，在相关函数不发生变换的一小段时间里，为了避免粒子陷入局部最优，提出了一种粒子个体极值和全局极值多样化扰动的新方法。该方法能有效地处理约束条件，尤其是大规模的约束问题。. 第三，在网格安全任务调度问题中，考虑到网格的安全性、真实性、保密性等需求，构造了一个动态带约束的多目标优化问题模型，并运用前述改进的粒子群算法求解，实验结果表明模型及算法的有效性。