In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over un...In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.展开更多
针对含风-光-柴-储的微电网多目标优化调度问题,提出一种基于多目标指数分布优化(multi-objective exponential distribution optimizer,MOEDO)算法的微电网优化调度框架。首先,构建包含风电、光伏、柴油机、微型汽轮机和储能系统的微...针对含风-光-柴-储的微电网多目标优化调度问题,提出一种基于多目标指数分布优化(multi-objective exponential distribution optimizer,MOEDO)算法的微电网优化调度框架。首先,构建包含风电、光伏、柴油机、微型汽轮机和储能系统的微电网模型,建立以运行成本和环保成本最小化为目标的多目标优化调度模型。其次,在指数分布优化(exponential distribution optimizer,EDO)算法基础上引入MOEDO算法进行优化。基于中国南部某实际微电网的24 h调度案例进行仿真验证,结果表明:环保成本最优场景下清洁能源占比达28.86%,运行成本最优场景下电网购电占比57.38%,综合成本最优场景实现清洁能源占比24.49%与电网购电占比45.01%的平衡,验证了MOEDO算法在平衡经济性与环境可持续性方面的有效性。展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 91748112,61991403,61991404,and 61991400)。
文摘In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.
文摘针对含风-光-柴-储的微电网多目标优化调度问题,提出一种基于多目标指数分布优化(multi-objective exponential distribution optimizer,MOEDO)算法的微电网优化调度框架。首先,构建包含风电、光伏、柴油机、微型汽轮机和储能系统的微电网模型,建立以运行成本和环保成本最小化为目标的多目标优化调度模型。其次,在指数分布优化(exponential distribution optimizer,EDO)算法基础上引入MOEDO算法进行优化。基于中国南部某实际微电网的24 h调度案例进行仿真验证,结果表明:环保成本最优场景下清洁能源占比达28.86%,运行成本最优场景下电网购电占比57.38%,综合成本最优场景实现清洁能源占比24.49%与电网购电占比45.01%的平衡,验证了MOEDO算法在平衡经济性与环境可持续性方面的有效性。
