Dynamic Constrained Optimization Problems (DCOPs) are difficult to solve because both the objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple sub-populations. To this end, the Dynamic Species-based Particle Swam Optimization (i.e., DSPSO), a representative multi-population algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named Moving Feasible Regions Benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

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Existing population-based Stochastic Search Algorithms (SSAs) are too time-consuming to solve dynamic optimal power flow (OPF). The solution proposed in this paper is to accelerate SSAs with memory. Two memory schemes, the similarity retrieval scheme and the mean-based immigrants scheme, are proposed and applied together to the Differential Evolution and Particle Swarm Optimizer, which are two representatives of SSAs. Experiments are conducted on modified IEEE 30-bus and IEEE 118-bus systems with changing load buses and the objective of minimizing real power transmission loss. The results show that the proposed schemes significantly improve the performance of the two existing algorithms, and that SSAs could be practical for tracking optima of dynamic OPF.Index Terms-Dynamic optimal power flow, memory, reactive dispatch problem, stochastic search methods.

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