Abstract: In recent years, though the number of natural disasters is decreasing, the cost of economic damages globally has seen an increase compared to the past two decades. One reason for higher economic losses is the consequence of disasters damaged the lifeline system, especially; the earthquake often has severe damaged to the power distribution system. An important issue faced by the local and federal authorities is the power distribution systems repair and restoration scheduling and logistic support. For the power distribution systems restoration scheduling problem, which includes the sequence for repairing the damaged components, i.e., buses, distribution lines, and assigning and routing for the repair crews? For the logistic support, which includes the materials allocation problem and the materials delivery problem? Specially, in determining the restoration schedule, it is important to consider the fact that the logistics support and geographical features. Therefore, a non-linear mixed integer programming model is first developed to maximize the utilities of restoration to describe the post-earthquake mountain areas power distribution systems restoration problem integrated with logistics support.
According to the mathematical model, the MATPOWER 6.0 is used to control the constraint sets of the voltage of buses and the current of the distribution line. Since the scheduling and routing of the repair crews and the delivers is similar to the vehicle routing problem, which has been proved to be a NP-hard problem. In order to conquer this problem, the bacterial colony chemotaxis optimization algorithm (BCCOA) is introduced and improved by the strategy of chaos migration, the strategy of differential evolution, the strategy of precision self-adaption, and the strategy of normalizing the value of the objective function; the BCCOA with these strategies is referred as improved BCCOA. In addition, the A* algorithm is employed to calculate the required travel time between each pair of nodes to dismiss the impacts of the geographical features.
Ultimately, the IEEE30, IEEE57, and IEEE118 buses system are employed to check the validation and utilizes of the improved BCCOA and the adopted strategies. The results show that: (1) The improved BCCOA has a good performance on the quality of solution and the CPU time when comparing with the enumerate method; (2) Only increase the capacity of restoration, the utilities of restoration increased 36.40% averagely, while only increase the capacity of materials supply support, due to limited of the capacity of restoration, the utilities of restoration only increased 7.99% averagely, but the delays of material supply support decreased 61.71%. When increasing the capacity of restoration and materials supply support simultaneously, the utilities of restoration be increased 38.23% averagely, the increased percentage nearly 209.14%. All of these results show that the logistic support is critical and practical to restore the power distribution system; and (3) The strategy of differential evolution is more powerful than the strategy of chaos migration, the strategy of chaos migration is more useful than the strategy of precision self-adaption, the strategy of normalizing the value of the objective function is dominated by the strategy of precision self-adaption, while the BCCOA is dominated by all of these strategies. These results indicate that the adopted strategies are really useful and helpful to improve the quality of strategy for restoring the post-earthquake mountain areas power distribution systems with the logistic support.

Key words: mountain areas, earthquake, power distribution systems restoration, logistic support, bacterial colony chemotaxis optimization algorithm