Applying ranking and selection procedures to long-term mitigation for improved network restoration

In this paper, we consider methods to determine the best single arc mitigation plan for improving rapid recovery of a network with a given level of statistical certainty. This problem is motivated by infrastructure managers interested in increasing the resilience of their systems through costly long-term mitigation procedures. Our problem is two stage, where we consider a small number of pre-event decisions for mitigation, with a large second-stage integer programming problem to capture the restoration process for each damage scenario and each mitigation plan. We consider a ranking and selection (R&S) procedure and compare its performance against a brute force method using standard statistical testing on problems with low, medium, and high damage levels. These comparisons are made by using the same computational effort for each method and comparing the level of confidence achieved to determine a best single arc mitigation plan and whether the same best single arc mitigation plan is found. We find that the R&S procedure can find a best single arc mitigation plan with 95 % confidence in all cases, and the brute force procedure, while identifying the same mitigation plan as being one of the best, is unable to determine a single best mitigation plan in all but one case. Having developed a general framework for determining the best single arc mitigation plan with statistical certainty for any network, we conclude with thoughts and challenges on how this framework can be expanded and applied to different problems.