Improve lower-bound estimation in A-CMTS without sacrificing efficiency

Develop a more accurate and computationally efficient lower-bound estimator for the high-level search in anytime congestion mitigation tree search (A-CMTS) for congestion mitigation path planning (CMPP); specifically, improve upon the current estimator LB = Length(π_min) + ΔC, where π_min is the shortest feasible path under the node’s forced and forbidden edge constraints and ΔC is the additional congestion cost from forced edges, so that the estimator more tightly bounds the minimum achievable total congestion cost while preserving practical runtime performance.

Background

A-CMTS is a two-level search algorithm that uses branch-and-bound with a lower bound (LB) to prune the search space when solving CMPP. The current LB used in the paper is an approximation defined as the sum of the length of the shortest feasible path (π_min) and the incremental congestion due to forced edges (ΔC).

A tighter LB could allow more aggressive and reliable pruning, potentially improving convergence speed and solution quality. However, any improvement must maintain computational efficiency suitable for large-scale instances, which motivates the open problem of designing a better LB estimator with strong performance characteristics.