Table 1 Notations of a mathematical model.
From: A learning-driven algorithm for maintenance team and UAV collaboration in restoring power network
Input variables | |
|---|---|
F | The set of faulty nodes, where \(|F|=n\) |
\(F^{\prime }\) | The set of unknown faulty nodes, where \(|F^{\prime }|=n^{\prime }\) and \(F^{\prime } \subseteq F\) |
\(h_{i}\) | The i-th maintenance team, \(i=1,2, \ldots , m_{1}\) |
\(u_{i}\) | The i-th UAV, \(i=1,2, \ldots , m_{2}\) |
\(\tau _{u_{i}, f_{j'}}\) | The detection time for detecting the unknown faulty node \(f_{j^{\prime }}\) |
\(p_{u_{i}, f_{j'}}\) | The probability of \(u_{i}\) accurately detecting the unknown faulty node \(f_{j^{\prime }}\) |
\(\tau _{h_{i}, f_{j}}\) | The repair time to restore the faulty node \(f_{j}\) |
\(\eta ^{+}\) | A coefficient of \(\tau _{h_{i}, f_{j}}\) when \(f_{j}\) is not accurately detected by UAV, \(\eta ^{+} \in [1.3,1.5]\) |
\(\eta ^{-}\) | A coefficient of \(\tau _{h_{i}, f_{j}}\) when \(f_{j}\) is accurately detected by UAV, \(\eta ^{-} \in [0.6,0.8]\) |
\(\delta\) | The fatigue factor of maintenance-team |
\(t_{u_{i}, 0, f_{j'}}\) | The flight time of \(u_{i}\) from its starting point to \(f_{j'}\) |
\(t_{u_{i}, f_{j'}, f_{k'}}\) | The flight time of \(u_{i}\) from \(f_{j'}\) to \(f_{k^{\prime }}\) |
\(t_{h_{i}, 0, f_{j}}\) | The travelling time of \(h_{i}\) from operation centre to \(f_{j}\) |
\(t_{h_{i}, f_{j}, f_{k}}\) | The travelling time of \(h_{i}\) from \(f_{j}\) to \(f_{k}\) |
Decision variables | |
\(\pi _{u_{i}}\) | The unknown faulty node scheduling sequence of \(u_{i}\) |
\(\pi _{h_{i}}\) | The faulty node scheduling sequence of \(h_{i}\) |
\(\pi =(\pi _{u}, \pi _{h})\) | A solution for the considered problem, where \(\pi _{u}=\{\pi _{u_{1}}, \pi _{u_{2}}, \ldots , \pi _{u_{m_{2}}}\}\) and \(\pi _{h}=\{\pi _{h_{i}}, \pi _{h_{2}}, \ldots , \pi _{h_{m_{1}}}\}\) |
