## 7 Conclusions and Perspectives  
New dual bounds for the EURO/ROADEF Challenge 2010 are provided in this paper hybridizing exact methods, heuristics, and ML techniques. Parametric surrogate relaxations illustrate the interest  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & **Pimal** & **[16].1** & **[16].2** & **[17]** & **New Lower Bound** & **Gap** & **Bound** & **M** & **Time/S** \\ \hline A1 & 169,474.5 M & [32] & 5.09\% & 2.31\% & 0.04\% & 169,460.609 M & 0.01\% & LB & 10 & OPT \\ A2 & 145,956.7 M & [32] & 10.83\% & 4.09\% & 0.25\% & 145,669.1154 M & 0.20\% & LB & 10 & OPT \\ A3 & 154,277.2 M & [32] & 10.72\% & 3.77\% & 0.37\% & 153,770.2050 M & 0.33\% & LB & 10 & OPT \\ A4 & 111,494.0 M & [15] & 26.07\% & 8.22\% & 1.52\% & 110,130.2886 M & 1.22\% & LB & 5 & 2400 \\ A5 & 124,543.9 M & [15] & 24.22\% & 9.70\% & 2.55\% & 122,035.5788 M & 2.01\% & LB & 3 & 2400 \\ \hline \(\sum\) A & 705,746.3 M & & 14.20\% & 5.24\% & 0.83\% & 701,065.7947 M & 0.66\% & & & \\ \hline B6 & 83,424.7 M & [28] & 56.44\% & 16.58\% & 5.30\% & 79,394.9322 M & 4.83\% & LB & 5 & 3600 \\ B7 & 81,099.7 M & [15] & 52.82\% & 15.50\% & 6.22\% & 76,499.2099 M & 5.67\% & LB(5) & 10 & 3600 \\ B8 & 81,899.7 M & [15] & 63.51\% & 23.57\% & 12.37\% & 72,322.5889 M & 11.69\% & LB(5) & 10 & 3600 \\ B9 & 81,689.5 M & [15] & 63.28\% & 21.67\% & 11.59\% & 72,811.720M & 10.87\% & LB(5) & 10 & 3600 \\ B10 & 77,767.0 M & [15] & 60.92\% & 18.03\% & 7.32\% & 72,462.8317 M & 6.82\% & LB(5) & 10 & 1800 \\ \hline \(\sum\) B & 405,880.6 M & & 59.74\% & 19.08\% & 8.56\% & 373,491.2828 M & 7.98\% & & \\ \hline X11 & 79,007.6 M & [15] & 57.75\% & 15.29\% & 5.45\% & 75,183.0108 M & 4.84\% & LB & 5 & 3600 \\ X12 & 77,564.0 M & [15] & 52.63\% & 14.19\% & 6.65\% & 72,986.7523 M & 5.90\% & LB & 5 & 3600 \\ X13 & 76,288.5 M & [15] & 66.20\% & 18.53\% & 7.59\% & 70,988.40356 M & 6.95\% & LB & 5 & 1800 \\ X14 & 76,149.8 M & [15] & 64.67\% & 17.21\% & 7.82\% & 70,549.09524 M & 7.35\% & LB & 5 & 1800 \\ X15 & 74,388.4 M & [15] & 61.76\% & 16.83\% & 8.11\% & 68,821.7327 M & 7.48\% & LB & 5 & 1800 \\ \hline \(\sum\) X & 383,398.3 M & 60.55\% & 16.39\%of dual heuristics for an industrial MILP: relaxations are parametrized to induce little degradation of the dual bound's quality, but it significantly improves the MILP solving capabilities, so that in defined time limits dual heuristics may provide better dual bounds than exact approaches. The scenario decomposition computes dual bounds for the original problem with a fixed number of scenarios, with a numerical interest to choose carefully the partitions of scenarios, using ML techniques. Combining these techniques leads to tractable computations of dual bounds for the EURO/ROADEF Challenge 2010, outclassing significantly the former best dual bounds of the literature. The quality of our dual bounds justifies the quality of the best primal solutions known, mainly in [15]. This work offers new perspectives. Using more powerful computers and more computation time may improve some reported results. Our approach is scalable to compute dual bounds in a given time limit and hardware configuration, which is useful for a real life application. We note special perspectives for the approach deployed by [26]: parametric MILP relaxations may be useful to accelerate Bender's decomposition, to compute quicker valid cuts and also to stabilize the Bender's decomposition. Considering bi-objective extension, implied by robust optimization considerations [38] or stability costs [24], we can compute dual bound-sets using computations of dual bounds from this paper using scalarization or epsilon-constraint methods. Lastly, we mention as a perspective that the results of Section 5 are valid for a general class of 2-stage stochastic problems, optimizing strategical problems like maintenance planning conjointly with an operational level as in [3]. Conceptualization, N.D. and E.-G.T. ; Methodology, N.D. and E.-G.T. ; Software, N.D.; Validation, N.D. and E.-G.T.