JSoko offers several solvers for automatically solving levels.
One of the solvers searches for push optimal solutions.
Currently this solver can solve 31 of the XSokoban levels push optimal.
My test run has been done on this computer:
CPU: Intel Core i5 6600K @4,6GHz
RAM: 32GB Corsair Vengeance LPX DDR4-3000
Level: 1 | Moves: 264 | Pushes: 97 | Time: 0.0s | Status : solved
Level: 2 | Moves: 539 | Pushes: 131 | Time: 0.0s | Status : solved
Level: 3 | Moves: 384 | Pushes: 134 | Time: 0.0s | Status : solved
Level: 4 | Moves: 995 | Pushes: 355 | Time: 0.2s | Status : solved
Level: 5 | Moves: 467 | Pushes: 143 | Time: 0.9s | Status : solved
Level: 6 | Moves: 345 | Pushes: 110 | Time: 0.0s | Status : solved
Level: 7 | Moves: 353 | Pushes: 88 | Time: 47.5s | Status : solved
Level: 9 | Moves: 694 | Pushes: 237 | Time: 1.9s | Status : solved
Level: 11 | Moves: 1042 | Pushes: 241 | Time: 483.6s | Status : solved
Level: 17 | Moves: 551 | Pushes: 213 | Time: 0.2s | Status : solved
Level: 19 | Moves: 1167 | Pushes: 302 | Time: 2625.0s | Status : solved
Level: 26 | Moves: 585 | Pushes: 195 | Time: 286.5s | Status : solved
Level: 27 | Moves: 1914 | Pushes: 363 | Time: 2315.1s | Status : solved
Level: 28 | Moves: 1045 | Pushes: 308 | Time: 2717.8s | Status : solved
Level: 38 | Moves: 378 | Pushes: 81 | Time: 0.6s | Status : solved
Level: 40 | Moves: 1417 | Pushes: 324 | Time: 28.7s | Status : solved
Level: 43 | Moves: 844 | Pushes: 146 | Time: 1022.5s | Status : solved
Level: 45 | Moves: 915 | Pushes: 300 | Time: 497.6s | Status : solved
Level: 48 | Moves: 731 | Pushes: 200 | Time: 108.0s | Status : solved
Level: 49 | Moves: 639 | Pushes: 124 | Time: 2443.7s | Status : solved
Level: 51 | Moves: 482 | Pushes: 118 | Time: 79.8s | Status : solved
Level: 54 | Moves: 940 | Pushes: 187 | Time: 3406.4s | Status : solved
Level: 55 | Moves: 653 | Pushes: 120 | Time: 19.7s | Status : solved
Level: 65 | Moves: 841 | Pushes: 211 | Time: 5.0s | Status : solved
Level: 78 | Moves: 412 | Pushes: 136 | Time: 3.1s | Status : solved
Level: 79 | Moves: 546 | Pushes: 174 | Time: 0.3s | Status : solved
Level: 80 | Moves: 678 | Pushes: 231 | Time: 0.0s | Status : solved
Level: 81 | Moves: 739 | Pushes: 173 | Time: 5.2s | Status : solved
Level: 82 | Moves: 468 | Pushes: 143 | Time: 0.1s | Status : solved
Level: 83 | Moves: 507 | Pushes: 194 | Time: 0.1s | Status : solved
Level: 86 | Moves: 652 | Pushes: 134 | Time: 0.0s | Status : solved