How to build the smallest trajectory of movement through the cells, having the ability to rearrange obstacles?

Question

Java

Good afternoon!
It is necessary to develop an algorithm for moving an object from cell A to cell B in such a way that the sum of movements of obstacles to clear the path + the sum of movements of the object itself is minimal. Movement is possible in 8 directions (forward/backward, left/right, diagonal). It should be borne in mind that the obstacles should then fall back into place.
Please tell me ideas for implementation, something good does not come to my mind.

Answer 1

We build a move tree, build an objective function, take one of the popular optimization algorithms on graphs (either an ant colony or simulated annealing), mix, but do not shake.