Pathfinding Algorithm with Moveable Obstacles

Question

Research

I have done some research on path-finding algorithms. I have come across some; such as A* & Dijkstra. In most of these algorithms they allow for weights for moving through certain paths. Some even allow for negative weights. Walls have infinite weight, since you can never move through them.

I have also read a little about path-finding algorithms where the obstacles are moving. However, my application is a little different. Instead of obstacles that move on their own, there are obstacles that can be moved by the algorithm.

Question

Is there a path-finding algorithm that accounts for moveable (weighted) objects?

Constraints

The algorithm needs to find the shortest path from A-to-B. It does not need to be efficient, as the maze is relatively small. Moveable obstacles must be weighted