"move forward toward" is correct and usable in written English.
You can use this phrase to describe an action of advancing in a certain direction. For example: The dogs moved forward toward the river in search of the lost Frisbee.
In OR, more number of next hop forwarders mean that the packets have more chance to move forward toward the destination at each transmission.
How can we move forward toward a better tomorrow?
It can move forward toward real peace, or it can slide back into turmoil.
"I only hope that they will... move forward toward a conciliatory, civilized, democratic and political environment in the future".
It means, they say, that the project is actually more likely to move forward toward recouping their investment.
But now it is time for the myriad Balkan peoples to move forward toward development and reconciliation.
"She is excited to get back on the campaign trail and to move forward toward a triumph over Barbara Boxer next Tuesday".
The success of the Shenzhou 9 launching and its docking maneuvers will allow China to move forward toward its goal of building a permanent space station by 2020.
The two leaders requested "American participation and leadership in facilitating efforts to overcome obstacles, rally regional and international support and move forward toward peace," Rice said.
And politically, every move forward toward greater Sunni Arab participation in the political process seems to be accompanied by at least one step back.
But Mr. Musharraf said he only hoped they would "move forward toward a conciliatory, civilized, democratic and political environment in the future".
