Consider an array of potential approaches (let’s say 15) that you are considering taking to solve some problem or accomplish some task. Assuming that each of these approaches reaches the end goal (signified by the circle in the graph below) at a different time, some being more effective than others. Consider the graph below where all end points contain the same amount of expected value and the time it takes to reach each point (y-axis) is uncertain.

What then is the best way to approach the decision of choosing a path (absent any information of how much time each path will take you)? Is it more effective to start off down one path without turning back? Or is it optimal to start out down and try as many paths as possible?

In this case path 14 ends up being the shortest…
Is there any body of research on this type of decision making under uncertainty?