Is it possible to hire graduate students as freelancers? I am currently working in the engineering industry. I am developing software in this field in my free time. I got stuck in some algorithm, and I'm looking for help from academia (either professors or students).

Is it possible to hire professors or students from universities to develop an algorithm for me?
Do universities have some kind of forum to invite projects for its researchers?

(I also considered the option to hire from popular websites for freelancers; however, it is difficult to find many people who freelance in engineering. My budget is  between 500 USD to 1000 USD for around 10 hours of work.)
While people are, perhaps rightly, poking at your estimate of how long this will take and your budget, yes, its entirely possible to hire graduate students as freelancers. I worked on several projects during my graduate career as a consultant or freelancer. Generally speaking, there aren't great university resources for it, though you might contact a professor who works in the area to see if he or she have any students who might be interested in a consulting gig.