How to cook the food such that no acrylamide is formed?

Salt your food well.

See for example this article (paywall, but the abstract is sufficient). You are unlikely to have calcium chloride in your kitchen, so you probably can't use the divalent cations route. But "monovalent cations, such as Na+, almost halved the acrylamide formed in the model system". Now, a model system is not a pan, but they at least found that the calcium example transfers well to frying, so (wet) salt is likely to work too.

Acid also seems to help, as shown in another paper. But note that they had to lower the surface pH of the potatoes to 4.0, which you may not want to do.

Note that the literature seems to concentrate on frying potatoes. We can hope that the methods are applicable to other foods, but I have seen no evidence for it yet.

First off here is my source www.cancer.org

Acrylamide does not appear to be in raw foods themselves. It is formed when certain starchy foods are cooked at temperatures above about 250° F. Cooking methods such as frying, baking, broiling, or roasting are more likely to produce acrylamide, while boiling, steaming, and microwaving appear less likely to do so. Cooking at high temperatures causes the Maillard reaction a chemical reaction between certain sugars and an amino acid (asparagine) in the food, which causes acrylamide to form. Longer cooking times and cooking at higher temperatures can increase the amount of acrylamide in foods further.

So according to my source, you would have to eliminate these factors. I don't see how you would be able to caramelize anything without using the Maillard reaction although, let alone use the Maillard reaction in your cooking, these factors are beneficial in successfully and properly performing the Maillard reaction.

Although read my comment above or visit the cancer.org website

The short answer is acrylamide can form in many foods when heated above 248F for an extended period of time.

If you are a big "griller" you may want to rethink that. Eat golden toast versus burnt toast. Eat golden fries versus brown crispy fries.

http://www.cancer.gov/about-cancer/causes-prevention/risk/diet/acrylamide-fact-sheet

http://www.fda.gov/Food/FoodborneIllnessContaminants/ChemicalContaminants/ucm053569.htm