A big part of this is committing to monogamy. I was just talking about this with my roommate last night - I have poly friends and they are some of the happiest people I know. The man (I'll call him M) has a legal wife (I'll call her N) and another woman in the relationship that he had a hand-fasting ceremony with (I'll call her K).
N is an introvert, K is an extrovert. M has different people to meet different needs. If he feels like staying in and watching Netflix and doing nothing N is there for him and K is fine going out by herself or with other friends. But if M wants to go out to NaNoWriMo events or other places where N isn't super comfortable he knows he can take K with him and N isn't going to be mad about it.
They are open with one another about the relationship and are fine with it. So M doesn't cheat on either one because he's getting what he wants and needs in a relationship and the pair are content where they are but also know their options are open to relationships with others should the need arise.
Same goes for my roommate - he and his husband are apart right now because the husband is military, so they have an open relationship. Both are free to find someone else to meet their respective needs until the military business stops and then they'll have to take time to re-evaluate their relationship and if that is still something they both still feel should be part of things or not.
Now that's not to say monogamy can't work for some people, but like most things in life it's subject to change. If people would be more open about "So yeah being monogamous isn't working for me at this moment in time I feel like something needs to change." instead of sitting and harboring those feelings because they feel like the absolutely must be monogamous in that relationship that's can certainly lead to cheating.
Humans are complex, and it's really difficult for just one person to meet all those needs. Relationships are not stagnant either, and people trying to hold on to what a relationship should be instead of allowing it to naturally be what it is instead of communicating the wants and needs is just as bad. But I do honestly hold that if people were more open and realized that committing to a single individual is not for everyone and were more open and trusting with relationships then there might be far less cheating in the world.