My own attempt at answering this question was to think for at least 5 minutes of ways in which a society could possibly avoid its people having their hearts broken, and evaluate the solutions on a do want/do not want scale.
The first method would be to never let anybody fall in love again. Either humans would be modified such that they would never feel love again, or they would be isolated such that they could never interact with the appropriate gender (so... straight men with each other, straight women with each other, gay men and lesbian women in single pairs, bisexuals by themselves, etc... if not just isolating everybody individually). This strikes me as completely unacceptable.
The second approach would be to avoid heartbreaks once a person has fallen in love. We consider the cases where a person might have his or her heart broken after that event: the other person might reject them initially, lie to them and string them along until revelation, love them back for a time but eventually stop feeling the same way and leave them, do something that causes first person to leave them while still being in love themselves (cheating, spousal rape, etc...), or be separated from the first person due to circumstances beyond control (death, physical separation due to economic circumstances, etc...). At least, those are all the ways I can think of.
Hopefully, by the time we can seriously talk about eliminating heartbreaks as an implementable policy, the latter will no longer be a serious consideration for people. The case of lying could be taken care of if humans were prevented from lying somehow, either in a specific case (humans can't lie to their partners while in a relationship/can't lie when saying "I love you"/some other constrain) or the general case (humans can't lie at all); I must admit that the former seems to me mildly attractive depending on how it is implemented. To handle the case of people falling out of love, humans could be modified such that they never fall out of love once they have become enamored of someone who loves them back and they have become lovers. This is definitely interesting; I can't see any immediate objections to that one that aren't part of the fully general "ick! You are changing me and taking away my free will" reflex. The rejection case could be solved by making it such that people reciprocate love once someone has fallen in love with them, maybe even changing orientations to do so; I don't really like this one. Comparing it with the last case discussed, the difference seems to be the difference between making a change and preserving a state; I'm not sure this is something I should care about much, so I will consider it more fully later. And the last case... oh, hell, I don't know. I don't think taking away the ability to do such things works without also removing the intentions, unless their partner never finds out about them.
The third way would be to let people fall in love, but only with people who would not break their hearts. It seems like creating human imitations who would always love one, a la Failed Utopia #4-2, is one possible venue of attack. It also looks like some ideas from the second set of situations coulde be re-applied with a bit of tweaking...
Aaaand I'm gonna stop there, because I just realized that on top of this, I have to consider all the cases for the polyamorists, too. Jesus Christ, people are complicated; Randall Munroe was right. Sorry if this seems confused, but that's mostly because it is; this is the first time I have seriously considered the problem. Still, I hope to have contributed something with my post.
Another possibility is to have everyone always being in love with everyone.
Utopia and Dystopia have something in common: they both confirm the moral sensibilities you started with. Whether the world is a libertarian utopia of the non-initiation of violence and everyone free to start their own business, or a hellish dystopia of government regulation and intrusion—you might like to find yourself in the first, and hate to find yourself in the second; but either way you nod and say, "Guess I was right all along."
So as an exercise in creativity, try writing them down side by side: Utopia, Dystopia, and Weirdtopia. The zig, the zag and the zog.
I'll start off with a worked example for public understanding of science:
Disclaimer 1: Not every sensibility we have is necessarily wrong. Originality is a goal of literature, not science; sometimes it's better to be right than to be new. But there are also such things as cached thoughts. At least in my own case, it turned out that trying to invent a world that went outside my pre-existing sensibilities, did me a world of good.
Disclaimer 2: This method is not universal: Not all interesting ideas fit this mold, and not all ideas that fit this mold are good ones. Still, it seems like an interesting technique.
If you're trying to write science fiction (where originality is a legitimate goal), then you can write down anything nonobvious for Weirdtopia, and you're done.
If you're trying to do Fun Theory, you have to come up with a Weirdtopia that's at least arguably-better than Utopia. This is harder but also directs you to more interesting regions of the answer space.
If you can make all your answers coherent with each other, you'll have quite a story setting on your hands. (Hope you know how to handle characterization, dialogue, description, conflict, and all that other stuff.)
Here's some partially completed challenges, where I wrote down a Utopia and a Dystopia (according to the moral sensibilities I started with before I did this exercise), but inventing a (better) Weirdtopia is left to the reader.
Economic...
Sexual...
Governmental...
Technological...
Cognitive...