Research has demonstrated that, when it comes to either very simple or very complex problems, brainstorming on our own is more productive than brainstorming in a group. And when problems are moderately complex, brainstorming in a group wins out over brainstorming on your own.
I’ll leave it to you to decide where your goal falls on the simplicity-complexity continuum. Having said all that, feel free to brainstorm in whatever way you prefer—on your own, in a group, or perhaps a bit of both.
Incidentally, when brainstorming in a group, it’s helpful to assign the role of scribe to someone other than yourself; this is because there’s a natural inclination to filter ideas as they’re presented to you. Sooner or later, someone will suggest something and you’ll find yourself thinking, “oh my Goodness; I could never do that!” But since it’s the scribe’s job to write everything down, you’ll have a list of every idea that was presented for further consideration.
And if you decide to brainstorm in a group, you can make the experience more pleasurable by inviting people over for brunch or dinner. Once everyone has his or her food and has settled in: you present your goal and the steps you’ve already taken, or attempted to take, in order to achieve it; let the group know where you’re stuck, e.g., a lack of resources, either internal (knowledge, skills, motivation) or external (access to the right tools and/or people); and let the brainstorming begin.