Brainstorming can be a useful exercise, and many books can help you with that process, such as The Riddle.
However, logic trees often aren’t discussed as an alternative brainstorming, but despite using a far more structured approach they can achieve a similar result. With a logic tree you start with a problem and map out solutions to it, trying to be exhaustive and comprehensive. Starting with broad areas and narrowing down to specifics that fall within scope of the broader areas, hence the ‘tree’ framework. It’s a far more structured approach than brainstorming, but it can lead to more complete analysis and, if done well, be just as creative.
The example below comes from the powerful problem solving blog. It starts with the problem of establishing a company as a high-end tailor and then maps out possible initial directions (build a brand, focus on quality, create a unique shopping experience) and then fleshes each idea out in increasing detail such as using the finest wool or associating with celebrities. It’s a simplified example, but it shows the underlying idea clearly – click on the image below to enlarge it.