How should I start my own private post-doc research project? I am interested in pursuing my own part-time postdoctoral research in computer science, with a view to getting one or two publications over the next two to three years. My motivations are personal interest, and also to keep my options open in case I decide to apply for an academic or research post in 2016.

I am not sure where I should start looking for a project.  Should I read academic papers until I get ideas?  Should I just try and brainstorm my own ideas?  Should I go back to my current university supervisor, or my previous PhD supervisor?

My Background

I am nearly 41 and married with two children (aged 10 and 13).  I gained my bachelor's in computing in 2006. In 2012 I submitted a thesis in artificial intelligence (case-based reasoning) and the PhD was awarded in 2013.  My family are not keen on moving and we live in an area with very few high-tech or academic employment opportunities. 

I can't see a way to extend my PhD research.  I have never worked as a post-doc; before the PhD I was a database administrator and immediately afterwards I was a software developer. 

Fortunately, late in 2013 I found a position on a UK government scheme known as Knowledge Transfer Partnerships.  I am employed by a Scottish university to work within an English manufacturing company, to use AI techniques to solve a particular engineering problem.  I am based at the manufacturing company and I see my university supervisor very rarely.  I am not allowed to publish anything from this employment. The contract ends in August 2016.

The KTP project will probably use standard AI methods; I won't be inventing any new techniques.  If the manufacturing company consented (and they will not!) it would be possible to publish, but it would only be as an interesting application of AI, not a new way of doing AI.

I have a substantial training budget (GBP £2000 a year) which—with the approval of my employer—I can spend going to conferences, buying books etc.

I have discussed the idea of doing research with my university supervisor, either performing experiments myself, or a literature review paper.  She made some nice noises but she was not overly enthusiastic.  I think she is worried that it will divert me from the KTP project (for which her university gets paid a lot of consultancy money) and possibly upset the construction company who I am based with.

My interests and skills lie in artificial intelligence (neural networks, case-based reasoning), computer-aided design and software engineering.

I still have my PhD supervisor on my LinkedIn page and I could approach her.  However, I worry that she will think it is strange if I ask to collaborate with her, given that I am currently employed by a different university.

I can commute to my current workplace (it's about an hour away) and there are 2 good universities (and another two not-so-good ones) about 60-90 minutes' commute from our family home, so location is the biggest restriction for me, I can't force my wife and children to move.
Partial answer: start reading!

Read for both breadth and depth, and be sure to occasionally step outside the boundaries of what you are familiar with, even exploring fields that seem only tangentially related. In the process, you will almost certainly discover an area that is begging to be explored further. Indulge yourself, dive into the literature, buy books and attend conferences (for which you say you have a budget), and keep excellent notes while doing so. 

You may discover that you can write a literature review fairly easily, and will probably also find that you have identified exactly what you wish to pursue for your research project. At worst, you will have spent many enjoyable hours increasing your knowledge; at best, you will be well on the way to completing your research.