While answer-set programming (ASP) is a successful approach to declarative problem solving optimisation can still be a challenge for it. Large-neighbourhood search (LNS) is a metaheuristic technique where parts of a solution are alternately destroyed and reconstructed, which has high but untapped potential for ASP solving. We present a framework for LNS optimisation for ASP, in which neighbourhoods can be specified either declaratively as part of the ASP encoding, or automatically generated by code. In the full paper, we illustrate the framework on different optimisation problems, some of which are notoriously difficult, including shift planning and a parallel machine scheduling problem from semi-conductor production which demonstrate the effectiveness of the LNS approach.