For many computational problems, the main concern is to find a best solution (e.g., a most preferred product configuration, a shortest plan, a most parsimonious phylogeny) with respect to some well-described criteria. On the other hand, in many real-world applications, computing a subset of good solutions that are similar/diverse may be desirable for better decision-making. For one reason, the given computational problem may have too many good solutions, and the user may want to examine only a few of them to pick one; in such cases, finding a few similar/diverse good solutions may be useful. Also, in many real-world applications the users usually take into account further criteria that are not included in the formulation of the optimization problem; in such cases, finding a few good solutions that are close to or distant from a particular set of solutions may be useful. With this motivation, we have studied various computational problems related to finding similar/diverse (resp. close/distant) solutions with respect to a given distance function, in the context of Answer Set Programming (ASP). We have introduced novel offline/online computational methods in ASP to solve such computational problems. We have modified an ASP solver according to one of our online methods, providing a useful tool (CLASP-NK) for various ASP applications. We have showed the applicability and effectiveness of our methods/tools in three domains: phylogeny reconstruction, AI planning, and biomedical query answering. Motivated by the promising results, we have developed computational tools to be used by the experts in these areas
