Finding similar/diverse solutions in answer set programming

For some computational problems (e.g., product configuration, planning, diagnosis, query answering, phylogeny reconstruction) computing a set of similar/diverse solutions may be desirable for better decision-making. With this motivation, we have studied several decision/optimization versions of this problem in the context of Answer Set Programming (ASP), analyzed their computational complexity, and introduced offline/online methods to compute similar/diverse solutions of such computational problems with respect to a given distance function. All these methods rely on the idea of computing solutions to a problem by means of finding the answer sets for an ASP program that describes the problem. The offline methods compute all solutions of a problem in advance using the ASP formulation of the problem with an existing ASP solver, like CLASP, and then identify similar/diverse solutions using some clustering methods (possibly in ASP as well). The online methods compute similar/diverse solutions of a problem following one of the three approaches: by reformulating the ASP representation of the problem to compute similar/diverse solutions at once using an existing ASP solver; by computing similar/diverse solutions iteratively (one after other) using an existing ASP solver; by modifying the search algorithm of an ASP solver to compute similar/diverse solutions incrementally. We have modified CLASP to implement the last online method and called it CLASP-NK. In the first two online methods, the given distance function is represented in ASP; in the last one however it is implemented in C++. We have showed the applicability and the effectiveness of these methods using CLASP or CLASP-NK on two sorts of problems with different distance measures: on a real-world problem in phylogenetics (i.e., reconstruction of similar/diverse phylogenies for Indo-European languages), and on several planning problems in a well-known domain (i.e., Blocks World). We have observed that in terms of computational efficiency (both time and space) the last online method outperforms the others; also it allows us to compute similar/diverse solutions when the distance function cannot be represented in ASP (e.g., due to some mathematical functions not supported by the ASP solvers) but can be easily implemented in C++.