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 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 in advance using the ASP formulation of the problem with an ASP solver, like Clasp, and then identify similar diverse solutions using clustering methods. The online methods compute similar diverse solutions following one of the three approaches: by reformulating the ASP representation of the problem to compute similar diverse solutions at once using an ASP solver; by computing similar diverse solutions iteratively (one after other) using an ASP solver; by modifying the search algorithm of an ASP solver to compute similar diverse solutions incrementally. We 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 it is implemented in C++. We showed the applicability and the effectiveness of these methods on reconstruction of similar diverse phylogenies for Indo-European languages, and on several planning problems in Blocks World. We observed that in terms of computational efficiency 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.
@cite_24: In many AI fields, the problem of finding out a solution which is as close as possible to a given configuration has to be faced. This paper addresses this problem in a propositional framework. The decision problem DISTANCE-SAT that consists in determining whether a propositional CNF formula admits a model that disagrees with a given partial interpretation on at most d variables, is introduced. The complexity of DISTANCE-SAT an d of several restrictions of it are identified. Two algorithms based on the well-known Davis Putnam search procedurea represented so as to solve DISTANCE-SAT. Their empirical evaluation enables deriving firm conclusionsa bout their respective performances and to relate the difficulty of DISTANCE-SAT with the difficulty of SAT from the practical side.
As for the computational complexity analysis, Proposition 1 of @cite_24 shows that in the general case distance-sat is -complete. However, determining whether @math has a model that disagrees with a complete interpretation @math on at most @math variables, where @math is a constant, is in .