In 2003, Brewka, Niemela and Truszczynski introduced answer-set optimization problems. They consist of two components: a logic program and a set of preference rules. Answer sets of the program represent possible outcomes; preferences determine a preorder on them. Of interest are answer sets of the program that are optimal with respect to the preferences. In this work, we consider computational problems concerning optimal answer sets. We implement and study several methods for the problems of computing an optimal answer set; computing another one, once the first one is found; and computing an optimal answer set that is similar to (respectively, dissimilar from) a given interpretation. For the problems of the existence of similar and dissimilar optimal answer set we establish their computational complexity.
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