Solving generalized optimization problems subject to SMT constraints

Abstract

In a classical constrained optimization problem, the logical relationship among the constraints is normally the logical conjunction. However, in many real applications, the relationship among the constraints might be more complex. This paper investigates a generalized class of optimization problems whose constraints are connected by various kinds of logical operators in addition to conjunction. Such optimization problems have been rarely studied in literature in contrast to the classical ones. A framework which integrates classical optimization procedures into the DPLL(T) architecture for solving Satisfiability Modulo Theories (SMT) problems is proposed. Two novel techniques for improving the solving efficiency w.r.t. linear arithmetic theory are also presented. Experiments show that the proposed techniques are quite effective. © 2012 Springer-Verlag.