Analysis of complex product design problem using an L-partition approach

Abstract

In this paper, we analyze the complex product design problem using the model of the partial maximum satisfiability problem. In previous papers, estimates of the cardinality of L-complexes of polyhedrons of the SAT and the MAX SAT problems were obtained. In this paper, a relation of the cardinality of the L-complexes of the partial MAX SAT problem and the corresponding SAT problem is obtained. Using this result, it is possible to obtain theoretical estimates of the cardinality of the L-complex of the polyhedron of the complex product design problem on the basis of similar estimates for the SAT and the MAX SAT problems.