An optimization approach for solving signomial discrete programming problems with free variables

Signomial discrete programming (SDP) problems occur frequently in engineering design. This paper proposes a generalized method to solve SDP problems with free variables. An SDP problem with free variables is first converted into another one containing non-negative variables, and then various non-convex signomial terms are transformed such that the original SDP problem becomes a convex integer program solvable to obtain a globally optimal solution. Compared with current SDP methods, the proposed method is capable of dealing with free variables of an SDP problem and is guaranteed to converge to a global optimum. In addition, several computationally efficient convexification rules for signomial terms are presented to enhance the efficiency of the optimization approach. Numerical examples in real applications are presented to demonstrate the usefulness of the proposed method.