  The optimization of chemical processes is challenging due to the
nonlinearities arising from process physics and discrete design decisions. In
particular, optimal synthesis and design of chemical processes can be posed as
a Generalized Disjunctive Programming (GDP) superstructure problem. Various
solution methods are available to address these problems, such as reformulating
them as Mixed-Integer Nonlinear Programming (MINLP) problems; nevertheless,
algorithms explicitly designed to solve the GDP problem and potentially
leverage its structure remain scarce. This paper presents the Logic-based
Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP
problems involving ordered Boolean variables. The LD-SDA reformulates these
ordered Boolean variables into integer decisions called external variables. The
LD-SDA solves the reformulated GDP problem using a two-level decomposition
approach where the upper-level subproblem determines external variable
configurations. Subsequently, the remaining continuous and discrete variables
are solved as a subproblem only involving those constraints relevant to the
given external variable arrangement, effectively taking advantage of the
structure of the GDP problem. The advantages of LD-SDA are illustrated through
a batch processing case study, a reactor superstructure, a distillation column,
and a catalytic distillation column, and its open-source implementation is
available online. The results show convergence efficiency and solution quality
improvements compared to conventional GDP and MINLP solvers.
