Optimization of chemical processes is challenging due to nonlinearities arising from chemical principles and discrete design decisions. The optimal synthesis and design of chemical processes can be posed as a Generalized Disjunctive Programming (GDP) problem. While reformulating GDP problems as Mixed-Integer Nonlinear Programming (MINLP) problems is common, specialized algorithms for GDP remain scarce. This study introduces the Logic-Based Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP problems involving ordered Boolean variables. LD-SDA transforms these variables into external integer decisions and uses a two-level decomposition: the upper-level sets external configurations, and the lower-level solves the remaining variables, efficiently exploiting the GDP structure. In the case studies presented in this work, including batch processing, reactor superstructures, and distillation columns, LD-SDA consistently outperforms conventional GDP and MINLP solvers, especially as the problem size grows. LD-SDA also proves superior when solving challenging problems where other solvers encounter difficulties finding optimal solutions.