Railway alignment design has evolved from traditional empirical approaches to more scientific methods, incorporating precise mathematical formulations and sophisticated optimization algorithms. This transition enables engineers to systematically analyze and refine railway alignments to enhance efficiency, safety, and cost-effectiveness while minimizing environmental impacts. A crucial aspect of this optimization process is the fundamental stage of identifying constraints and formulating the objective function. Constraints, such as geometric requirements, geographical limitations, construction risks, land availability, and operational requirements, define the feasible design space. Meanwhile, the objective function quantifies optimization goals, whether minimizing construction costs, reducing environmental impact, or enhancing operational efficiency. Therefore, this chapter will introduce the mathematical expression of railway alignment parameters and systematically provide an in-depth discussion of constraints and design objective functions in the railway alignment design optimization process.