Overcoming Constraints: The Critical Role of Penalty Functions as Constraint-Handling Methods in Structural Optimization

Optimization problems are common in many fields, including engineering, finance, and logistics. These problems often involve complex objective functions and multiple constraints that must be satisfied simultaneously. To solve such problems, various optimization algorithms have been developed that employ different constraint-handling methods. This chapter provides an overview of these methods and compares their effectiveness in solving optimization problems. The most commonly used methods, including penalty functions, are discussed and evaluated. The optimum design of framed structures is a complex problem that requires balancing a variety of competing objectives, such as minimizing weight while maintaining structural integrity. Several constraint-handling methods are applied to these structures, and their performance are compared in terms of solution quality, computational efficiency, and robustness. The results show that the choice of constraint-handling method can significantly affect the optimization outcome and that different methods may be more effective depending on the specific problem and constraints involved.