Structural Optimization plays a critical role in improving the efficiency, cost-effectiveness, and sustainability of engineering designs. This paper presents a comparative study of Single-Objective and multi-Objective Optimization in the structural design process. Single-Objective problems focus on optimizing just one Objective, such as minimizing weight or cost, while other important aspects are treated as constraints like deflections and strength requirements. Multi-Objective Optimization addresses multiple conflicting Objectives, such as balancing cost, with displacement treated as a secondary Objective and strength requirements defined as constraints within the given limits. Both Optimization approaches are carried out using Chaos Game Optimization (CGO). While Single-Objective Optimization produces a definitive optimal solution that can be used directly in the final design, multi-Objective Optimization results in a set of trade-off solutions (Pareto front), requiring a decision-making process based on design codes and practical criteria to select the most appropriate design. Through a real-world case study, this research will assess the performance of both Optimization strategies, providing insights into their suitability for modern structural engineering challenges.