Multi-Objective Optimization of Reinforced Concrete Spread Footings Using NSGA-II: Minimizing Concrete Volume and Steel Weight

This paper presents a multi-objective optimization framework for the design of reinforced concrete spread footings, minimizing concrete volume and steel reinforcement weight simultaneously. The problem is formulated with three geometric decision variables (footing length, width, and height) subject to structural
and geotechnical constraints derived from ABNT NBR 6118:2023 and classical foundation design criteria. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is adopted as the solution method, extended with a gene-directed mutation operator that guarantees a complete phenotypic perturbation across all design variables at each mutation event. Three case studies, ranging from centred compression to large-scale combined loading, demonstrate that the algorithm consistently produces smooth, well-populated Pareto fronts within 25 generations. Results show that moderate increases in footing height yield disproportionate reductions in steel weight, a trade-off insight not available from conventional deterministic design procedures.