A Carbon-Aware Multi-Objective Framework for Catalog-Constrained RC Slab Design: Diagnosing Mapping Bias and Penalty Traps in Discrete Structural Optimization

Reducing embodied carbon in reinforced concrete structures requires optimization frameworks capable of navigating the discrete design catalogs that govern practical construction. When continuous-space metaheuristics are applied to such catalog-constrained problems, they encounter two systematic errors that have received limited diagnostic attention: mapping bias arising from the continuous-to-discrete transformation, and penalty traps induced by scalar constraint aggregation. This study analyzes the mathematical origins of both errors and evaluates targeted corrections within a multi-objective particle swarm optimization framework, applied to an 11-variable ACI 318-19-compliant slab problem minimizing embodied carbon and long-term deflection, with concrete strength and reinforcement grade as decision variables. Mapping bias is addressed through a Linear Scaling operator. Chi-square tests confirm that boundary catalog entries, sampled with approximately 49% deficit under conventional rounding, are restored to within 1.4% of the expected frequency, and the operator reproduces the expected boundary frequency exactly under non-uniform particle distributions, where rounding suppresses boundary entries by up to 76%. Penalty traps are addressed through a Pareto dominance architecture; across five loading scenarios the weighted-sum thickness distribution differs significantly from the Pareto-based archive (Kolmogorov-Smirnov, p < 0.001), the weighted-sum attractor migrating from 147 to 305 mm as deflection demand increases. An ablation shows the two corrections to be complementary: the mapping operator governs access to the catalog boundaries, the constraint-handling architecture the width of the region explored. Comparison across five multi-objective algorithms indicates that the choice of optimizer is secondary. With both corrections applied, Hypervolume varies by 0.4% to 1.9% across the five algorithms and Pareto cardinality by at most three solutions, margins an order of magnitude below the effects of the two errors. In catalog-constrained design, the encoding matters more than the search mechanism.