## 4 Results and Discussion
### Multi-Objective Optimization Results  
The bi-objective optimization problem was solved using the NSGA-II evolutionary algorithm, with a population size of 200 and 250 generations. The resulting Pareto front consists of 174 non-dominated solutions, each representing a unique trade-off configuration between total cost and CO\({}_{2}\) emissions associated with steel slag utilization in road base layers. Figure 10 illustrates the distribution of the Pareto-optimal set in the objective space, revealing a smooth and well-formed frontier indicative of good diversity and convergence. The observed trade-off structure follows the expected inverse pattern: reductions in unit cost are generally accompanied by increases in CO\({}_{2}\) emissions, and vice versa. The Pareto front spans a solution domain where cost ranges from 18.5 to 41.2 USD/m\({}^{3}\), and CO\({}_{2}\) emissions vary between 45.6 and 138.2 kg/m\({}^{3}\). This broad distribution provides a high-resolution design space for policy-sensitive infrastructure planning. Several inflection points--or \"knee points\"--were identified along the front, offering efficient trade-off solutions. For instance, Point A (cost-optimal) minimizes total cost (18.5 USD/m\({}^{3}\)) but corresponds to one of the highest emission values (137.8 kg/m\({}^{3}\)), Point C (emission-optimal) yields the lowest emissions (45.6 kg/m\({}^{3}\)) at a substantially higher cost (40.9 USD/m\({}^{3}\)), and Point B (balanced solution) represents a pragmatic middle ground, balancing moderate cost (25.3 USD/m\({}^{3}\)) and emissions (87.2 kg/m\({}^{3}\)), which may be particularly valuable in policy frameworks with carbon pricing or life-cycle-based procurement. All three highlighted points (A, B, and C) were extracted directly from the NSGA-II solution pool under the same feasibility constraints discussed in Section 3.4. From an engineering optimization perspective, these solutions map directly to operational decisions. Cost-optimal configurations generally exploit long-distance transportation from low-cost slag suppliers, minimal pre-processing, and low electricity price regions--often at the expense of higher grid CO\({}_{2}\) intensity and unaddressed moisture content. In contrast, low-emission scenarios are associated with shorter transport distances (<40 km), low initial moisture content (<5%), and grid locations with renewable-heavy electricity generation. These trends are consistent with the findings of [PERSON] et al. [78], who emphasized the critical role of energy quality--not just quantity--in determining life-cycle environmental outcomes of materials. Comparative results in similar multi-objective studies support the observed solution structure. For instance, [PERSON] et al. [79] employed NSGA-II for sustainable concrete mix optimization and reported similar nonlinear trade-off boundaries. Pareto extremes--a phenomenon observable in Figure 7, where incremental gains in emissions reduction beyond 55 kg/m\({}^{3}\) require disproportionately higher cost increases. Figure 10: Pareto front: cost and CO\({}_{2}\) Emission trade-off. [PERSON] et al. [80] also demonstrated that for pavement design, the integration of energy source carbon intensity into optimization models significantly reshapes the feasible envelope of performance. Importantly, this analysis demonstrates that no single configuration can simultaneously minimize both objectives. Hence, decision makers must select solutions that align with regional regulatory frameworks, carbon tax structures, and material supply chain constraints. For instance, in jurisdictions with explicit carbon pricing, the shadow price of carbon may shift the optimal point toward the emission-efficient end of the frontier. Conversely, in regions where budget constraints dominate and environmental regulations are less stringent, cost-optimal or balanced solutions may be more feasible. The value of the Pareto front is further enhanced by its actionability.