optimization-methodslisted

# Optimization Methods for AEC Computational Design ## 1. Optimization in AEC Design ### The Role of Optimization Optimization is the systematic process of finding the best solution from a set of feasible alternatives according to one or more criteria. In the Architecture, Engineering, and Construction (AEC) industry, optimization transforms design from an intuition-driven craft into a rigorous, evidence-based discipline that can explore thousands of alternatives in the time a human designer evaluates a handful. Every AEC project embeds optimization problems whether practitioners recognize them or not. Selecting a column grid that minimizes steel tonnage, arranging rooms to maximize adjacency satisfaction, routing ductwork to minimize pressure loss, or shaping a facade to balance daylight and solar heat gain -- all are optimization problems with design variables, objectives, and constraints. ### Design Optimization vs. Mathematical Optimization Mathematical optimization seeks a global or local extremum of a function subject to constraints, governed by theorems about convexity, differentiability, and feasibility. Design optimization in AEC adds layers of complexity: - **Multiple stakeholders** with conflicting objectives (cost vs. aesthetics vs. performance) - **Mixed variable types**: continuous (member thickness), discrete (bolt count), categorical (material grade), topological (connectivity) - **Expensive evaluations**: a single FEA run may take minutes; a CFD simula