Abstract
Shell-and-tube heat exchangers are critical assets in the process industries, yet their design optimization typically relies on deterministic formulations that ignore operational variability. This study presents a systematic comparison of four optimization approaches, spanning three paradigms for decision-making under uncertainty, applied to shell-and-tube heat exchanger design. The objective minimizes total annualized cost (comprising capital and pumping costs) subject to thermal duty, pressure drop, velocity, and geometric constraints. Six uncertain parameters are modeled across three categories: mass flowrates (coefficient of variation = 10%), inlet temperatures (coefficient of variation = 2%), and fouling resistances (uniform distribution). Shell-side heat transfer is computed via the Bell-Delaware method, while tube-side correlations follow Sieder-Tate. The four approaches benchmarked are: (1) deterministic optimization as a baseline, (2) sample-average approximation, a classical stochastic programming method, (3) box-constrained robust optimization, which guards against worst-case realizations without probabilistic assumptions, and (4) Wasserstein distributionally robust optimization, which hedges against distributional ambiguity. Results reveal a clear cost-robustness hierarchy: deterministic designs yield the lowest expected cost but lack formal guarantees, sample-average approximation balances cost and reliability with modest computational overhead, the distributionally robust approach achieves the tightest cost dispersion at a moderate premium, and robust optimization delivers the highest feasibility guarantees at the greatest cost. These findings provide practitioners with quantitative guidance for selecting an appropriate optimization paradigm based on reliability requirements, data availability, and computational budget.