Is building retrofit off-frontier, or just equity-undervalued?
Inv 12 and Inv 23 both optimize a scalar objective. The headline — "wildfire beats transport beats building" — rests on a single dimension of value (deaths avoided). The CEC GFO-25-304 explicitly asks for DAC equity analysis, and Inv 19 showed indoor AQ retrofits take B2 from 47 to 341 deaths avoided (~7× outdoor-only benefit). Three-objective tradeoff: health, equity, cost.
NSGA-II (Deb et al. 2002) solves this by computing the full Pareto frontier — the set of non-dominated portfolios where no single objective can improve without sacrificing another. Each frontier point is a policy option.
From single-scalar to full frontier
100 non-dominated portfolios
Three-objective NSGA-II run: 100 population x 80 generations with SBX crossover (η=15) and polynomial mutation (η=20, p=0.2). Design space spans wildfire reduction 0-10%, transport/building spend 0-$4B each, indoor AQ 0-$2B, DTE on/off. Objectives are evaluated through a deterministic linear surrogate (rfaq/optimization/pareto_frontier.py) calibrated to Inv 23 mean deaths/cost for portfolios A, B, C (exact) and E (within ~45 deaths). The surrogate does not re-draw Inv 21's CRF posterior or apply Inv 23's VSL scalarization.
Each dot is a Pareto-optimal portfolio. Color = DAC health share (violet ~0.20, gold ~0.24). X-axis = cost ($B), Y-axis = deaths avoided / yr.
Three extremes on the frontier
Max-health corner: 3853 deaths/yr at $12.97B. Loads on wildfire reduction and transport: x = [0.1, 3.89, 3.79, 2.0, 0.01].
Max-equity corner: DAC share 0.231 at $5.27B. Weighted toward indoor AQ and building retrofit.
Min-cost corner: Free-lunch baseline. T1+B1+DTE only; 1013 deaths/yr at $0B.
Which seed portfolios does the frontier dominate?
Six candidate seeds: 4 Inv 23 portfolios (A, B, C, E) plus 2 new design points constructed for this study (indoor_focus, balanced_2B). The NSGA-II Pareto set dominates 4 and leaves 2 on or near the frontier. Inv 23's F_maximum ($13.9B) and G_sequential (BO-optimal) are excluded because they use levers outside this 5-dim basis.
| Portfolio | Deaths | DAC share | Cost | Status |
|---|---|---|---|---|
| A_free_lunch | 1015 | 0.210 | $0.00B | On frontier |
| B_transport_2B | 1383 | 0.208 | $2.00B | Dominated |
| C_wildfire | 1739 | 0.219 | $1.65B | On frontier |
| E_smart | 1789 | 0.220 | $2.15B | Dominated |
| indoor_focus | 1315 | 0.233 | $2.00B | Dominated |
| balanced_2B | 1666 | 0.221 | $2.49B | Dominated |
Headline: E_smart (wildfire 5% + building $0.5B + DTE) is dominated. The best Pareto improvement delivers +133 deaths/yr with essentially the same cost, by rebalancing toward indoor AQ. Building retrofits are not off-frontier — they belong in a balanced indoor + wildfire portfolio that Inv 23's discrete seeds never enumerate.
Scope of "dominated": deterministic 3-objective frontier — deaths, DAC-deaths, cost. No VSL, no Monte Carlo, no robustness lens.
Inv 23 ranks the same seeds on a scalar net-benefit (deaths × VSL − cost) over MC draws of the Inv 21 CRF posterior, with CVaR and info-gap layers on top. Re-scoring these Pareto points through that pipeline is the natural next step.
Portfolio recommendation
Rather than committing to Inv 23's E_smart, planners should consider a family of Pareto-optimal options with explicit (health, equity, cost) knobs. The max-equity corner reaches DAC share 0.231, essentially matching the 0.233 ceiling set by indoor_focus (the highest-DAC seed in this study's candidate set, itself dominated by the frontier). It does so without sacrificing 71% of the max-health target.
Method: NSGA-II (Deb et al. 2002), SBX + polynomial mutation, 80 generations, 3-objective non-dominated sorting with crowding distance. Objective surrogate: deterministic linear model in rfaq/optimization/pareto_frontier.py — NOT Inv 23's MC net-benefit pipeline.