A decision-support framework for fair building retrofit allocation under multi-hazard risk

Hazard mitigation planning often misses distributional effects, producing unequal outcomes for vulnerable groups. We present a building-level, multi-objective optimization framework that treats equity as a first-class objective alongside efficiency. Equity is measured with the decomposable Theil index, which summarizes how unevenly mitigation resources are distributed across demographic and housing categories. Efficiency objectives are expected economic loss, average building repair time (days), and the number of displaced people under coupled earthquake–tsunami hazards. Using high-resolution community-scale impact modeling for Seaside, Oregon, we compute exact pairwise Pareto frontiers via an ɛ ɛ -constraint mixed-integer linear program with a piecewise-linear approximation of the Theil term, and approximate the full four-objective trade-off surface with a state-of-the-art many-objective evolutionary algorithm. Across multiple budgets and 500- and 1000-year events, results reveal non-linear equity–efficiency trade-offs: higher budgets shift frontiers toward the ideal region and expand the set of portfolios that jointly improve equity and efficiency, yet conflicts remain—most notably between economic loss reduction and equity. The framework yields transparent, reproducible frontiers and spatially explicit portfolios that can be used as inputs to stakeholder deliberation, rather than as prescriptive “single best” solutions. By making the distributional consequences of different investment strategies explicit and quantifiable, the approach provides a quantitative foundation for a more informed, transparent, and equitable planning process, thereby advancing procedural as well as distributive justice.