Simulation-based multi-objective building design optimization must find Pareto-optimal trade-offs (e.g., heating energy demand versus thermal discomfort) among combinatorially many design options, each requiring a costly annual building-performance simulation. Talami, Wright and Howard (2025) showed that a field-grouped two-stage sequential search — optimizing building geometry and fabric first, then HVAC system and controls, with exhaustive (full-factorial) search inside each stage and iterative re-runs seeded from previously found Pareto solutions — reproduced 100% of the full-factorial Pareto set for an open-plan office in Nottingham (UK) across four problem scales and four weather/internal-load variants, while using 91.2% fewer simulation evaluations, and outperformed NSGA-II under the same budget. That evidence covers one building archetype, one discrete option catalog, one climate, and two objectives. The open problem is to establish the conditions under which this sequential decomposition preserves full-factorial Pareto fidelity at comparable computational savings — across other building typologies, differently-cardinalized discrete option sets, climate regions, and additional objectives (cooling, life-cycle cost, carbon emissions); and how the configuration compares with NSGA-II, its equal-budget comparator in the source study, under equivalent evaluation budgets across diverse problem instances.

Background

Performance-based building design requires evaluating many candidate combinations of design variables — building geometry (e.g., orientation, window-to-wall ratios, depth of daylit zone), fabric (e.g., wall and roof insulation, glazing type), HVAC (heating, ventilation and air-conditioning) system sizing, and controls (e.g., setpoints, control strategies) — against objectives such as annual energy demand and thermal discomfort hours, using whole-building thermal simulation. Because each candidate requires a full annual simulation, evaluating the entire design space is expensive, and the number of combinations grows multiplicatively with the number of variables. A full factorial search enumerates every combination and is the only approach guaranteed to find the complete set of Pareto-optimal solutions (the non-dominated designs for which no other design is better in one objective without being worse in another; this set forms the Pareto front), but its cost is prohibitive at scale. Population-based metaheuristics such as NSGA-II (Non-Dominated Sorting Genetic Algorithm, a widely used evolutionary multi-objective algorithm) sample the space more cheaply but give no guarantee of finding all global optima. Decomposition approaches attack the cost problem by splitting the variable set into subproblems solved in stages, passing solutions forward. Prior multi-stage studies include Verbeeck and Hens (2007), who optimized dwelling envelope variables first and then combined the optimal envelopes with heating-system measures; Hamdy, Hasan and Siren (2013), whose three-stage approach (envelope and heat recovery, then HVAC, then renewables) reduced computational cost for cost-optimal nearly-zero-energy design in Finland; Ascione et al. (2019), whose Harlequin framework optimized building geometry, envelope, and operation in sequential phases for a Milan case; and Evins (2015), who layered optimization of building and energy-system design above operational variables for a London case. These studies reported good solutions but did not benchmark their staged searches against a complete full-factorial enumeration, so the fidelity of the decomposition itself was unmeasured. Related decomposition lines include hierarchical and parallel decomposition (Li et al. 2021, 2022) and cyclic overlapping block coordinate search (Brunetti 2016). Gagnon, Gosselin and Armand Decker (2019) compared a sequential (architecture-then-heating-system) protocol against simultaneous holistic optimization on a residential building with carbon-footprint, life-cycle-cost, and thermal-comfort objectives, both driven by NSGA-II, and found the sequential protocol found fewer optimal solutions at higher computational cost, attributing the loss to irreversible early variable selections. Against this backdrop, Talami, Wright and Howard (2021, 2025) developed a sequential approach in which the design variables are grouped into stages by professional field, each stage is solved by exhaustive search over its own variables, and iterative runs re-start the process from each Pareto solution found so far. Their 2025 study benchmarked 24 configurations of this sequential search against a full factorial search on a multi-scale open-plan office case study (874 to 4,147,200 design options, Nottingham UK weather, discrete option sets from the paper's Appendix A, objectives of heating energy demand and thermal discomfort): the two-stage field-grouped configuration (geometry+fabric, then HVAC+controls) recovered the complete full-factorial Pareto set at every scale and in all four weather/internal-load variants of the largest problem, using 100,700 function evaluations (a 91.2% reduction), whereas NSGA-II with the same budget found 73.5% of the global optima. The evaluation, however, was confined to that single case: one office archetype, one discrete option catalog, one climate, two objectives, and exhaustive search within every stage. The paper's conclusion asserts the approach is adaptable to other building types, climates, and objectives, but offers no evidence beyond the tested scope, and the published literature to date contains no such evidence either.

Problem Statement

The open problem is to determine, with full-factorial ground truth where feasible, whether the field-grouped two-stage sequential multi-objective optimization approach for building performance design — stage 1 optimizing building geometry and fabric variables, stage 2 optimizing HVAC-system and control variables, each stage solved by exhaustive search over its own variables with optimal solutions passed forward and iterative re-runs seeded from previously identified Pareto optima — preserves its demonstrated properties outside the single tested case, and to characterize when it does. Concretely, two linked questions serve this single objective: (1) Does the configuration reproduce the complete full-factorial Pareto-optimal solution set, at a computational saving of the same order as the reported 91.2% reduction in simulation evaluations, along each of four required dimensions — other building typologies (e.g., residential, educational, or healthcare buildings); design-option sets with different cardinalities; climate regions other than Nottingham (UK); and objective definitions beyond heating energy demand and thermal discomfort (e.g., cooling energy, life-cycle cost, or carbon emissions) — where a resolution must demonstrate the property along each dimension but need not cover every combination of them? (2) Under equivalent practical evaluation budgets across diverse problem instances, how does NSGA-II — the equal-budget comparator benchmarked in the source study — compare with the sequential approach, given the reported finding that NSGA-II found only 73.5% of the global optima at the same budget on the tested case? The question, over the set of instances studied, is which conditions (typology, option-set structure, climate, objective structure, stage-grouping, budget regime) determine whether the sequential decomposition does or does not preserve full-factorial Pareto fidelity, so that the reported solution sets can be attributed to the method rather than to the particular instance tested; question (1) is bounded to a documented characterization over the declared instance set — rather than coverage of every possible instance — and question (2) is the comparison between the sequential approach and NSGA-II at equivalent evaluation budgets over the same declared instance set.

References

  1. Talami, R., Wright, J., Howard, B. (2025). Evaluating the effectiveness, reliability and efficiency of a multi-objective sequential optimization approach for building performance design. Energy and Buildings 329:115242. DOI 10.1016/j.enbuild.2024.115242. https://doi.org/10.1016/j.enbuild.2024.115242
  2. Talami, R., Wright, J., Howard, B. (2024, preprint). Evaluating the effectiveness, reliability and efficiency of a multi-objective sequential optimization approach for building performance design. arXiv:2501.14742. https://arxiv.org/abs/2501.14742
  3. Bonyadi, N., Talami, R., Lee, B. (2026). Breaking-down building design problems with decomposition approaches: A review. Energy and Built Environment 7:903–924. DOI 10.1016/j.enbenv.2025.05.005. https://doi.org/10.1016/j.enbenv.2025.05.005
  4. Gagnon, R., Gosselin, L., Armand Decker, S. (2019). Performance of a sequential versus holistic building design approach using multi-objective optimization. Journal of Building Engineering 26:100883. DOI 10.1016/j.jobe.2019.100883. https://doi.org/10.1016/j.jobe.2019.100883
  5. Talami, R., Wright, J., Howard, B. (2021). Multi-criteria robustness assessment of a sequential whole-building design optimization. Proceedings of Building Simulation 2021: 17th Conference of IBPSA. DOI 10.26868/25222708.2021.30818. https://doi.org/10.26868/25222708.2021.30818
  6. Li, Y., Bonyadi, N., Papakyriakou, A., Lee, B. (2021). A hierarchical decomposition approach for multi-level building design optimization. Journal of Building Engineering 44:103272. DOI 10.1016/j.jobe.2021.103272. https://doi.org/10.1016/j.jobe.2021.103272
  7. Li, Y., Bonyadi, N., Lee, B. (2022). A parallel decomposition approach for building design optimization. Journal of Building Engineering 54:104574. DOI 10.1016/j.jobe.2022.104574. https://doi.org/10.1016/j.jobe.2022.104574
  8. Brunetti, G. (2016). Cyclic overlapping block coordinate search for optimizing building design. Automation in Construction 71:242–261. DOI 10.1016/j.autcon.2016.08.014. https://doi.org/10.1016/j.autcon.2016.08.014
  9. Verbeeck, G., Hens, H. (2007). Life cycle optimization of extremely low energy dwellings. Journal of Building Physics 31:143–177. DOI 10.1177/1744259107079880. https://doi.org/10.1177/1744259107079880
  10. Hamdy, M., Hasan, A., Siren, K. (2013). A multi-stage optimization method for cost-optimal and nearly-zero-energy building solutions in line with the EPBD-recast 2010. Energy and Buildings 56:189–203. DOI 10.1016/j.enbuild.2012.08.023. https://doi.org/10.1016/j.enbuild.2012.08.023
  11. Ascione, F., Bianco, N., Mauro, G., Vanoli, G. P. (2019). A new comprehensive framework for the multi-objective optimization of building energy design: Harlequin. Applied Energy 241:331–361. DOI 10.1016/j.apenergy.2019.03.028. https://doi.org/10.1016/j.apenergy.2019.03.028
  12. Evins, R. (2015). Multi-level optimization of building design, energy system sizing and operation. Energy 90:1775–1789. DOI 10.1016/j.energy.2015.07.007. https://doi.org/10.1016/j.energy.2015.07.007
  13. Aburabi’e, M., Bataineh, K., Al-Kabaha, Y. (2025). Multi objective design optimization of residential buildings: energy consumption, life cycle cost and thermal discomfort based on NSGA-II. Innovative Infrastructure Solutions 10:354. DOI 10.1007/s41062-025-02158-9. https://doi.org/10.1007/s41062-025-02158-9
  14. Nazari, F., Yan, W. (2025). A case study on evaluating genetic algorithms for early building design optimization: comparison with random and grid searches. arXiv:2504.08106. https://arxiv.org/abs/2504.08106