Techno-Socio-Economic Heat Supply Options

• The paper presents advanced optimization methods, using MILP and metaheuristics, to derive Pareto-optimal heat supply options that balance technical, economic, environmental, and social metrics.
• It integrates detailed mathematical modeling and modern algorithms such as NSGA-II and Benders Decomposition to optimize network design, technology assignment, and energy flows.
• Case studies reveal that implementing these optimal configurations can significantly reduce CO₂ emissions, lower costs, and enhance energy equity in community-scale systems.

Techno-socio-economically Pareto-optimal heat supply options are solution sets for municipal or community-scale heating systems that are simultaneously optimal with respect to technical (reliability, performance), economic (investment and operational costs), environmental (CO₂-equivalent and pollutant emissions), and social (equity, poverty, stakeholder acceptability) objectives. Such options form a non-dominated front in multi-objective space: no option can be improved in one dimension without degrading another. Recent research employs detailed mathematical and computational models, advanced optimization techniques, and stakeholder- or data-driven workflows to systematically identify, rigorously evaluate, and contextualize these optimal configurations for district, decentralized multi-energy, and integrated community energy systems (Schilt et al., 10 Sep 2025, Yadav et al., 10 Apr 2025, Schönfeldt et al., 8 Dec 2025, Körber et al., 2022).

1. Foundations and Definitions

A solution is “techno-socio-economically Pareto-optimal” if, compared to all others, no improvement in technical, economic, or environmental-social metrics is possible without sacrificing at least one other metric. Formally, given a vector of objective functions $$\mathbf{F}(x, y) = [z_\mathrm{tech},\;\mathrm{TOTEX}_{\mathrm{ann}},\;\mathrm{CO}_2\mathrm{E}_\mathrm{ann},\;\mathrm{MKT}]$$—representing technical reliability gap ($z_\mathrm{tech}$), total annualized cost (TOTEX), annual CO₂-equivalents, and market/self-consumption rate (MKT)—a solution $(x^*,y^*)$ is Pareto-optimal if no other $(x,y)$ exists such that all objectives improve or stay the same and at least one strictly improves (Körber et al., 2022, Schönfeldt et al., 8 Dec 2025, Yadav et al., 10 Apr 2025).

In the context of heat supply, these metrics commonly include:

• Technical: unserved heat, supply–demand balancing, reliability, infrastructure adequacy.
• Economic: capital expenditure, O&M costs, total cost of supply, energy rates.
• Environmental: annual or lifetime CO₂-equivalent emissions, PM₂.₅, local pollutants.
• Social: energy poverty indices, burden (% income spent), equity, acceptability, self-consumption and sharing rates.

2. Mathematical Modeling and Objective Formulation

Multi-objective models structure the problem as a constrained mathematical program, typically a large-scale MILP or hybrid MILP-metaheuristic. The investment (design) and operational (dispatch) decisions are either separated (“here-and-now” vs “wait-and-see”) or coupled (Körber et al., 2022). Objectives are defined as follows:

$$\min_{x,y} \; \bigl[ z_\mathrm{tech}(x,y), \; \mathrm{TOTEX}_{\mathrm{ann}}(x,y), \; \mathrm{CO}_2\mathrm{E}_{\mathrm{ann}}(x,y), \; -\mathrm{self\text{-}consumption}(x,y) \bigr]$$

Where, for instance,

• $\mathrm{TOTEX}_{\mathrm{ann}}$ aggregates annuitized investments, pipe costs, and operational expenditures,
• $\mathrm{CO_2E}_{\mathrm{ann}}$ incorporates both operational emissions (e.g., $gwp_{j,t}^\mathrm{oper}\,y_{b,j,t}$) and embedded emissions from installation ($gwp_j^{\mathrm{CAPEX,fix}}$ and $gwp_j^{\mathrm{CAPEX,var}}$),
• $\mathrm{MKT}$ measures the fraction of energy generated that is directly self-consumed or shared.

Subject to constraints:

• Network topology and pipe sizing,
• Mutually exclusive heat supply technology selection per building unit (Schönfeldt et al., 8 Dec 2025),
• Load and flow balance at each node or building for each timestep,
• Equipment, insulation, PV, and battery sizing bounds,
• Demand coverage,
• Regulatory and market-regime constraints (energy-sharing group sizes, export tariffs).

Stakeholder preferences can enter as explicit weights or selection of acceptable trade-offs on the front (Körber et al., 2022).

3. Decomposition and Optimization Methodologies

High-dimensionality and combinatorial complexity drive the need for sophisticated hybrid solution approaches:

• Energy-aware aggregation: Reduces MILP size and variable count by clustering buildings simultaneously by energy demand, solar PV potential, and connection cost, then spatially grouping these archetypes to balance solution tractability and spatial network cost (Schönfeldt et al., 8 Dec 2025).
• Genetic Algorithms (GA): NSGA-II and its derivatives address the network topology and assignment superstructure, with chromosomes encoding pipe/route selection, group assignment, and technology allocations (Körber et al., 2022).
• Benders Decomposition (BD): Decouples investment and operational subproblems, using dual cuts from the operational MILP to drive investment master problem (Körber et al., 2022).
• Lagrange Relaxation (LR): Decouples peer-coupled or geographically linked constraints, creating independent per-building subproblems whose coupling is enforced via iteratively updated multipliers.
• Alternative metaheuristics: NSGA-II is also used as in (Schönfeldt et al., 8 Dec 2025), enabling direct sampling of the multi-objective non-dominated set without scalarization.

Specific models may additionally use $\epsilon$-constraint (as in (Schilt et al., 10 Sep 2025)), MCDA weighting frameworks (Yadav et al., 10 Apr 2025), and various hierarchical spatial clusterings (Schönfeldt et al., 8 Dec 2025).

4. Case Studies and Pareto-Optimal Portfolios

The output is typically a discrete or continuous Pareto front in the objective space; trade-offs are visualized to guide decision-making. The following table synthesizes representative Pareto-optimal solutions from literature:

Option	System Features	Cost	CO₂	Social/Tech Indices
Decentral HP	HP (COP 3.8), PV, TES; no network	↑	↓↓↓	↑ self-cons., 0% sharing
Hybrid	Gas-CHP, HP, PV, BESS; partial DHN	→	↓↓	22% sharing, lower reliability risk
Ultra-Low Cost	Gas boiler, small PV, minimal storage	↓↓↓	↑↑	Poor emissions, low social benefit
DHN+Storage	Seasonal TES, high DHN coverage, wood/WtE-CHP	↑↑	↓↓↓	Replaces individual fossil use
Coordinated HP	HP w/ control, battery, partial PV, staged backup	↓↓	↓↓	Improved equity/reliability

For example, in Bern, integrating 15 GWh of TES by shifting WtE summer surplus to winter peaks eliminated 8 GWh of CCGT heat and increased WtE utilization by 20%, with cost savings per avoided tonne CO₂ improved by 10–15% (Schilt et al., 10 Sep 2025). In Neu-Schwachhausen, Pareto-optimal points ranged from gas-boiler-dominated (low investment, high emissions) to balanced portfolios with high HP and DHN shares, where emissions dropped from 1.7 to 0.22 t CO₂/(pers·a) as investment rose (Schönfeldt et al., 8 Dec 2025). In the Alaska community, coordinated HP deployment plus community PV reduced annual CO₂e by 34.5% and energy poverty by 9 percentage points relative to baseline (Yadav et al., 10 Apr 2025).

5. Integration of Socio-Economic and Policy Dimensions

Pareto-optimal heat supply configuration identification integrates explicit social metrics:

• Energy poverty, equity, and burden (fraction of income spent on energy) are calculated for each configuration (Yadav et al., 10 Apr 2025).
• Market and policy constraints such as tariffs, export pricing, and maximum peer-group diameter shape the feasible set and the attainable front (Körber et al., 2022).
• Stakeholder weights and MCDA methods allow communities and utilities to select compromise solutions at “knees” of the Pareto curve, maximizing collective benefit or equity according to local priorities (Yadav et al., 10 Apr 2025, Schilt et al., 10 Sep 2025).

The expansion of DHN coverage, as illustrated in Bern (α rising from 0.18 to 0.50), displaces individual boilers, providing both environmental and social dividends through emissions abatement and reduced local pollution, directly benefiting residents (Schilt et al., 10 Sep 2025).

6. Workflow and Design Guidelines

An end-to-end algorithmic workflow emerges:

1. Data Aggregation: Collect geospatial, building, and energy use data; normalize and compress multi-temporal features for each building (Schönfeldt et al., 8 Dec 2025).
2. Clustering: Apply k-means or mixed-mode clustering for both energy indicators and spatial grouping, balancing complexity ($N_V \approx K \times G$) and network line length.
3. Technology/Network Assignment: Assign supply technology per archetype and group; enforce mutual exclusivity of HP, DHN, or boiler per cluster (Schönfeldt et al., 8 Dec 2025).
4. Multi-objective Optimization: Solve MILP or metaheuristic problem; apply NSGA-II, $\epsilon$-constraint, or hybrid GA–BD–LR decomposition (Schönfeldt et al., 8 Dec 2025, Körber et al., 2022, Schilt et al., 10 Sep 2025).
5. Pareto Front Extraction: Identify, archive, and visualize non-dominated solutions; select “anchor” points (cost-optimal, emissions-optimal, compromise) for further stakeholder evaluation (Schilt et al., 10 Sep 2025).
6. Sensitivity & Scenario Analysis: Vary key parameters (fuel prices, emissions factors, demand growth, policy constraints) to test front stability and resilience.

Generalizable recommendations include:

• Use energy-aware aggregation to enable model tractability without excess bias (Schönfeldt et al., 8 Dec 2025).
• Strategically expand DHNs to target high fossil use districts (Schilt et al., 10 Sep 2025).
• Systematically apply MCDA or social weights in portfolio selection (Yadav et al., 10 Apr 2025).
• Employ demand-side management (coordinated HP operation) to enhance both reliability and social outcomes, especially in off-grid or network-constrained settings (Yadav et al., 10 Apr 2025).

7. Limitations, Sensitivities, and Future Outlook

The construction of techno-socio-economically Pareto-optimal solution sets is sensitive to data uncertainties, especially in building inventories, demand forecasts, and fuel/technology prices (Schilt et al., 10 Sep 2025, Schönfeldt et al., 8 Dec 2025). Capital costs for infrastructure (e.g., TES) are not always included and can shift the “elbow” of the Pareto front; levelized or discounted cash flow analysis is required for a full picture. Socio-political shifts—tariff changes, subsidy programs, shifts in stakeholder priorities—alter the optimal region and require flexible frameworks (Körber et al., 2022).

A continuing trend is the development of modular, open-source workflows deployable for rapid urban or community-scale scenario analysis, with the explicit inclusion of social factors and dynamic regulatory adaptation. As empirical datasets improve and computational techniques scale, these methods are increasingly central to evidence-based urban energy transition policy (Schönfeldt et al., 8 Dec 2025, Yadav et al., 10 Apr 2025, Schilt et al., 10 Sep 2025, Körber et al., 2022).