Physically Constrained Agentic AI for Energy Scheduling

Abstract: Agentic AI extends energy management beyond fixed-form interaction by translating natural-language requests into coordinated scheduling actions. We present a hierarchical ReAct Energy Management System (EMS) in which one orchestrator coordinates specialist agent types for shiftable appliances, EV charging, and thermal control. Physical authorization is separated from language generation: a deterministic critic reconstructs each integrated day-ahead candidate and checks its schema, appliance cycles, device power, thermal comfort, and, when active, the whole power feeder limit. Across Qwen 3.5 checkpoints, single-appliance mixed-integer schedules were feasible in 83.3 percent of runs. Localized feedback produced no accepted coupled schedule, whereas a multi-step policy authorized 6/6 current coupled runs: 3/3 for 27B and 3/3 for 35B-A3B. The standard occupied-window policy permits pre-conditioning, enforces comfort from 09:00-18:00. Every accepted schedule passed an independent final replay. Feasible costs were 2522.499 JPY for 27B and 1592.697 JPY for 35B-A3B, which are slightly higher than the mathematical optimization optimum of 1343.380 JPY. These results establish a fail-closed workflow for agentic MIP and MILP energy scheduling under the declared physical model.

• The paper introduces a fail-closed architecture in which LLM agents propose household energy schedules, while a deterministic critic alone authorizes candidates after checking schema, thermal, device, and feeder constraints.
• Multi-step coupled feedback accepted all 6 of 6 current Qwen whole-home schedules, whereas localized feedback accepted 0 of 54 initial candidates; however, the best LLM schedule cost 18.56% more than the Gurobi optimum.
• The results show that LLM feasibility depends on coupled physical validation and feedback, with heat-pump trajectories especially difficult for unaided agents and broader deployment requiring uncertainty margins, real-time feedback, and field testing.

Motivation and problem statement

Day-ahead residential energy scheduling requires reconciling a household's natural-language intent with tariffs, weather, calendar constraints, and device physics. LLM interfaces can recover typed scheduling parameters from dialogue, and agentic architectures can delegate heterogeneous decisions to device specialists. The authors identify the central obstacle as authorization: individually plausible specialist outputs can conflict after integration, because appliances share a feeder and heat-pump commands jointly determine a common thermal state. A plausible-looking schedule is therefore not evidence that coupled electrical and thermal constraints hold.

The paper's design response is a strict separation between schedule generation and physical authorization. Agents may propose and revise actions under a ReAct loop, but only a deterministic critic may release the exact serialized final candidate. This fail-closed boundary is the paper's core architectural claim: no tool call, plausible explanation, or optimizer status constitutes authorization by itself.

Architecture: hierarchical ReAct coordination with a deterministic critic

The system comprises one orchestrator plus three specialist agent types—shiftable appliances (instantiated as separate washing-machine and dishwasher prompts), EV charging, and heat-pump control. Binary agents return a single integer start for an uninterrupted cycle; the thermal agent returns a variable-power day-ahead trajectory over $N=96$ fifteen-minute slots. The orchestrator freezes one tariff and weather context before any proposal and integrates specialist outputs into a single candidate containing three appliance starts and 96 heat-pump powers.

The declared physical model couples whole-home power $P_t^{\mathrm{tot}} = p_t + \sum_a P_a y_{a,t}$ with first-order thermal dynamics $$T_{t+1} = a_m(1000\,p_t) + b_m T_t + c_m T_t^{\mathrm{out}} + d_m$$, device bounds ($0 \le p_t \le 12$ kW), an occupied comfort band of 22–24 °C from 09:00–18:00, and a 12-kW feeder limit active in the integrated MILP class. JEPX 30-min prices are expanded to slot resolution; coefficients are linear surrogates for heating and cooling modes.

The critic validates in a fixed order: schema check, binary-cycle reconstruction from integer starts (rather than trusting model-supplied on/off arrays), heat-pump command rounding and bounds, unclipped thermal state propagation, and aggregate feeder checks when declared. Accepted candidates are replayed once more without modification before authorization; missing, malformed, failed, or budget-exhausted candidates are rejected. Two feedback policies are distinguished:

• Localized feedback: reports only the first violated transition. Under this policy, none of the 54 initial whole-home candidates was accepted.
• Multi-step coupled policy: supplies all 40 controls spanning the comfort window, caps power by residual feeder headroom, identifies conflicting appliances, and requests one complete resubmission. It also enforces zero post-window heat-pump power as part of the standard occupied-window policy.

The per-transition feedback is sign-safe: ordering interval endpoints before intersection yields a valid feasible power interval $[\underline p_t, \overline p_t]$ in both heating and cooling modes, and an empty interval signals that the predecessor state cannot be repaired at that step, forcing earlier controls to change or the candidate to be rejected.

A shared acceptance invariant applies uniformly to actor schedules, deterministic-repair schedules, and solver outputs alike, so all reported gaps compare feasible schedules rather than penalized invalid ones.

Experimental design

Three tasks isolate increasing numerical coupling: a single-appliance MIP (one valid start among washing machine, dishwasher, or EV cycles), a heat-pump LP over six reachable and two deliberately unreachable frozen weather-price cases, and a whole-home MILP jointly scheduling three binary cycles plus the heat pump under the feeder limit. Pyomo 6.9.3 with Gurobi 11.0 provides matched references, and solver outputs pass through the same independent critic—which also catches unit, ordering, and serialization errors outside the optimizer.

Six local Qwen 3.5 checkpoints (0.8B–35B-A3B) run with temperature-zero decoding and three repetitions. The initial benchmark contains 252 LLM runs; the matched current-policy coupled comparison covers only 27B and 35B-A3B (three runs each) against ten Pyomo/Gurobi solves on an August 1, 2026 Osaka/Kansai request using JEPX spot prices and Open-Meteo weather. Smaller checkpoints were not rerun under the final coupled policy and are excluded—a scope restriction stated plainly by the authors. Artifacts retain every proposal, validation result, token count, and latency; regression tests cover price expansion, cost arithmetic, thermal bounds, unreachable-state rejection, and all three formulations.

Results

Single-appliance MIP. Across 54 Qwen runs, feasibility reached 83.3% and exact optimality 33.3%. The 0.8B checkpoint achieved only 66.7% feasibility with 0% optimality, while 2B and 4B reached full feasibility—the smallest models timed out on the coupled task entirely.

Heat-pump LP. Continuous coupling proved hardest: no raw or critic-revised actor trajectory passed the thermal replay across all 108 reachable runs. The explicitly labeled deterministic-repair variant recovered every reachable case and correctly rejected both unreachable cases (initial temperatures of 10 °C and 35 °C from which the first transition cannot reach the band). The authors are careful not to count repair-path successes as unaided LLM scheduling.

Coupled MILP. Localized feedback produced zero accepted schedules out of 54 initial candidates. The multi-step policy changed the outcome without relaxing validation: all 6/6 current Qwen schedules were accepted (3/3 for both 27B and 35B-A3B), each satisfying the uninterrupted cycles, heat-pump bounds, 12-kW feeder limit, occupied-window comfort, and post-window shutdown. Repetitions within each model were identical. The initial 27B proposal violated the thermal upper bound and passed in round two after complete revision; 35B-A3B passed in round three.

Method	MIP feasible	MIP optimal	Coupled accepted	Cost (JPY)
Qwen 3.5 0.8B	66.7%	0.0%	—	n/a
Qwen 3.5 2B	100.0%	0.0%	—	n/a
Qwen 3.5 4B	100.0%	66.7%	—	n/a
Qwen 3.5 9B	66.7%	0.0%	—	n/a
Qwen 3.5 27B	66.7%	66.7%	3/3	2522.499
Qwen 3.5 35B-A3B	100.0%	66.7%	3/3	1592.697
Pyomo/Gurobi	100.0%	100.0%	3/3	1343.380

Cost gaps are substantial: 35B-A3B landed 18.56% above the optimum (1592.697 vs. 1343.380 JPY; 104.439 vs. 92.052 kWh), while 27B was 87.77% above (2522.499 JPY; 138.515 kWh)—58.38% more expensive than 35B-A3B despite a lower peak, driven by a late 18:00 EV start and an expensive heat-pump trajectory. Both Qwen schedules used zero post-18:00 heat-pump energy. Latency is reported but explicitly not normalized: Gurobi built and solved in a median 0.0487 s versus 84.84 s (27B) and 33.92 s (35B-A3B) for the actor–critic pipeline on different hardware paths.

The failure taxonomy is informative: recorded failures spanned omitted critic calls, malformed arrays, timeouts, pointwise-feasible-but-later-infeasible trajectories, incomplete revisions after feedback, retained feeder conflicts, and budget exhaustion. Only some are thermal-reasoning failures; schema adherence and tool-call syntax are distinct from physical feasibility, so tool use and checkpoint scale cannot serve as authorization proxies. Notably, the smaller-checkpoint coupled entries ended in timeout or power conflict rather than silent constraint violation—consistent with the fail-closed design.

Limitations and open questions

The authors concede several boundaries directly. Post-hoc perturbations of the thermal coefficient $a_m$ by ±10% or the initial temperature by ±2 °C reduced feasibility, showing that acceptance is conditional on the encoded coefficients and state; calibrated uncertainty sets, tightened margins, or receding-horizon measurement feedback are required before broader operational claims. The authorization claim is deliberately narrower than deployment safety: the model omits humidity, heat-pump cycling and ramping, battery state of charge, appliance interruption, forecast uncertainty, protective relays, communication loss, and occupant overrides. Thermal coefficients are prototype surrogates, and the weather-price cases are controlled evaluations rather than a representative sample of Japanese homes. Field testing and a multi-agent-versus-monolithic ablation remain outside the current evidence, and the small coupled sample ($n=3$ per checkpoint, single request date) limits statistical generalization.

Conclusion

The paper establishes a fail-closed workflow for agentic MIP/MILP energy scheduling in which semantic agents interpret intent and propose revisions while only a deterministic evaluation of the exact action object may release a schedule. Its decisive empirical result is that coupled multi-step critic feedback enabled all 6/6 current 27B and 35B-A3B whole-home schedules while every invalid candidate remained blocked, at cost premiums of 18.56% and 87.77% over the matched Gurobi optimum. Acceptance remains conditional on the encoded schema, thermal surrogate, device limits, and feeder constraint; extending the invariant to uncertain dynamics and closed-loop field conditions is the principal question the work leaves open.