Multiobjective Home Appliances Scheduling Considering Customer Thermal Discomfort: A Multistep Look-ahead ADP-Based Approach

Babak Jeddi; Gerard Ledwich; Yateendra Mishra

arxiv: 1907.03252 · v1 · pith:GASAADM3new · submitted 2019-07-07 · 🧮 math.OC · eess.SP

Multiobjective Home Appliances Scheduling Considering Customer Thermal Discomfort: A Multistep Look-ahead ADP-Based Approach

Babak Jeddi , Yateendra Mishra , Gerard Ledwich This is my paper

Pith reviewed 2026-05-25 01:41 UTC · model grok-4.3

classification 🧮 math.OC eess.SP

keywords home energy managementmultiobjective schedulingapproximate dynamic programmingthermal discomfortappliance schedulingdynamic programmingphotovoltaicsenergy storage

0 comments

The pith

A multistep look-ahead ADP approach solves multiobjective home energy management to trade off electricity payment against thermal discomfort.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces MO_HEMU, a multiobjective home energy management unit, to schedule appliances while balancing electricity costs and thermal discomfort under time-varying prices. Devices include solar PV, battery storage, deferrable appliances, and thermal appliances, with discomfort measured by deviations in indoor and hot water temperatures from ideal values. The problem is cast as a dynamic program and solved using a multistep look-ahead algorithm that approximates the solution by considering only a limited number of future stages. This enables customers to identify preferred trade-offs between payment and discomfort through simulation results.

Core claim

The MO_HEMU is formulated as a dynamic program and a method based on the approximated dynamic programming is used as the scheduling algorithm. The developed method, called multistep look ahead algorithm, is an iterative algorithm that overcomes the curse of dimensionality of the exact DP by choosing a decision based on a limited number of stages ahead. The effectiveness of the proposed model is investigated through numerical simulations. The proposed MO_HEMU enables customers to find the desired trade off between electricity payment and a discomfort level.

What carries the argument

Multistep look-ahead algorithm, an iterative approximation to dynamic programming that selects each decision by evaluating a limited future horizon instead of the full horizon.

If this is right

Customers obtain explicit trade-off curves between electricity payment and thermal discomfort.
The algorithm schedules solar PV, battery, deferrable and thermal appliances in response to time-varying prices.
Thermal discomfort is modeled as temperature deviation for both space heating and hot water.
The approach makes dynamic programming tractable for realistic household instances by limiting the look-ahead depth.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same approximation technique might apply to other multiobjective stochastic control problems in energy systems.
Varying the look-ahead horizon length could be used as a tunable parameter to adjust computation time versus solution quality.
Incorporating uncertainty in user behavior or weather forecasts would be a natural next extension of the model.

Load-bearing premise

The multistep look-ahead approximation produces decisions close enough to the true optimal dynamic program that the reported cost-discomfort trade-offs remain meaningful.

What would settle it

Solve the exact dynamic program for a reduced problem with short time horizon and few devices, then check if the multistep look-ahead method recovers similar cost and discomfort values.

Figures

Figures reproduced from arXiv: 1907.03252 by Babak Jeddi, Gerard Ledwich, Yateendra Mishra.

read the original abstract

This paper proposes a multiobjective home energy management unit (MO_HEMU) to balance the electricity payment and thermal discomfort of a household by properly scheduling devices in a time varying price environment. The thermal discomfort is measured by the deviation of indoor and hot water temperature from the users ideal temperature. The home devices include solar Photovoltaics, a battery storage system, deferrable, and thermal appliances. The proposed MOHEMU is formulated as a dynamic program and a method based on the approximated dynamic programming is used as the scheduling algorithm. The developed method, called multistep look ahead algorithm, is an iterative algorithm that overcomes the curse of dimensionality of the exact DP by choosing a decision based on a limited number of stages ahead. The effectiveness of the proposed model is investigated through numerical simulations. The proposed MO_HEMU enables customers to find the desired trade off between electricity payment and a discomfort level.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The multistep look-ahead ADP application lacks any error bound or optimality-gap check, so the claimed cost-discomfort trade-offs rest on an untested approximation.

read the letter

The key thing here is that the multistep look-ahead ADP is presented without any check on how well it approximates the true dynamic program. The claimed ability to find good payment-discomfort trade-offs therefore rests on an untested assumption. The paper sets up a multiobjective optimization for home energy management that includes solar PV, battery storage, deferrable appliances, and thermal loads like heating and hot water. Discomfort is quantified as deviation from ideal temperatures. It casts the scheduling as a stochastic dynamic program and replaces the exact solution with an iterative algorithm that looks a limited number of stages ahead to pick decisions. This is a standard way to handle the dimensionality problem in ADP applications to energy scheduling. The inclusion of both cost and explicit thermal discomfort makes the objective customer-focused, which fits the residential demand response context. The formulation looks solid on paper for the devices and price signals. The multistep aspect is described as iterative, which might help in practice. Where it falls short is the complete absence of any analysis on the quality of the approximation. There are no bounds on the error from the limited lookahead, no proof of convergence as the horizon or iterations increase, and no numerical comparison to an exact solution on a toy problem. The numerical simulations are referenced but without reported baselines or optimality gaps, so the effectiveness claim is hard to evaluate. The free parameters like lookahead length and discomfort weight are noted but not analyzed for sensitivity. This paper is for specialists in home energy management units and demand response algorithms. Someone working on similar ADP applications might find the device modeling useful. It does not rise to the level where I would recommend it for peer review, because the central technical claim lacks supporting evidence on the approximation accuracy. The thinking is clear in setting up the model, but the gap on validation is too big.

Referee Report

1 major / 1 minor

Summary. The paper proposes a multiobjective home energy management unit (MO_HEMU) to schedule home appliances including solar PV, battery storage, deferrable and thermal appliances under time-varying electricity prices. The goal is to balance electricity payment and thermal discomfort, where discomfort is quantified by deviations of indoor and hot water temperatures from user ideals. The problem is formulated as a finite-horizon stochastic dynamic program, solved approximately using a multistep look-ahead approximated dynamic programming (ADP) algorithm that is iterative and claimed to overcome the curse of dimensionality. Numerical simulations are presented to show the effectiveness, with the claim that the approach enables customers to achieve desired trade-offs between cost and discomfort.

Significance. If the multistep look-ahead ADP is validated to yield decisions close to the optimal dynamic programming solution, this work would offer a practical computational method for multi-objective scheduling in residential energy systems that accounts for customer thermal comfort preferences. Such methods could be relevant for implementing demand response in smart grids with renewable integration and storage. The explicit multiobjective formulation and use of ADP for thermal load scheduling represent a reasonable technical contribution, though the lack of approximation quality assessment reduces its current significance.

major comments (1)

[Abstract] The claim that the proposed MO_HEMU enables customers to find the desired trade-off between electricity payment and discomfort level rests on the multistep look-ahead ADP producing decisions sufficiently close to the true optimal dynamic program. However, the manuscript provides no bound on the value-function approximation error, no convergence argument as the lookahead depth or iteration count increases, and no numerical comparison against an exactly solvable small instance. This is a load-bearing issue for the central claim, as the reported cost-discomfort trade-offs may be unreliable if the approximation introduces systematic bias.

minor comments (1)

The abstract mentions 'numerical simulations' but does not specify the simulation setup, such as the time horizon, price signals, or thermal model parameters used.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment regarding the approximation quality of the multistep look-ahead ADP below.

read point-by-point responses

Referee: [Abstract] The claim that the proposed MO_HEMU enables customers to find the desired trade-off between electricity payment and discomfort level rests on the multistep look-ahead ADP producing decisions sufficiently close to the true optimal dynamic program. However, the manuscript provides no bound on the value-function approximation error, no convergence argument as the lookahead depth or iteration count increases, and no numerical comparison against an exactly solvable small instance. This is a load-bearing issue for the central claim, as the reported cost-discomfort trade-offs may be unreliable if the approximation introduces systematic bias.

Authors: We agree that the manuscript does not provide theoretical bounds on the value-function approximation error or convergence arguments as the lookahead depth or iteration count increases. The multistep look-ahead ADP is presented as a practical heuristic to address the curse of dimensionality for the finite-horizon stochastic dynamic program with continuous states arising from thermal dynamics. Its effectiveness is supported by numerical simulations demonstrating achievable cost-discomfort trade-offs under time-varying prices. We will revise the abstract to qualify the central claim as providing a practical computational approach validated through simulations, rather than implying proximity to the optimal DP solution. We will also add a small-scale numerical comparison on a simplified deterministic instance to illustrate approximation behavior where an exact solution is computable. Deriving general error bounds is outside the scope of this applied work. revision: partial

standing simulated objections not resolved

Providing a bound on the value-function approximation error or a convergence argument for the multistep look-ahead ADP as lookahead depth or iteration count increases.

Circularity Check

0 steps flagged

No circularity: algorithmic approximation stands on its own formulation

full rationale

The paper states the MO_HEMU problem as a finite-horizon stochastic dynamic program and replaces exact solution with an iterative multistep look-ahead ADP procedure that selects decisions by limited forward simulation. No parameter is fitted to a data subset and then relabeled a prediction; no self-citation supplies a uniqueness theorem or ansatz that defines the reported trade-off surface; the algorithm is described without reference to prior author work that would make the outcome tautological. The numerical simulations are presented as external validation rather than internal re-derivation, so the derivation chain does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields almost no explicit free parameters or axioms. The discomfort metric (temperature deviation) and the choice of look-ahead horizon are implicit modeling choices whose values are not stated.

free parameters (2)

look-ahead horizon length
The multistep look-ahead algorithm requires choosing how many stages ahead to consider; this number is not given and would be tuned in practice.
discomfort weighting factor
The multiobjective formulation must combine payment and discomfort into a single objective or Pareto front; the relative weight is a free parameter not reported.

pith-pipeline@v0.9.0 · 5690 in / 1200 out tokens · 21412 ms · 2026-05-25T01:41:08.611394+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The proposed MO-HEMU is formulated as a dynamic program and a method based on the approximated dynamic programming is used as the scheduling algorithm. The developed method, called multistep look-ahead algorithm...
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The MO formulation is based on the ε-constrained technique...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

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BSS: The state of charge (SOC) defines the state variable, i.e., ௧ ௧ , where ௠௔௫ሿ. The decision variable ௧ ௕ controls charging (௧ ௕൒0) and discharging (௧ ௕൏ 0 ) constrained by charging/discharging rates, i.e.,௧ ௕∈ ௠௔௫ሿ. Transition function of BSS state is. The battery power is obtained by: ௧ ௕ ݐ௟ ௗ ௕ ݐ௟ ௧ିଵ)ି (1) where { 0 , . } and (. )ି = min{0, . } . E...

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Dishwasher and laundry appliances belong to this class

Deferrable non-interruptible appliances: The starting time of these appliances can be delayed across the day, but once the appliance ܣis turned on, it has to work for Iୟ time slots uninterruptedly to finish its task. Dishwasher and laundry appliances belong to this class. The power consumption at each time might be different. Assuming ଵ ଶ ூೌ ௔} and ௔ሿ as ...

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The controller finds the best time slots within ௙ሿ for the operation of appliance ܨwith ௙ total job length

Deferrable interruptible appliances: These appliances, such as Plug-in electrical vehicles (PEVs), can be turned on and off multiple times. The controller finds the best time slots within ௙ሿ for the operation of appliance ܨwith ௙ total job length. At t ∉ ሾα୤,β ୤ሿ, s୲ ୤=u ୲ ୤ =0 . If the appliance is switched on during ௙+1 ) , the state moves to st+1 f =s ...

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The state variables are defined by the indoor and hot water temperature

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+ܬ௧)൯ൟ (10) ௧ାଵ=݂௧) ௧ ௧ ௧ ௠௔௫} ௧ ௧ ௧ ଵ ூಶೈಹ ௠௜௡ ௧ ௠௔௫ ௐ ൟ ௧ ௧ ௧ ଵ ூಲ಴ ௠௜௡ ௧ ௠௔௫ ௜௡ ൟ where ௧ ௧ ௧ ௧ ௧ ௕൯ is the total state space and u୲=൫ u୲ ୟ ,u ୲ ୤ ,u ୲ ୅େ,u ୲ ୉୛ୌ,u ୲ ୠ ൯ is the total decision space at time slot t. gt(st,L t) is the one-stage objective function (which can be either of CoEC or TDL) and J୲(s୲) is the optimal cost-to-go at state ௧ and tim...

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The determination of ࢚is often problem-dependent

instead of ௧). The determination of ࢚is often problem-dependent. One potential option is to select some important variables of the problem and do minimization over the feasible decisions related to these variables, while keeping the decisions of the remaining variables at some nominal values. This approach can be specifically useful in MLA in which the or...

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In the formulated HEMU, for example, the sets of charging/discharging decisions for the BSS, i.e., ௧ ௕, can be nominated to build such a ௧)

is used for the one-stage look-ahead approximations, while the reduced decision set ௧) is used for the multi-step look-ahead approximations. In the formulated HEMU, for example, the sets of charging/discharging decisions for the BSS, i.e., ௧ ௕, can be nominated to build such a ௧). C. Multiobjective Formulation The proposed MO-HEMU is stated as follows: mi...

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An advantage of this technique is that it allows the decision maker to have control over the Pareto front by correctly choosing the values of kଶ

solutions as the Pareto list are found. An advantage of this technique is that it allows the decision maker to have control over the Pareto front by correctly choosing the values of kଶ. The choice of a higher value for ଶ results in more solutions in the Pareto list with better density but at the expense of higher calculation time. In this paper kଶ=6 . IV....

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A single objective optimization problem for minimizing CoEC is solved for each case study with three MLAs including OLA, TLA, and three-step look-ahead algorithm (TSLA)

Single objective optimization: First, in order to evaluate the performance of the developed MLA in terms of the solution quality and computational time, different case studies with a different combination of devices and thus a different number of state and decision variables are defined as follows: • Case #1: only deferrable appliances are considered; • C...

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Multiobjective optimization: Finally, the MO-HEMU model is solved by the TSLA considering all devices (case #5) and the obtained Pareto list is displayed in Fig. 6. The choice of the best compromise solution from this list depends on the preferences of the customer; whether minimizing the electricity cost is her priority or minimizing thermal discomfort i...

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[1] [1]

The decision variable ௧ ௕ controls charging (௧ ௕൒0) and discharging (௧ ௕൏ 0 ) constrained by charging/discharging rates, i.e.,௧ ௕∈ ௠௔௫ሿ

BSS: The state of charge (SOC) defines the state variable, i.e., ௧ ௧ , where ௠௔௫ሿ. The decision variable ௧ ௕ controls charging (௧ ௕൒0) and discharging (௧ ௕൏ 0 ) constrained by charging/discharging rates, i.e.,௧ ௕∈ ௠௔௫ሿ. Transition function of BSS state is. The battery power is obtained by: ௧ ௕ ݐ௟ ௗ ௕ ݐ௟ ௧ିଵ)ି (1) where { 0 , . } and (. )ି = min{0, . } . E...

work page

[2] [2]

Dishwasher and laundry appliances belong to this class

Deferrable non-interruptible appliances: The starting time of these appliances can be delayed across the day, but once the appliance ܣis turned on, it has to work for Iୟ time slots uninterruptedly to finish its task. Dishwasher and laundry appliances belong to this class. The power consumption at each time might be different. Assuming ଵ ଶ ூೌ ௔} and ௔ሿ as ...

work page

[3] [3]

The controller finds the best time slots within ௙ሿ for the operation of appliance ܨwith ௙ total job length

Deferrable interruptible appliances: These appliances, such as Plug-in electrical vehicles (PEVs), can be turned on and off multiple times. The controller finds the best time slots within ௙ሿ for the operation of appliance ܨwith ௙ total job length. At t ∉ ሾα୤,β ୤ሿ, s୲ ୤=u ୲ ୤ =0 . If the appliance is switched on during ௙+1 ) , the state moves to st+1 f =s ...

work page

[4] [4]

The state variables are defined by the indoor and hot water temperature

Thermal appliances: The controller adjusts the power consumption of AC and EWH to keep the indoor temperature and temperature of the water inside the tank within the customer desired range. The state variables are defined by the indoor and hot water temperature. That is s୲ ୅େ≜T e m୲ ୧୬ and ௧ ௧ ௐ where ௧ ௠௜௡ ௠௔௫௜௡ ൧ and ௧ ௐ ∈ ௠௜௡ ௠௔௫ௐ ൧. The decision varia...

work page

[5] [5]

gt(st,L t) is the one-stage objective function (which can be either of CoEC or TDL) and J୲(s୲) is the optimal cost-to-go at state ௧ and time t

+ܬ௧)൯ൟ (10) ௧ାଵ=݂௧) ௧ ௧ ௧ ௠௔௫} ௧ ௧ ௧ ଵ ூಶೈಹ ௠௜௡ ௧ ௠௔௫ ௐ ൟ ௧ ௧ ௧ ଵ ூಲ಴ ௠௜௡ ௧ ௠௔௫ ௜௡ ൟ where ௧ ௧ ௧ ௧ ௧ ௕൯ is the total state space and u୲=൫ u୲ ୟ ,u ୲ ୤ ,u ୲ ୅େ,u ୲ ୉୛ୌ,u ୲ ୠ ൯ is the total decision space at time slot t. gt(st,L t) is the one-stage objective function (which can be either of CoEC or TDL) and J୲(s୲) is the optimal cost-to-go at state ௧ and tim...

work page

[6] [6]

The determination of ࢚is often problem-dependent

instead of ௧). The determination of ࢚is often problem-dependent. One potential option is to select some important variables of the problem and do minimization over the feasible decisions related to these variables, while keeping the decisions of the remaining variables at some nominal values. This approach can be specifically useful in MLA in which the or...

work page

[7] [7]

In the formulated HEMU, for example, the sets of charging/discharging decisions for the BSS, i.e., ௧ ௕, can be nominated to build such a ௧)

is used for the one-stage look-ahead approximations, while the reduced decision set ௧) is used for the multi-step look-ahead approximations. In the formulated HEMU, for example, the sets of charging/discharging decisions for the BSS, i.e., ௧ ௕, can be nominated to build such a ௧). C. Multiobjective Formulation The proposed MO-HEMU is stated as follows: mi...

work page

[8] [8]

An advantage of this technique is that it allows the decision maker to have control over the Pareto front by correctly choosing the values of kଶ

solutions as the Pareto list are found. An advantage of this technique is that it allows the decision maker to have control over the Pareto front by correctly choosing the values of kଶ. The choice of a higher value for ଶ results in more solutions in the Pareto list with better density but at the expense of higher calculation time. In this paper kଶ=6 . IV....

work page

[9] [9]

A single objective optimization problem for minimizing CoEC is solved for each case study with three MLAs including OLA, TLA, and three-step look-ahead algorithm (TSLA)

Single objective optimization: First, in order to evaluate the performance of the developed MLA in terms of the solution quality and computational time, different case studies with a different combination of devices and thus a different number of state and decision variables are defined as follows: • Case #1: only deferrable appliances are considered; • C...

work page

[10] [10]

Multiobjective optimization: Finally, the MO-HEMU model is solved by the TSLA considering all devices (case #5) and the obtained Pareto list is displayed in Fig. 6. The choice of the best compromise solution from this list depends on the preferences of the customer; whether minimizing the electricity cost is her priority or minimizing thermal discomfort i...

work page

[11] [11]

Demand Response for Residential Appliances via Customer Reward Scheme,

C. Vivekananthan, Y. Mishra, G. Ledwich, and F. Li, "Demand Response for Residential Appliances via Customer Reward Scheme," IEEE Trans. Smart Grid, vol. 5, no. 2, pp. 809-820, 2014

work page 2014

[12] [12]

Home energy management systems: A review of modelling and complexity,

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