Beyond Similarity: Heterogeneous Graph Learning for Multi-Objective Food Substitution in Charitable Food Agencies

Naimur Rahman Chowdhury; Limon Bin Hossain

cs.AIAug 22, 2026

Beyond Similarity: Heterogeneous Graph Learning for Multi-Objective Food Substitution in Charitable Food Agencies

Authors: Naimur Rahman Chowdhury, Limon Bin Hossain

Organizations: Department of Industrial and Systems Engineering North Carolina State University Raleigh, NC, USA · Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Dhaka, Bangladesh

Abstract

Charitable food agencies play an important role in alleviating food insecurity by distributing donated food to people in need. However, they rely on ad hoc in-kind donations and often face shortages of specific foods, so they offer substitutes. A good food substitution requires matching household preferences, nutritional needs, and item similarity. Agencies have limited direct records of consumption behavior due to resource constraints, making it challenging to make an appropriate substitution decision that meets multiple criteria. In this study, we propose a heterogeneous graph neural network (HeteroGNN), a source-grounded recommendation framework for food substitution in charitable food agencies. We first build a unified relational graph from large-scale public data sources, combining household behavior on food consumption and food nutrient information in the United States (US) context. We treat the substitution recommendation as a multi-objective ranking problem with three targets, including behavior affinity, health suitability, and substitution similarity. We train and validate the proposed framework under standard graph relationship and adverse cold-start settings by removing relational edges from the graph. Our results show that the proposed framework leverages relational information beyond node features in predicting consumption behavior. Additionally, the proposed framework remains robust with sparsity when the model receives incomplete information about behavior and nutrient features. Finally, we show the weak correlation among different objectives, thereby justifying the multi-objective framing as a replacement for an aggregated decision. The proposed framework can help downstream charitable agency decision-makers make contextspecific substitution recommendations with limited information available.

Figures & tables

Fig. 1 : Complete data construction with food catalog, population and behavior relations for heterogeneous graph.

Quantity	Count
People	26,250
Household/respondent contexts	16,759
Demographic household groups	42
Foods with nutrient evidence	9,903
Food–nutrient records	102,441
Consumption lines	188,148

TABLE I : Scale of the data in the graph construction.

Objective	Supervision	Interpretation
Behavior affinity	Observed group–food relation vs. sampled unobserved relation	The probability that the food is familiar or behaviorally plausible for the household group.
Health suitability	Profile-weighted food-health score	Nutrient-density suitability for the health-profile mix associated with the group.
Substitution similarity	Directional mapped catalog-pair score	The degree to which a candidate can play the same role as the requested item.
Composite ranking	Weighted combination over the three predictions	Inspectable decision support rather than a single uninterpretable score.

TABLE II : Interpretation of the multi-objective recommendation.

Node type	Feature name	Description	Encoding type
Household group	Member count	Number of respondent contexts in the group	Discrete
Household group	Mean household size	Average household size within the group	Discrete
Household group	Mean income-to-poverty ratio	Average income-to-poverty ratio within the group	Continuous
Household group	SNAP share	Share of group members participating in SNAP	Continuous proportion
Household group	Poverty band	Discretized income-to-poverty category	One-hot binary
Household group	Household-size band	Discretized household-size category	One-hot binary

TABLE III : Node feature construction for the heterogeneous graph.

Hyperparameter	Value
Node embedding dimension	64
Message-passing layers	2
Activation function	ReLU
Aggregation function	Sum
Dropout	0.218
Optimizer	AdamW

TABLE IV : Model hyperparameters and training Settings.

Metric		HeteroGNN	MLP	BPR	LightGCN
Behavior affinity	ROC-AUC	0.9480	0.9009	0.9144	0.9369
	PR-AUC	0.9027	0.7809	0.8467	0.8838
	Precision@5	0.9952	0.8000	0.9667	0.9667
	Recall@5	0.0262	0.0186	0.0244	0.0240
	NDCG@5	0.9965	0.8039	0.9724	0.9699
Health suitability	MAE	0.0182	0.0128	0.0756	0.0765

TABLE V : Performance comparison under the standard evaluation setting. Best results in bold .

Metric		HeteroGNN		MLP		BPR		LightGCN
		CS-F	CS-G	CS-F	CS-G	CS-F	CS-G	CS-F	CS-G
Behavior affinity	ROC-AUC	0.8381	0.6070	0.8973	0.8971	0.4959	0.3883	0.4887	0.5323
	PR-AUC	0.6932	0.4367	0.7739	0.7618	0.3347	0.2749	0.3511	0.3910
	Precision@5	0.5143	0.2500	0.7857	0.8750	0.3333	0.1500	0.2238	0.3750
	Recall@5	0.0108	0.0008	0.0179	0.0024	0.0057	0.0006	0.0039	0.0009
	NDCG@5	0.4656	0.2500	0.8012	0.8453	0.3390	0.1517	0.2405	0.3750

TABLE VI : Performance comparison under the cold-start evaluation settings. CS-F = cold-start food; CS-G = cold-start household group.

Attribute	Level	ROC-AUC
Poverty band	Above 2 $\times$ poverty	0.470
	Below poverty	0.781
	1–2 $\times$ poverty	0.667
SNAP band	Non-SNAP	0.590
SNAP band	SNAP	0.619
Household size	Large	0.640

TABLE VII: Behavior Affinity Performance by Household Demographic Segment (Cold-Start Group Split)

	Behavior Sparsity				Nutrient Sparsity
	Behavior ROC AUC $\uparrow$		Health MAE $\downarrow$		Behavior ROC AUC $\uparrow$		Health MAE $\downarrow$
Removed	GNN	MLP	GNN	MLP	GNN	MLP	GNN	MLP
0%	0.9444	0.8890	0.0285	0.0262	0.9444	0.8890	0.0285	0.0262
10%	0.9474	0.8889	0.0283	0.0263	0.9433	0.8895	0.0329	0.0254
30%	0.9442	0.8889	0.0290	0.0265	0.9388	0.8890	0.0327	0.0285
50%	0.9378	0.8889	0.0292	0.0265	0.9469	0.8876	0.0379	0.0481

TABLE VIII : Robustness of HeteroGNN and MLP in incomplete information.

	Pearson			Spearman
	Behavior	Health	Similarity	Behavior	Health	Similarity
Behavior affinity	1.000	$-$ 0.067	0.090	1.000	0.521	0.311
Health suitability	$-$ 0.067	1.000	0.070	0.521	1.000	0.421
Substitution similarity	0.090	0.070	1.000	0.311	0.421	1.000

TABLE IX : Correlations among the three objectives.

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