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Beyond Similarity: Heterogeneous Graph Learning for Multi-Objective Food Substitution in Charitable Food Agencies
Naimur Rahman Chowdhury, Limon Bin Hossain
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%
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Summary
This paper proposes HeteroGNN, a heterogeneous graph neural network framework for multi-objective food substitution recommendations in charitable food agencies. The model integrates public data sources (USDA, NHANES, FoodAPS) to construct a relational graph linking household groups, foods, nutrients, and categories. It predicts three distinct objectives: behavior affinity, health suitability, and substitution similarity, allowing for interpretable trade-offs in decision-making. The framework demonstrates robustness in standard and cold-start settings, outperforming baselines like LightGCN and MLP in predicting consumption behavior by leveraging relational structure beyond node features.
Entities (14)
Relation Signals (12)
HeteroGNN → proposesfor → Food Substitution
confidence 95% · we propose a heterogeneous graph neural network (HeteroGNN)... for food substitution in charitable food agencies
Food → contains → Nutrient
confidence 90% · food–nutrient content... relations
HeteroGNN → outperforms → BPR
confidence 90% · HeteroGNN... outperform MLP... BPR benefits from optimizing... but lacks auxiliary relational evidence
HeteroGNN → outperforms → LightGCN
confidence 90% · HeteroGNN achieves the highest difference in performance on behavior affinity... These results marginally surpass LightGCN
HeteroGNN → predicts → Substitution Similarity
confidence 90% · We treat the substitution recommendation as a multi-objective ranking problem with three targets, including substitution similarity
HeteroGNN → predicts → Behavior Affinity
confidence 90% · We treat the substitution recommendation as a multi-objective ranking problem with three targets, including behavior affinity
HeteroGNN → predicts → Health Suitability
confidence 90% · We treat the substitution recommendation as a multi-objective ranking problem with three targets, including health suitability
HeteroGNN → usesdatafrom →
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Abstract
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.
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- Source: https://arxiv.org/abs/2608.21979v1
- Canonical: https://arxiv.org/abs/2608.21979v1
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Beyond Similarity: Heterogeneous Graph Learning for Multi-Objective Food Substitution in Charitable Food Agencies Naimur Rahman Chowdhury Affiliation: The work was done prior to joining Amazon. Department of Industrial and Systems Engineering North Carolina State University Raleigh, NC, USA nchowdh2@ncsu.edu Limon Bin Hossain Affiliation: Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Dhaka, Bangladesh mdlimonbinhossain@gmail.com 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 context-specific substitution recommendations with limited information available. Index Terms: Food Substitution, Heterogeneous Graph Neural Networks, Multi-Objective Recommendation, Public Nutrition I Introduction In the United States (US), one in six people is served by food banks and their associated partner agencies, such as food pantries and soup kitchens, which play an important role in reducing food insecurity [19]. However, these charitable food agencies are heavily dependent on external in-kind donations, which limit their ability to cater to food-insecure communities [5, 24]. Hence, these organizations often have to provide substitutes for requested or preferred items to food-insecure households from their limited catalog [23, 1]. However, being a good food substitute requires several components, including familiarity within the household, nutritional suitability for household members, and similarity to the requested item [26, 27]. A substitute for a requested food item is less attractive if the household does not recognize it, has a dietary restriction that conflicts with it, or receives a nutritionally poor option. This substitution decision for a charitable agency volunteer is non-trivial, since households served are heterogeneous in demographic characteristics and often have little or no directly observed preference history to the agencies with limited data management capacity [11]. Public data on household food consumption provide dietary patterns and familiarity [4, 30], but no current public dataset provides structured records of household context, requested foods, and offered substitutes, so a recommendation system may rely on indirect behavioral signals. The most relevant studies on charitable food agencies have focused on forecasting donation quantity and timing [6, 24, 25], but modeling the substitution decision itself still remains unexplored. In food substitution recommendations for requested items, to match preferences across multiple dimensions (affinity, nutritional values, and similarity), the system needs to rely on behavioral evidence, keeping familiarity, health, and similarity rather than a general recommender that is trained on direct user-item interaction [15, 10] to optimize a single score [21, 2]. This process generalizes to foods and household groups that it has not directly observed. To this end, although the final substitution score can be analytically obtained when all relevant information is available, the challenge arises with sparse, highly interdependent inputs that are scattered across separate data sources. Moreover, an analytical form struggles to produce a recommendation score when the input is incomplete. This can be addressed by learning latent representations across the relational structure, inferring recommendations from weakly observed relationships, and then generalizing them to unseen foods or household groups. In this study, we propose a heterogeneous graph neural network (HeteroGNN) to complement heuristic alternatives requiring enumeration in every combination of nutrition, consumption behavior, and food similarity that becomes harder to maintain as the number of foods, household groups, and relations grow. We leverage extensive public data sources [29, 30, 4] to extract household consumption behavior, nutritional information, and similarity. Finally, we propose a recommendation framework that produces a ranked list of substitutes with three objectives, i.e., behavior affinity, health suitability, and substitution similarity. Keeping these three scores distinct lets a downstream evaluator inspect the trade-offs behind a recommendation. The objectives of this study are as follows. • To develop a heterogeneous graph framework that integrates a sparse public dataset into a unified relational structure for food substitute recommendation. • To jointly learn behavior affinity, health suitability, and substitution similarity as complementary objectives, preserving downstream decision makers’ ability to evaluate trade-offs in recommendations. • To evaluate the robustness of the learning framework in reliable recommendation performance under incomplete and sparse information, where traditional systems struggle. I Methods We formulate a decision problem where U denotes the set of household-group contexts, and ℱF the set of foods in the agency catalog. Here, ℛ⊆ℱR is the set of possible requested foods by a household. For a request from context u∈u for food r∈ℛr , the system receives a candidate set (r)⊆ℱC(r) of substitutes. We aim to rank the candidates f∈(r)f (r) along three objectives shown in Eq. 1. S(u,r,f)=(Sb(u,f),Sh(u,f),Ss(r,f)),S(u,r,f)= (S_b(u,f),\,S_h(u,f),\,S_s(r,f) ), (1) where SbS_b is behavior affinity, ShS_h is health suitability, and SsS_s is substitution similarity. Our learning model estimates S^b S_b, S^h S_h, and S^s S_s separately. I-A Dataset and Graph Construction We construct the relational structure from four public data sources. Each source contributes a distinct type of information to the pipeline. First, we use the USDA FoodData Central Foundation Foods [29] that provides nutrient profiles for basic food items. Second, we use the Food and Nutrient Database for Dietary Studies (FNDDS) [28], which provides standardized food codes. Together, these two datasets form the basic food catalog. The National Health and Nutrition Examination Survey (NHANES) [4] data provide demographic information, dietary records, and health indicators. Additionally, the FoodAPS [30] dataset provides household and individual food acquisition records. These two sources are combined to obtain information on population and behavior. Moreover, we incorporate nutrition guidance from Healthy Eating Research [13] to rank foods specifically for the charitable food supplies. The construction process follows two streams as shown in Figure 1. One stream builds the food catalog and substitution pairs. The other builds a relational database of persons, households, and observed food behavior. We merge them finally into a single heterogeneous graph. Fig. 1: Complete data construction with food catalog, population and behavior relations for heterogeneous graph. For the food catalog, we use a list of generic items relevant to charitable food agencies [17] and link each item to the USDA FoodData Central Foundation Foods record. Any missing target nutrients are filled from mapped FNDDS records. We then construct directional substitution pairs using culinary-use overlap, food category, form, and nutrient closeness. The largest construction involves the relational database linking person and household records from NHANES and FoodAPS. We combine the records to build household-context groups using income band, household size, and SNAP participation. We aggregate reported NHANES consumption and FoodAPS acquisition records at the household-group level for behavioral evidence. This produces a heterogeneous graph with four node types: household groups, foods, nutrients, and categories. The main relations families are household-group–food behavior, food–nutrient content, food–category membership, and food–food substitution similarity. Table I summarizes the scale of the constructed relational structure. TABLE I: Scale of the data in the graph construction. 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 Acquisition items 254,587 Group–food behavior edges 59,552 I-B Objective Targets In this section, we define the three targets in the objective in substitute ranking described in Eq. 1. I-B1 Behavior Affinity Target For each observed household-group-food pair (u,f)(u,f), the database records the number of occasions and the total grams acquired. The behavior target is constructed from observed occasions defined in Eq. 2. yb(u,f)=log(1+occasionsu,f)maxf′log(1+occasionsu,f′).y_b(u,f)= (1+occasions_u,f ) _f (1+occasions_u,f ). (2) Eq. 2 follows implicit feedback [14], in which the strength of an observed interaction is modeled as a monotonic function of its frequency rather than assumed to scale linearly with raw counts. For the binary behavior head, observed group–food pairs are treated as positive behavior evidence, and unobserved pairs are sampled as negative examples, as defined in Bayesian Personalized Ranking (BPR) [20]. A similar approach is used in graph-based recommenders, including Neural Graph Collaborative Filtering [31] and LightGCN [12]. I-B2 Health Suitability Target The relational database constructed from NHANES and FoodAPS records contains six profile-specific health scores, i.e., general, diabetes, hypertension, obesity, child nutrition, and senior nutrition, for members in a household group. Each food–profile score is a nutrient-density score based on beneficial and limiting nutrients, following practical guidance for charitable food environments [13]. Beneficial nutrients are mapped as in Eq. 3, whereas Eq. 4 maps limiting nutrients. c+(f,n)=min(max(af,n,0)ρn, 1),c^+(f,n)= \! ( (a_f,n,0) _n,\,1 ), (3) c−(f,n)=1−min(max(af,n,0)ρn, 1),c^-(f,n)=1- \! ( (a_f,n,0) _n,\,1 ), (4) where af,na_f,n is the per-100 g nutrient amount and ρn _n is the profile reference amount. The profile-specific score is defined in Eq. 5 that follows the Nutrient-Rich Foods (NRF) index, which scores foods on a per-reference-amount basis [7, 9, 8]. H(f,p)=∑n∈fwp,nc(f,n)∑n∈fwp,n.H(f,p)= _n _fw_p,n\,c(f,n) _n _fw_p,n. (5) For household group u, the profile mixture πu,p _u,p is estimated from observed health indicators in the group. The final group–food health target is defined in Eq. 6. yh(u,f)=∑p∈πu,pH(f,p).y_h(u,f)= _p _u,pH(f,p). (6) I-B3 Substitution Similarity Target We build directional candidate pairs from the food catalog for substitution. Each pair combines culinary-use, category, form, and nutrient-profile components. Only pairs whose request and substitute foods map to nodes in the FNDDS graph. The similarity target is denoted by ys(r,f)∈[0,1]y_s(r,f)∈[0,1]. I-C HeteroGNN In this section, we describe the main components of the HeteroGNN architecture. I-C1 Relational Message Passing Let xvτx^τ_v denote the input feature vector for node v of type τ. A type-specific encoder maps each input into a hidden representation, hv(0)=σ(Wτxvτ+bτ).h^(0)_v=σ (W_τx^τ_v+b_τ ). (7) For each message-passing layer ℓ , relation-specific transformations aggregate information from neighboring nodes, h~v(ℓ+1)=Wτ(v)selfhv(ℓ)+∑ρ∈ℛG∑u∈ρ(v)ωu,vρWρhu(ℓ), h^( +1)_v=W^self_τ(v)h^( )_v+ _ρ _G\ _u _ρ(v)ω^ρ_u,vW_ρh^( )_u, (8) where ρ indexes graph relations and ωu,vρω^ρ_u,v is the edge weight. The output is normalized and passed through a nonlinearity, hv(ℓ+1)=ReLU(LayerNorm(h~v(ℓ+1))).h^( +1)_v=ReLU (LayerNorm ( h^( +1)_v ) ). (9) Multiple message-passing layers are used in an inductive graph representation [15, 10]. I-C2 Heads and Training Objective After HeteroGNN encoding, three prediction heads operate on node-pair embeddings, S^b(u,f) S_b(u,f) =gb([hu,hf]), =g_b ([h_u,h_f] ), (10) S^h(u,f) S_h(u,f) =gh([hu,hf]), =g_h ([h_u,h_f] ), (11) S^s(r,f) S_s(r,f) =gs([hr,hf]). =g_s ([h_r,h_f] ). (12) Each head is a small feed-forward network with a sigmoid output. The model is trained with a joint loss, ℒ=λbℒb+λhℒh+λsℒs,L= _bL_b+ _hL_h+ _sL_s, (13) where the current implementation sets all three weights to one. Behavior uses binary cross entropy, ℒb=−1|b|∑(u,f,y)∈b[ylogS^b(u,f)+(1−y)log(1−S^b(u,f))], splitL_b=- 1|D_b| _(u,f,y) _b [&y S_b(u,f)\\ &+(1-y) (1- S_b(u,f) ) ], split (14) and health and similarity use mean-squared error, ℒh _h =1|h|∑(u,f,y)∈h(S^h(u,f)−y)2, = 1|D_h| _(u,f,y) _h ( S_h(u,f)-y )^2, (15) ℒs _s =1|s|∑(r,f,y)∈s(S^s(r,f)−y)2. = 1|D_s| _(r,f,y) _s ( S_s(r,f)-y )^2. (16) I-D Weighted Multi-Objective Score The model produces three predicted scores per candidate. A weighted score is used for the composite scoring as in Eq. 17. R(u,r,f)=αbS^b(u,f)+αhS^h(u,f)+αsS^s(r,f),R(u,r,f)= _b S_b(u,f)+ _h S_h(u,f)+ _s S_s(r,f), (17) αb _b, αh _h, and αs _s are the weights for each objective, providing downstream decision-makers with the flexibility to evaluate trade-offs among recommendations. For this study, we use a uniform weight across the three targets. Table I demonstrates the three objectives and their interpretation. TABLE I: Interpretation of the multi-objective recommendation. 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. I Experimental Setup The objective of the experiments is to evaluate the performance of HeteroGNN on the three substitution targets, thus the final composite score, and how that performance degrades when foods or population groups are unseen during behavior supervision. Table I shows all four node-level features used for training. All continuous features are standardized before training. TABLE I: Node feature construction for the heterogeneous graph. 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 Household group SNAP band SNAP or non-SNAP group label One-hot binary Household group Health-profile mixture Estimated mixture over nutrition profiles described in Section I-B2 Continuous proportions Food Log nutrient values Log-transformed nutrient density values for the nutrients Continuous Food Nutrient indicators Indicator for whether each nutrient value is missing Binary Food Source release Food source release (e.g., FNDDS cycle) One-hot binary Food Category code FNDDS food category code Continuous/numeric Nutrient Nutrient direction Whether higher values are beneficial or limiting Signed numeric Nutrient Reference amount Nutrient-specific reference value used for score normalization Continuous, log-transformed Nutrient Average profile weight Mean importance of the nutrient across the six health profiles Continuous Category Category code Numeric food-category identifier numeric Category Food count Number of foods observed in the category Continuous We use three validation settings. The standard setting uses a random 70/10/20 partition of observed behavior edges, with the final 20 percent held out for evaluation. To evaluate HeteroGNN’s performance when relational supervision is unavailable, we perform two cold-start settings. In the cold-start food setting, 1,774 food nodes are withheld from the behavior relation, and all food similarity edges connected to these held-out foods are removed from the training graph. Similarly, in the cold-start household-group setting, 8 of the 42 household groups are withheld from the behavior supervision. In both cold-start settings, node attributes remain available to see whether the model generalizes from feature information despite the absence of a behavioral relationship. We construct the training pipeline to reflect the three training settings. In the standard split, we randomly partition the observed behavior edges, whereas in the cold-start-food split, label edges that connect held-out foods are removed from the training graph. In the cold-start-household-group split, behavior edges touching held-out groups are removed. At inference time, the trained model receives a household group, a requested food, and a set of feasible candidates, and predicts behavior, health, and similarity scores for each candidate. Finally, to compare the model’s performance, we select baselines ranging from simple heuristics to advanced graph models to establish performance bounds and isolate our contributions. We begin with the simplest approach, i.e., Bayesian Personalized Ranking (BPR), that optimizes for observed items to rank above unobserved ones. However, it struggles in understanding auxiliary relations (e.g., recipes, store locations) [16] and is highly sensitive to data sparsity. To capture more complex patterns, we use a Multi-Layer Perceptron (MLP) that learns a flexible, nonlinear interaction between user and item feature vectors. It captures more complex patterns, and performance generally improves with model depth. However, it does not inherently capture relational structure. Recognizing the importance of relational structure, LightGCN [12] is a simplified Graph Neural Network (GNN) that removes nonlinear activations and feature transformations, focusing on neighborhood aggregation and layer combination. For our final training architecture, we leverage a tree-structured Parzen Estimator sampler and an early-pruner to find the best hyperparameter [32]. The best trial selects a hidden dimension of 64, 2 message-passing layers, ReLU activation, sum aggregation, and a dropout of 0.218. Table IV summarizes the main training settings. TABLE IV: Model hyperparameters and training Settings. Hyperparameter Value Node embedding dimension 64 Message-passing layers 2 Activation function ReLU Aggregation function Sum Dropout 0.218 Optimizer AdamW Learning rate 0.01 Weight decay 0.0001 Negative samples per positive behavior edge 2 Maximum health examples per training split 60,000 IV Results and Discussion We organize the results around the questions the experimental design was built to answer. We first report the evaluation accuracy on the standard setting and then discuss cold-start generalization. We highlight, in particular, the demographic segments that drive the cold-start household-group gap. Finally, we discuss the multi-objective trade-offs produced by the three heads. IV-A Evaluation and Comparisons The performance of the proposed HeteroGNN model was evaluated against baseline models MLP, BPR, and LightGCN across three evaluation settings (shown in Table ). All evaluations across HeteroGNN and baseline models are performed under the identical split and supervision. Additionally, baseline models are trained on the same information and features, with the same supervision. In the standard setting, HeteroGNN achieves the highest difference in performance on behavior affinity, with an ROC-AUC of 0.9480 and a PR-AUC of 0.9027. These results marginally surpass LightGCN (0.937, 0.884) and outperform MLP (0.901, 0.781). This demonstrates that the good relational structure is the primary mechanism driving behavior affinity prediction. While MLP leverages household and food attributes and captures nonlinear interactions, it lacks the capacity to propagate information through food–nutrient, food–category, and food–food relations. BPR benefits from optimizing the implicit ordering of behavior but lacks auxiliary relational evidence. LightGCN performs more closely to HeteroGNN due to its graph information propagation, but its homogeneous filtering architecture does not explicitly differentiate among semantic relation types. HeteroGNN surpasses these baselines by maintaining relation-specific message passing and heterogeneous representation learning. Furthermore, HeteroGNN achieves a Precision@5 of 0.995 and a Recall@5 of 0.026, reflecting that a household group’s positive set may contain significantly more than five behaviorally plausible foods. Moreover, a top-5 recommendation list can capture only a small portion of the positives in a large set, even when all recommended items are correct. These results demonstrate that HeteroGNN is highly effective at ensuring precision at the top of the recommendation list. In contrast with the behavior affinity, the health suitability prediction results show a different pattern. To evaluate performance, we report MAE to measure the accuracy of predicted health scores and the Spearman correlation to assess how well the predicted ranking of substitutions aligns with the ground-truth. Here, MLP achieves better performance with an MAE of 0.0128 and a Spearman correlation of 0.982, outperforming HeteroGNN (0.0182, 0.962), while BPR and LightGCN perform worse than HeteroGNN. These results indicate that when explicit nutrient attributes are present, a feature-based MLP can predict health suitability with high accuracy and outperform strong learning mechanisms that capture relational structure. From this result, we infer that health suitability is primarily a feature-based prediction task, as nutrient composition and demographic health profiles are sufficiently represented in node features and provide little benefit to relational propagation, instead introducing noise. For the substitution similarity objective, HeteroGNN and MLP exhibit comparable performance, with MAE values of 0.0222 and 0.0344, respectively, whereas BPR and LightGCN perform worse. The limited supervision set for similarity likely accounts for the lack of advantage observed with graph-based methods, as there is insufficient relational signal to propagate, allowing the simpler MLP to remain competitive. BPR’s near-random health predictions, indicated by a Spearman ρ of 0.101, highlight that optimizing for pairwise preference ranking does not provide a useful inductive bias for nutrient-density regression. Finally, the weighted multi-objective score for HeteroGNN is 0.9628, compared to 0.9164 for MLP, 0.9211 for BPR, and 0.9267 for LightGCN. MLP’s weaker performance on behavior tasks, despite using the same node features, confirms that the graph structure encodes relational information not captured by node features alone. Finally, this finding demonstrates that a single ranking mechanism cannot effectively address all three objectives. LightGCN’s strong performance in behavior prediction but poor results in health suitability prediction also confirm that health suitability prediction is not a collaborative filtering problem, but it requires nutrient composition and demographic features rather than relational propagation through behavior edges. TABLE V: Performance comparison under the standard evaluation setting. Best results in bold. 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 RMSE 0.0266 0.0177 0.1052 0.1053 Spearman ρ 0.9617 0.9823 0.1013 0.1182 Substitution similarity MAE 0.0222 0.0344 0.0820 0.0689 RMSE 0.0561 0.0844 0.1720 0.1533 Spearman ρ 0.6973 0.6900 0.6515 0.6699 Weighted Multi-Objective Score 0.9628 0.9164 0.9211 0.9267 IV-B Cold-Start Generalization The cold-start evaluation settings are intended to reveal how graph networks generalize to unseen entities when the entire node loses behavioral supervision. Notably, this differs from performance under incomplete data, which demonstrates robustness (we discuss this in Section IV-C). Under cold-start setting, HeteroGNN’s behavior affinity ROC-AUC decreases from 0.9480 to 0.8381 for unseen foods and further to 0.6070 for unseen household groups (shown in Table VI). This indicates that HeteroGNN’s primary source of predictive power remains the observed group–food behavioral structure, suggesting that the model struggles when behavioral edges are absent. Under the cold-start group setting, the behavior ROC-AUC falls to 0.6070, and the PR-AUC to 0.4367. However, in terms of health suitability, the MAE remains 0.0245, with a Spearman correlation of 0.9641; for substitution similarity, the MAE is 0.0333, with a Spearman correlation of 0.6932. This suggests that the model does not fail under group cold start, but struggles to recover unseen household behavioral preferences. To elaborate on the performance trend, the divergence is architecturally expected in HeteroGNN, since health suitability is primarily a function of food nutrient composition and the household’s health profile, whereas substitution similarity is primarily a function of the relationship between the requested and candidate foods. Both can therefore be inferred from relatively stable feature information. Behavior affinity, however, depends strong relational structure. When an entire group is unseen during behavior supervision, there is no direct relational evidence from which to infer its latent food preferences. On the other hand, the MLP’s behavior affinity under cold start is stable and outperforms HeteroGNN in cold-start settings. This suggests that MLP is relying heavily on static node attributes, which remain available in both cold-start experiments, whereas HeteroGNN exploits relational behavior information that disappears when the relevant nodes are held out. Consequently, the MLP becomes unusually competitive when relational supervision is deliberately removed. We observe a similar trend in health suitability, with MLP outperforming HeteroGNN. This indicates that health suitability can be predicted from node features and structural similarity to known foods, without requiring direct behavioral edges. Similarly, similarity MAE rises substantially from 0.0222 to 0.1260 in cold-start food for HeteroGNN, a wider degradation than any other objective, because similarity edges connected to held-out foods are removed, eliminating the primary relational signal for this objective. In the cold-start household group, however, similarity MAE rises to only 0.0333, indicating that similarity prediction depends on food-food relations rather than household-specific information. TABLE VI: Performance comparison under the cold-start evaluation settings. CS-F = cold-start food; CS-G = cold-start household group. 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 Health suitability MAE 0.0492 0.0245 0.0140 0.0143 0.0772 0.0762 0.0771 0.0825 RMSE 0.0616 0.0329 0.0200 0.0196 0.1071 0.1076 0.1071 0.1100 Spearman ρ 0.8609 0.9641 0.9807 0.9795 0.0140 0.0941 0.0151 0.1015 Substitution similarity MAE 0.1260 0.0333 0.0672 0.0491 0.1234 0.0818 0.1416 0.0751 RMSE 0.2977 0.1130 0.1883 0.1521 0.2732 0.1971 0.3217 0.1511 Spearman ρ 0.6848 0.6932 0.6786 0.6493 0.6401 0.6216 0.6384 0.6691 Weighted Multi-Objective Score 0.7894 0.7666 0.9146 0.9082 0.7054 0.6592 0.6907 0.7351 IV-B1 Fairness Across Demographic Segments The aggregate cold-start household group ROC-AUC of 0.607 hides considerable variation across household segments. Table VII breaks the same held-out predictions down by poverty band, SNAP participation, and household size. We observe that the generalization is best for households below the poverty line, ROC-AUC 0.781, and worst for small households, ROC-AUC 0.324, which is worse than a random ranker. Large households generalize moderately well (0.640), and single-person households sit in between (0.659). On the contrary, the SNAP status produces a smaller spread than the poverty band or household size. The results particularly reveal that the model generalizes poorly to small households. For implication, practitioners should treat cold-start behavior predictions for small household groups with particular caution. TABLE VII: Behavior Affinity Performance by Household Demographic Segment (Cold-Start Group Split) Attribute Level ROC-AUC Poverty band Above 2× poverty 0.470 Below poverty 0.781 1–2× poverty 0.667 SNAP band Non-SNAP 0.590 SNAP 0.619 Household size Large 0.640 Single 0.659 Small 0.324 IV-C Sparsity Analysis We use sparsity analysis to address data shortages at the facility level. Charitable food banks often serve groups for whom only partial information is available. In humanitarian logistics, this ensures equity by distributing aid in proportion to actual needs, even when those needs are not well-documented in existing datasets [22]. We perform different sparsity analyses. First, we randomly remove interaction edges (as opposed to completely removing all edges in a cold-start setting), which is defined as behavior sparsity. Second, we remove nutritional feature columns, a phenomenon known as nutrient sparsity. This tests the loss of relational and attribute information separately. Removing behavior relations affects behavior affinity prediction and impacts health scoring, whereas removing nutrient features impacts health scoring but can also affect behavioral affinity. Therefore, we report the ROC AUC for behavioral affinity and the MAE for health suitability in both analyses. The sparsity experiments (Table VIII) provide an important explanation for why HeteroGNN remains useful despite this cold-start limitation. The HeteroGNN outperforms MLP at all removal levels, with ROC AUC dropping only 0.7% (0.9444 to 0.9378) from 0% to 50% removal, while MLP remains steady at 0.889. The slight increase at 10% removal shows GNN’s robustness to moderate data loss, indicating removed edges were not critical. MLP’s flat AUC demonstrates insensitivity to behavioral sparsity, since it does not benefit from relational input. On the other hand, MLP has lower health MAE than GNN at all behavior removal levels (0%: 0.0285 vs. 0.0262; 50%: 0.0292 vs. 0.0265). Under nutrient sparsity, GNN is more robust, leading to a higher ROC AUC, while MLP remains stable but at a lower level. For health suitability MAE, MLP starts better but drops sharply at 50% removal (GNN: 0.0379, MLP: 0.0481). GNN’s robustness shows it leverages relational structure when features are lost. Across eight perturbations on sparsity, HeteroGNN’s AUC drops marginally and remains robust under severe sparsity. MLP matches or surpass GNN performance on for health suitability when nutrient features are present, but under information loss, GNN’s relational modeling performs better in MAE. TABLE VIII: Robustness of HeteroGNN and MLP in incomplete information. Behavior Sparsity Nutrient Sparsity Behavior ROC AUC ↑ Health MAE ↓ Behavior ROC AUC ↑ Health MAE ↓ 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 IV-D Multi-Objective Trade-offs Table IX reports the Pearson and Spearman correlation among the three predicted objectives. Behavior affinity and health suitability are weakly negatively correlated, −0.067-0.067. This is consistent with the common practice that familiar, frequently consumed foods are not always the most nutrient-rich. Behavior affinity and similarity are weakly positively correlated (0.0900.090), whereas health suitability and substitution similarity are weakly positively correlated (0.0700.070). None of these correlations is strong enough to claim that one objective serves as a reliable proxy for another, which provides quantitative justification for keeping the three separate targets as proposed in our framework. However, a practical consideration is that the weighted score in Eq. (17) is sensitive to how the three weights αb _b, αh _h, and αs _s are set. Since the objectives are only weakly related, shifting weights can change which candidate ranks first. Hence, a downstream decision maker reviewing a candidate should set condition-driven weights for ranking. For example, for a person with health conditions, the weight on αh _h should be higher than the other two factors to dominate the health suitability component of the composite score. The Spearman correlations also reflect that the objectives remain sufficiently independent to justify multi-objective optimization rather than a single target. TABLE IX: Correlations among the three objectives. 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 V Related Work V-A Food Assistance Operations and the Substitution Decision Gap Food assistance research focuses on minimizing the gap between what a food bank has on hand and what a household needs [1], which includes allocating scarce donated inventory across facilities [18], forecasting donation volume and timing [6]. These studies focus on distributing donated food upon its arrival. However, once a household requests an item that is unavailable at distribution time, choosing a substitute is a ranking problem over a candidate set conditioned on that household. To our best knowledge, none of the existing studies focus on this aspect, leaving a gap between planning how much food arrives and deciding what to hand over when a specific request cannot be met. V-B Public Nutrition and Acquisition A set of public data collection describes what people eat and what households acquire, without addressing substitution preferences directly. NHANES records dietary recall and health indicators at The person level [4, 3], whereas FoodAPS records household-level acquisition [30], and FNDDS links the food codes in both surveys to nutrient composition [28, 29]. Existing work treats these sources as population-level descriptive statistics rather than as relational evidence linking people, households, foods, and nutrients. This study uses the same public instruments but keeps observed behavior and accepted substitution explicit throughout, and links persons, household groups, foods, nutrients, and categories into a single evidence graph rather than a set of separate survey tables. V-C Multi-Objective Recommendation Classic recommender systems reduce a recommendation to one relevance score, typically learned from collaborative filtering over dense user-item interaction histories [21]. Hybrid and multi-objective approaches show that collapsing distinct evidence into one number hides tradeoffs a reviewer prefers to see [2]. For food bank substitution, ranking by familiarity alone reinforces existing nutritional gaps in frequently acquired staples, whereas ranking by health score alone can suggest foods a household cannot prepare or recognize, and ranking by similarity alone can ignore a real health constraint. As the correlation analysis in Table IX shows, these three signals are only weakly associated with one another across the collected evidence, which provides an empirical basis for treating them as separate targets rather than one blended score. V-D Graph Neural Networks for Heterogeneous Recommendation GNNs offer a natural representation for recommendation problems involving users, items, and their relations. Graph convolutional networks establish neighborhood aggregation for propagating information across a graph [15], and GraphSAGE made this aggregation inductive, letting a trained model embed nodes unseen during training as long as they carry features [10]. Web-scale systems built on graph convolution confirm that this representation improves recommendation quality whenever relation structure carries real signal [33, 31]. This body of work, however, is built around a single node type and single relation type: users, items, and their interactions. In sum, food-bank operations research plans supply, but require modeling the substitution decision. Additionally, public nutrition and acquisition data describe behavior, but a strong relational structure across them is absent. Finally, graph neural models support heterogeneous, inductive representation learning in principle, which is leveraged in this study to close the previously mentioned gaps. VI Conclusion and Future Work This study formalizes food substitution as a multi-objective ranking problem with three separate objectives: behavior affinity, health suitability, and substitution similarity. These dimensions cannot be collapsed into a single score without losing decision-relevant information. To address this, we develop heteroGNN that integrates four disparate public data sources into a unified relational structure. Our results show that relational information adds predictive value beyond node features alone, delivering a practical, source-grounded decision-support framework for food bank volunteers who currently make substitution decisions without systematic guidance. Our results show that health and similarity predictions remain robust under cold-start conditions, whereas behavior prediction collapses, indicating that a single architecture cannot serve all objectives well. However, the sparsity analyses show that graph relations can compensate for incomplete behavioral or nutritional information, supporting the motivation for heterogeneous graph learning. Several limitations follow directly from the findings of this study. First, the substitution similarity head is trained on only 56 mapped directional labels after the 124 catalog-level pairs are mapped to the graph’s food population. This small label count is the main reason the substitution similarity MAE degrades the most under cold-start-food. Second, the cold-start-household group result is estimated from only 8 held-out groups out of 42, so the aggregate ROC-AUC of 0.607 is itself a noisy estimate, and the segment breakdown in Section IV-B1 shows that this aggregate conceals a range from 0.324 to 0.781. Third, we use the single architecture under standard settings with optimal hyperparameters and then reuse across all validation splits, which require a setting-specific tuning. Future work should account for feasible constraints, such as food preparation requirements and cultural acceptability beyond what consumption data capture. Additionally, incorporation of richer household context beyond the current demographic grouping, including cultural food preferences, preparation constraints, and household member age distributions, can make the graph more informed. 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