Adaptive Constraint Relaxation in Personalized Nutrition Recommendations: An LLM-Driven Knowledge Graph Retrieval Approach

Abstract

Personalized food recommendation systems must balance various constraints, including medical guidelines, nutritional needs, and individual preferences. However, existing methods often struggle with overly restrictive queries, frequently failing to generate recommendations when no exact match exists. To address this challenge, we propose an adaptive knowledge graph (KG) retrieval framework that integrates Large Language Models (LLMs) for intelligent constraint relaxation. Our approach dynamically prioritizes constraints, ensuring that critical dietary requirements remain intact while selectively relaxing less essential ones. By leveraging LLM-driven constraint analysis and structured relaxation strategies, our system significantly enhances recommendation coverage without compromising key dietary needs, while maintaining optimal recommendation performance. Experimental results on both the original and the extended-constraint dataset demonstrate that our method successfully retrieves recommendations in cases where previous approaches fail, achieving higher retrieval accuracy and a balanced tradeoff between flexibility and adherence to dietary constraints. The code is public available at https://github.com/zpf0117b2/adaptiveRetrieval

1. Introduction

With the rising prevalence of diet-related health issues, personalized food recommendation systems have become crucial in promoting healthier eating habits while accommodating individual dietary needs.^{1, 2, 3, 4, 5} These systems must balance multiple constraints from different sources, spanning health requirements, dietary guidelines, nutritional targets, and personal preferences. Recent advancements^{6, 7, 8} have framed food recommendation as a constrained question-answering task over food knowledge graphs (KGs). However, existing approaches struggle when queries impose overly strict constraints, often leading to situations where no valid recommendations can be returned.⁹ A major limitation of traditional constraint-based retrieval systems is their rigid, “all-or-nothing” approach.^{9, 10} When no food item meets all the specified constraints—a frequent issue in highly personalized recommendations—these systems do not return any results. This problem is especially critical in health-sensitive scenarios where some constraints, such as medical dietary restrictions, hold a higher priority than others, such as personal taste preferences. For example, consider a user with diabetes who needs a breakfast recommendation. They must adhere to medical guidelines restricting carbohydrate intake to between 5 and 30 grams while avoiding peanuts due to an allergy. Additionally, they personally prefer high-protein meals, enjoy avocado, and dislike shrimp. A strict constraint-matching system might fail to find an exact match,^{3, 1} leaving the user without any viable recommendation. In such cases, an adaptive approach that intelligently relaxes constraints is essential.^{4, 11} While previous work in food recommendation has explored incorporating user preferences^{12, 13, 14} and adhering to health guidelines,¹⁵ existing methods lack a flexible mechanism for dynamically resolving constraint conflicts.

To address these limitations, we propose an adaptive KG retrieval framework that utilizes Large Language Models (LLMs) for intelligent constraint relaxation. Our approach extends LLM-driven KG retrieval¹⁶ and LLM-powered constraint analysis¹⁸ to dynamically balance strict dietary requirements with flexible user preferences while enhancing recommendation coverage. Our method is designed to retrieve relevant KG data when an initial query fails due to overly restrictive constraints. It identifies “unimportant” constraints in real-world scenarios and applies an adaptive algorithm to loosen them selectively (which is called constraints relaxation), enabling more effective KG retrieval. Constraint relaxation is a practical solution to this over-constraining issue, allowing for selective flexibility while preserving essential requirements.¹⁰ LLMs provide a powerful tool for this process, using their advanced semantic reasoning capabilities to assess constraint importance and guide a structured relaxation strategy.¹⁹ This integration ensures that recommendations remain both accurate and personalized, even in complex and restrictive scenarios.

Our key contributions include:

1. To the best of our knowledge, we are the first to identify and systematically investigate the challenge of overly restrictive dietary constraints, which often lead to retrieval failures. To overcome this, we introduce a constraint relaxation mechanism that selectively loosens constraints while preserving critical dietary needs.

2. We develop a retrieval module that leverages LLMs to intelligently analyze and perform KG queries to yield recommendations. Based on this, we introduce a novel adaptive retrieval strategy, where LLMs dynamically assess constraint priority and selectively relax non-essential constraints to maximize retrieval success while maintaining dietary compliance.

3. We conduct extensive evaluations on benchmark and extended-constraint datasets, demonstrating that our method significantly improves recommendation success rates. Specifically, our approach achieves a 98.1% increase in Constraint Inclusion Rate (CIR), with successful retrievals achieving an average F1 score of 79.0%. These results highlight the effectiveness of our adaptive constraint relaxation strategy in real-world scenarios.

The rest of this paper is organized as follows: Section 2 reviews related work on KG-based question answering and food recommendation systems. Section 3 details our methodology, including LLM-powered constraint analysis and hierarchical relaxation algorithms. Section 4 presents experimental results and user studies. Finally, section 5 discusses the broader implications of our findings and future research directions.

2. Related Works

Our work builds upon several key research directions: KG-based food recommendation, constraint relaxation in recommender systems, and LLM-enhanced KG retrieval.

KG-Based Food Recommendation. KGs have emerged as a powerful tool for food recommendation systems due to their ability to capture rich semantic relationships among ingredients, recipes, and nutritional information. Prior studies introduced FoodKG,¹⁶ a large-scale food KG integrating recipes, ingredients, and nutrient data, and associated applications.^{20, 21, 22} Other research has framed food recommendation as a constrained question-answering task,^{3, 4, 8} incorporating both user preferences and health guidelines.^{23, 7, 24} These methods, however, often struggle when multiple constraints lead to overly restrictive query results, limiting their practical applicability in real-world personalized recommendation settings.

Constraint Relaxation in Recommender Systems. In constraint-based recommendation systems, an over-constraining problem can arise when strict filtering eliminates all viable options. To address this, various constraint relaxation techniques have been proposed.^{25, 26} Multi-layer constraint relaxation strategies have been developed for KG retrieval, identifying minimal sets of constraints to relax.^{27, 28} In the context of food recommendation, prior work has attempted to balance health requirements and user preferences,³ but these approaches lack a structured, adaptive mechanism to dynamically resolve conflicting constraints.

LLMs for KG Retrieval. Recent advances in LLMs have opened new possibilities for KG retrieval and reasoning. Studies have demonstrated that LLMs can effectively understand and prioritize different types of constraints in KG queries.^{18, 7} In particular, Liu et. al.²⁹ proposed using LLMs as neural retrievers for KGs, showing improved performance in capturing semantic relationships compared to traditional embedding-based approaches.

Our work extends these directions by introducing an adaptive constraint relaxation mechanism guided by LLMs. Unlike previous approaches that use fixed rules or manual prioritization for constraint relaxation, our method leverages LLMs to dynamically assess constraint importance based on the specific context and user requirements.

3. Method

System Overview: Our method aims to adaptively retrieve the KG with the relaxation of constraints. The system consists of two main components: (1) an LLM-driven KG base retrieval module without constraint relaxation, and (2) an adaptive pipeline for retrieving KG with relaxed constraints. The second component includes two parts: a constraint analyzer that leverages LLMs to infer and prioritize constraints from user queries and preferences, and an adaptive retrieval module that relaxes constraints during retrieval. Figure 1 illustrates an example of running our system, and Figure 2 illustrates the overall architecture of our system.

Figure 1:

The demonstration of the pipeline proposed by base methods (upper half, following previous methods that cannot handle strict constraints) compared to our adaptive retrieval method (lower half that can handle strict constraints with constraints relaxation). Previous methods will treat all constraints as the same importance, thus they will retrieve the KG using all constraints at once (upper half). In contrast, we propose to relax the constraints and retrieve the KG afterwards (lower half) when the KG Query with too many constraints returns None and yield no recommendation. The constraint relaxation will follow the importance (more importance indicated by lower PRL) inferred by LLMs. We use FoodKG¹⁶ as retrieval target, a comprehensive KG integrating approximately one million recipes, 7.7 thousand nutrient records from the USDA,¹⁷ and 7.3 thousand food types.

Figure 2:

Framework of our proposed LLM-driven KG retrieval, base and adaptive version.

3.1. LLM-driven KG retrieval - base module:

The base module serves as the foundation for our system, as shown in Figure 2 upper half. Given a natural language query Q, we leverage LLM to parse it and infer it into a set of constraints categories C = {c₁, c₂, …, c_n}. Each constraint c_i is represented as a tuple:

$$c_i\hspace{0.17em}=\hspace{0.17em}\left(entity,relation,value\right)$$ (1)

where entity refers to the target entity (e.g., “bread” or “carbs”), relation denotes the relationship type (e.g., whether contain the entity “Yes/No”, or the nutrition range), value specifies the constraint value or range. The parsed constraints are then converted into a structured query that is compatible with the KG. The query will be used to retrieve the relevant information from the FoodKG and output the retrieval results as recommendation results.

3.2. LLM-driven KG retrieval - adaptive module:

The purpose of this module is to retrieve results from the KG when the original KG query with all constraints yields nothing due to too many strict constraints. Our module is built to identify some “unimportant” constraints in real scenarios, and use an adaptive algorithm to retrieve the KG results by adaptively loosening these “unimportant” constraints.

LLM driven Constraint Inference and Prioritization

Given a user query and associated preferences, our system first employs the LLM to infer and structure the constraints. The LLM assigns an extra key attribute, Priority Level (PRL), to each constraint, based on inferred importance (a larger PRL indicates lower importance and more chance to be removed):

$$c_i^{\ast }\hspace{0.17em}=\hspace{0.17em}\left(entity,relation,value,PRL\right)$$ (2)

The examples of $c_i^{\ast }$ are shown in Figure 1.

Constraints Relaxation

Given structured constraints with priority $C^{*}\hspace{0.17em}=\hspace{0.17em}\left\{c_1^{*},c_2^{*},\dots ,c_n^{*}\right\}$ with associated priorities PRL($c_i^{*}$) for each constraint $c_i^{*}$, we can deduct the relaxable constraints set $U^{*}\hspace{0.17em}=\hspace{0.17em}\left\{C^{*}|PRL\left(c_n^{\ast }\right)>threshold\right\}$ given a PRL threshold, the goal is to generate all possible combinations of relaxable constraints R based on the PRL. The generation algorithm is presented in Algorithm 1.

Algorithm 1: Relaxable constraints set calculation.

The relaxable constraints set R is an ordered list generated starting from the lowest priority constraints. At each step, new elements in ordered combinations of constraints at the same or lower priority levels are appended, progressively moving toward higher priority constraints. This process continues until the strictest or user-defined priority level, which cannot be removed, is reached. For example, for constraints (a, b, c, d, e) with PRL 2, 3, 3, 4, 1:

$$R\hspace{0.17em}=\hspace{0.17em}\left[\left(d\right)\right]\hspace{0.17em}+\hspace{0.17em}\left[\left(c\right),\left(b\right),\left(d,c\right),\left(d,b\right),\left(b,c\right),\left(d,b,c\right)\right]+\left[\left(a\right),\left(d,a\right),\left(d,b,a\right),\left(d,c,a\right),\left(d,b,c,a\right)\right]$$

Adaptive Retrieval

With the calculation of the relaxable constraint set R, we implement a novel adaptive retrieval under constraint relaxation as shown in Algorithm 2, on top of base KG retrieval module:

Algorithm 2 Adaptive retrieval on KG with constraint relaxation, where we set larger PRL for larger possibility to be relaxed.

Our proposed adaptive retrieval module iteratively removes constraints from each possible combinations of relaxable constraints in R and then queries the KG. The module follows these principles: (1) it always removes the constraint with the lowest priority as described in Algorithm 1 and minimizes the number of constraints removed (line 8); (2) if multiple relaxable constraints set have the same priority and number of constraints, their results are merged (lines 8–10, and 12–14); (3) the process stops early once a valid result is found for a specific set of relaxable constraints set with the same priority level and number of constraints (following principle 2). This adaptive retrieval algorithm ensures that the relaxed recommendations still remain personalized, even when highly restrictive constraints would yield no results.

4. Experiments

We evaluate the performance of our proposed LLM-guided adaptive constraint relaxation approach against several competitive baselines on the personalized food recommendation benchmark created by previous work.⁶

Dataset, Metrics, and Implementation Details: For our experiments we use FoodKG¹⁶ as the primary retrieval target. A detailed overview of FoodKG utilization is provided in Figure 1 and more information about the FoodKG is available at (https://foodkg.github.io). Health guidelines from the ADA Lifestyle Management guidelines³⁰ are incorporated to provide clinical practice recommendations and nutrient requirements.

We follow the original benchmark setup as explained in Wang et al.,⁶ which combine user query provided by FoodKG with the healthcare guideline and personal preference, thus generating long query input and attempting to recommend the recipe within FoodKG. An example is shown on Figure 1 lower half. We evaluate the performance using several metrics following previous methods.^{31, 32, 33} These metrics include: Mean Average Precision (MAP), which measures the precision of the top-k retrieved recommendations; Mean Average Recall (MAR), which assesses the recall of relevant recommendations across different query types; Mean Average F1-score (MAF1), which is the harmonic mean of precision and recall, providing a balanced measure of retrieval performance.

We compare our method against previous food recommendation methods: Basic embedding-based Knowledge Base Question Answering (KBQA) method utilizing Bag-of-Word (BOW) vectors;³⁴ A KBQA method called BAMnet³² that retrieves answers by jointly embedding the question and KG subgraph; A personalized embedding-based KBQA method called P-MatchNN³⁵ that utilizes bidirectional LSTM³² for embedding; A personalized food recommendation system called pFoodReQ⁶ that directly considers user preferences in food suggestions.

Our system is implemented without training or finetuning. The generated results are zero-shot. For LLM, We use GPT-3.5 with temperature=0.1 for constraint inference. For KG retrieval and processing, we use the same JSON-based querying as previous methods.^{32, 12, 6}

Evaluation of the Adaptive Retrieval Method

We further extend the constraints of the benchmark dataset6 to evaluate the effectiveness of our proposed adaptive retrieval method on recovered items. Specifically, we randomly introduce nutrient and personal preferences as constraints that conflict with the existing ground truth recommendation results, yielding no recommendations. The performance is assessed based on the effectiveness of recovering ground truth recommendation results. An illustrative example is shown in the lower half of Figure 1. In this case, we impose three constraints: (1) a specific protein requirement, (2) exclusion of shrimp, and (3) inclusion of avocado. As a result, the retrieval output is empty. Our approach successfully recovers keto bread by relaxing the protein constraint, demonstrating its adaptability in handling conflicting constraints.

To comprehensively evaluate the effectiveness of recovering ground truth recommendation results, we introduce a set of metrics that measure both the effectiveness of constraint relaxation and the relevance of results. Coverage Improvement Rate (CIR) = $\frac{\text{\#}\hspace{0.17em}\text{adaptive}\hspace{0.17em}\text{retrievals}\hspace{0.17em}\text{with}\hspace{0.17em}\text{results}}{\text{\#}\hspace{0.17em}\text{strict}\hspace{0.17em}\text{retrievals}\hspace{0.17em}\text{with}\hspace{0.17em}\text{no}\hspace{0.17em}\text{result}}$ (quantifies how often our adaptive approach produces results when strict retrieval fails, providing insight into the system’s ability to overcome retrieval failures), Constraint Relaxation Efficiency (CRE) = Average $\left(\frac{\text{\#}\hspace{0.17em}\text{relaxed}\hspace{0.17em}\text{constraints}}{\#\hspace{0.17em}\text{total}\hspace{0.17em}\text{constraints}}\right)$ (measures the proportion of constraints that needed to be relaxed to obtain results, with lower values indicating more efficient relaxation), and Success Rate (SR) = $\frac{\text{\#}\hspace{0.17em}\text{adaptive}\hspace{0.17em}\text{retrievals}\hspace{0.17em}\text{with}\hspace{0.17em}{F}_1>0.05}{\text{\#}\hspace{0.17em}\text{adaptive}\hspace{0.17em}\text{retrievals}}$ (computes the percentage of adaptive retrievals that exceed a minimum relevance threshold (F1 > 0.05), establishing a binary measure of useful retrievals). We also evaluate the MAP, MAR, and MAF1 of those successful retrieval results (defined as F1 > 0.05). Together, these metrics offer a multi-dimensional assessment of how effectively our adaptive retrieval approach balances the competing goals of maximizing result coverage while preserving relevance to the original query constraints.

Results : Table 1 presents the main experimental results comparing our method against baselines. Our base approach outperforms all baseline methods by a significant margin: a 13.1% absolute improvement in MAP, a 12.1% absolute improvement in MAR, and an 10.4% absolute improvement in MAF1. The relaxed version of our approach also shows substantial improvements over the baselines, with an 12.3% absolute improvement in MAP, a 13.4% absolute improvement in MAR, and an 11.7% absolute improvement in MAF1. These results highlight the effectiveness of our LLM-guided approach, especially in terms of recall (MAR) and F1 score (MAF1), which demonstrate that our method retrieves highly relevant recommendations. Notably, the adaptive retrieval mechanism yields a slight performance improvement, indicating its robustness.

Table 1:

Experimental results (in %) on the benchmarking dataset in personalized food recommendation systems.

Method	Mean Average Precision (MAP)	Mean Average Recall (MAR)	Mean Average F1 (MAF1)
BOW34	2.1	2.0	2.3
BAMnet32	3.1	3.0	3.1
P-MatchNN35	45.5	45.1	41.2
pFoodReQ6	62.7	61.8	63.7
Ours (base)	75.8	73.9	74.1
Ours (Adaptive)	76.0	75.2	74.4

Figure 3 illustrates the effectiveness of our proposed adaptive retrieval with constraint relaxation. While all previous methods fail to return results on our extended-constraint dataset, where queries contain an excessive number of constraints (i.e., SR = 0 and CIR = 0, making CRE inapplicable), our approach achieves a 98.1% increase in CIR. This suggests that nearly all test cases successfully generate recommendations with a minimal number of relaxed constraints, as reflected in the low CRE value. This improvement stems from our adaptive retrieval method, which selectively relaxes constraints based on the priority inferred by the LLM. However, when the original constraints have a lower priority than the extended constraints, it can introduce bias in the recommendations, leading to deviations from expected outcomes. This bias is also evident in the low SR and the lower MAR of successfully recovered outputs. It is important to note that SR is measured by comparing recommendations to the ground truth, which strictly adheres to the original constraints. However, in real-world applications, even if a recommendation is classified as “failed” by our evaluation criteria, it still complies with the relaxed constraints and may remain useful to users. An example in Figure 5 demonstrates how the LLM infers constraint priorities based on user input. In this scenario, the user is allergic to crabmeat, so the “no crabmeat” constraint is assigned a high priority. The LLM does not distinguish between “original” and extended constraints; rather, it prioritizes them dynamically based on user-provided information. The quality of the successful recovered outputs, measured by MAP, MAR, and MAF1, remains high, indicating that our retrieval under relaxed constraints still generates reliable recommendations rather than random selections.

Figure 3:

Metrics of Retrieval Effectiveness Evaluation and Performance Evaluation on Successful Retrieval.

Figure 5:

An example of LLM processed Constraint. For easier programming, we set lowest value for the highest priority (“HIGHEST”, “HIGH”, “MEDIUM”, “LOW” correspond to the Priority Level: PRL=0,1,2,3). For the “is positive”, “True” means containing the item, while “False” means not containing the item. LLM can infer that “not containing crabmeat” is highest priority as the user is allergic to them.

We further analyze the successful retrieval performance of our method on the extended-constraint dataset, as illustrated in Figure 4. Firstly, in subfigure (a), we observe that the majority of successful retrievals achieve an F1 score above 60%, with more than half reaching a perfect F1 score of 1.0. This indicates that when our adaptive retrieval is successful, it often retrieves highly relevant results with minimal deviation from the expected output. The rightmost peak at 1.0 suggests that, in many cases, constraint relaxation effectively refines queries without significantly altering the intended recommendations. Secondly, subfigure (b) presents the relationship between the proportion of relaxed constraints and the F1 score for successful cases. The scattered distribution of points indicates that the degree of constraint relaxation does not strongly correlate with retrieval accuracy. This suggests that once retrieval succeeds, the quality of the recommendations remains stable regardless of how many constraints were relaxed. In other words, our adaptive retrieval strategy effectively mitigates the over-constraining issue while maintaining recommendation quality, even when constraints need to be adjusted dynamically.

Figure 4:

Detailed analysis of successful retrieval using our method on extended-constraint dataset.

Case Study: A case study of our proposed approach is shown in Figure 1. The input is a user query requesting a bread-based breakfast while accounting for multiple constraints with varying priority levels (PRL). As we can see, the constraints can be categorized into four distinct tiers: fundamental requirements (PRL=0, including the mandatory inclusion of bread), medical constraints (PRL=1, encompassing a peanut allergy and carbohydrate restriction of 5-30g), nutritional requirements (PRL=2, specifying a high protein content exceeding 18.67%), and personal preferences (PRL=3, indicating an aversion to shrimp and preference for avocado). BAMNet³² and PFoodReq⁶ returns None for this query and exit. However, our pipeline employs a two-stage approach for handling this query: first, it utilizes an LLM to infer and classify these constraints based on the input query, then queries a KG to identify suitable recipes. When the initial KG query yields no results, the system implements a constraint relaxation protocol as introduced in Section 3. This protocol progressively relaxes constraints in order of ascending priority, beginning with personal preferences (PRL=3) on avocado and shrimp, and proceeding to higher-priority constraints only when necessary (protein constraint, PRL=2). The process terminates after relaxed KG query (without protein constraint) yields positive results (keto bread as in the upper half figure). The case study demonstrates that the system successfully identifies viable recommendations after relaxing the protein constraint, producing suggestions such as keto bread variants, while maintaining critical medical constraints.

5. Conclusion

In this paper, we introduced an adaptive KG retrieval framework that integrates LLMs to address the challenge of overly restrictive dietary constraints in personalized nutrition recommendations. Our method employs LLM-driven constraint prioritization and structured relaxation to expand retrieval coverage while maintaining adherence to essential dietary requirements. Experimental evaluations demonstrate the effectiveness of our approach, showing a significant improvement in successful retrieval rates and recommendation accuracy compared to traditional methods. Furthermore, our analysis reveals that constraint relaxation does not necessarily degrade recommendation quality, as the LLM effectively balances flexibility and dietary compliance. While our method significantly improves retrieval outcomes, future work could explore refining constraint prioritization techniques and integrating real-time user feedback to enhance adaptability. Additionally, expanding the KG with more diverse and context-aware dietary information could further improve personalization. Our findings underscore the potential of LLM-powered adaptive retrieval systems in overcoming limitations in personalized recommendation frameworks, paving the way for more inclusive and effective dietary guidance solutions. While our system is adaptive, LLM-based semantic reasoning for PRL is inherently non-deterministic. For instance, the outputs of the LLM can vary across different prompts or even between runs with the same prompt. Although we have carefully crafted our prompt (as in the public code) to reduce this variability, some degree of uncertainty remains. We highlight this as a consideration for future work.