Ontology-Driven Optimization

• Ontology-driven optimization is a framework that employs formal ontologies to encode domain semantics, structuring and automating optimization workflows.
• It integrates methods like schema transformation, solver selection, and query rewriting by mapping ontological relationships to optimization objectives and constraints.
• Validated across fields such as knowledge graphs and ML, this approach achieves significant performance gains and systematic automation in computational settings.

Ontology-driven optimization is the systematic use of domain ontologies to formally guide and constrain optimization workflows across a variety of computational settings. In this paradigm, ontologies—formal, machine-interpretable representations comprising classes, properties, axioms, and constraints—are leveraged to model problem spaces, encode optimization objectives and strategies, orchestrate transformations, and ultimately drive the selection, execution, and evaluation of algorithmic solutions. Ontology-driven optimization unifies traditional quantitative cost/benefit optimization, knowledge-based solver selection, schema and query transformations in data management, heuristic configuration in reasoning engines, and even prompt structuring in LLM interfaces. The defining feature is that domain semantics, expressed via ontological formalisms, become first-class inputs to the optimization process, enabling systematic exploitation of high-level structure for performance improvement, automation, and generalizability.

1. Ontology as Substrate for Optimization Semantics

In ontology-driven optimization, the ontology formalizes the foundational structure of the domain, acting as a semantic substrate on which optimization is orchestrated. Ontologies are typically modeled as tuples $$(\mathcal{C}, \mathcal{R}, \mathcal{P}, \sqsubseteq)$$, where $\mathcal{C}$ is a finite set of concept names (e.g., classes, problem types), $\mathcal{P}$ is a set of data-properties (attributes), $\mathcal{R}$ is a set of object-properties (relations, transformations), and $\sqsubseteq$ is a subclass (or variant) hierarchy. For example, in the domain-specific knowledge graph setting, the ontology encodes both entity classes and the multiplicity, inheritance, and union relationships among them (Lei et al., 2020). In optimization method taxonomies, the ontology introduces classes for problem types (ConvexOptima, NonlinearProgram, etc.), method classes (FirstOrderMethod, Metaheuristic), and their interrelations via description logic axioms and object/data properties (Nasution, 2012).

This ontological foundation allows derivation of formal mappings from problem instances to canonical classes, properties, and relations, enabling downstream processes (schema transformation, heuristic selection, benchmarking, etc.) to operate over a semantically consistent, logic-rich abstraction of the application domain.

2. Optimization Formulations and Objective Encodings

With the ontology established, domain knowledge is transformed into explicit optimization objectives or search spaces. In property-graph schema optimization, the set of possible schema transformation rules is parameterized by the ontology, with decision variables $x_r\in\{0,1\}$ for each relationship $r \in \mathcal{R}$, denoting whether a particular schema rewrite (e.g., buffer materialization, data-property replication via 1:M or M:N edge, inheritance or union flattening) is applied (Lei et al., 2020). The objective is to maximize aggregate benefit—usually defined as reduction in expected query cost or number of edge traversals—subject to resource constraints (e.g., a total space budget $S$):

$$\text{maximize} \quad Z = \sum_{r \in \mathcal{R}} \text{Benefit}(r) x_r \qquad \text{subject to} \quad \sum_{r \in \mathcal{R}} \text{Cost}(r) x_r \leq S$$

with domain-specific cost/benefit models parameterized by ontology-derived usage statistics and property sizes.

Ontology-driven frameworks for optimization method taxonomies formalize mapping from problem instances to solution strategies via object properties (e.g., $\text{usesStrategy}$, $\text{hasMethod}$), enabling reasoning systems to synthesize appropriate solver pipelines based on logical inference over the formalization (Nasution, 2012). In knowledge-based optimization, this abstraction encodes not only types, but also domain-theoretic results (Weierstrass, KKT, Envelope, and Maximum theorems) and their role in validation or solver initialization.

3. Algorithmic Patterns: Ontology-Guided Schema and Query Transformation

Ontology-driven optimization enables the systematic application of transformation rules derived from the ontology. For instance, in knowledge graph schema optimization, each ontological relationship $r$ with a particular multiplicity or inheritance type yields a candidate transformation (Algorithmic Rules $\mathcal{T}_r$: union, inheritance, one-to-many, many-to-many), synthesized from the ontology's structure (Lei et al., 2020). Transformations are filtered, prioritized, and selected via heuristics derived from ontology-based centrality (concept-centric algorithms using an ontology PageRank over $\mathcal{C}$) or from per-relation benefit/cost analysis (relation-centric strategies via 0/1 knapsack FPTAS over $\mathcal{R}$); see also the explicit pseudocode for concept-centric (Algorithm 5) and relation-centric (Algorithm 6) search.

In ontological-database query optimization, the ontology (modeled as a set of tuple-generating dependencies, TGDs) provides the formal rules for query rewriting and minimization. Backward-chaining and resolution-style algorithms use the ontology to enumerate the space of equivalent first-order query rewritings, while optimized methods leverage dependency graphs and “atom-coverage” elimination heuristics—valid only for linear TGDs—to shrink and prune the rewriting space without compromising soundness or completeness (Gottlob et al., 2014, Gottlob et al., 2011). Here, the ontology both determines admissible transformations and justifies elimination criteria via propagation paths in the dependency graph associated with $\Sigma$.

4. Knowledge-Based and Machine Learning Enhancements

A further dimension is the automation of optimization by reasoning systems that operate directly on the ontology. Knowledge-based optimization leverages description-logic reasoners or rule engines (e.g., Pellet, HermiT, SWRL) to classify new instances into ontology classes and trigger method/strategy selection rules (e.g., selecting $\text{InteriorPointMethod}$ for small ConvexOptima, or $\text{MetaheuristicStrategy}$ for NonconvexProgram) (Nasution, 2012). The selection protocol is cemented by SWRL-like rules that encode ontology-class-discriminant heuristics.

In operator and query optimization within ML or orchestration loops, ontologies serve as the backbone for constructing feature spaces and embedding topologies for machine learning models. For example, OntoTune (Yue et al., 10 Nov 2025) constructs a task-driven ontology relating SQL templates, plan operators, catalog metadata, configuration arms, and empirical performance, then uses this knowledge graph to derive semantically rich matrix and graph embeddings for convolutional and graph-based learning algorithms, enabling both improved prediction of query performance and direct integration into exploration/exploitation policies.

Similarly, in the optimization of rule-ordering heuristics for tableau-based OWL reasoners, ontology statistics (e.g., counts of $\forall, \exists, \geq, \leq$ use in axioms) guide supervised learning procedures (SVM-based models) that predict optimal expansion rule priority sets, based solely on extracted ontology features, resulting in observed performance gains of up to $1\,500\times$ over non-ontology-aware heuristics (Mehri et al., 2018).

5. Applications Across Domains

Ontology-driven optimization has demonstrated impact across a wide range of domains:

• Knowledge Graphs: Property graph schema optimization using ontology-extracted relationship types, centrality, and query workload frequency achieves up to two orders of magnitude runtime reductions on both Neo4j and JanusGraph over medical and financial enterprise graphs (Lei et al., 2020).
• Query Answering: Ontology-based rewriting and query minimization yields compact, FO-rewritable query plans compatible with standard RDBMS execution, with coverage-based elimination reducing UCQ size by up to $98\%$ in some real-world ontologies (Gottlob et al., 2014, Gottlob et al., 2011).
• Algorithm Selection: Taxonomy-driven optimization enables automated solver dispatch and strategy synthesis (e.g., mapping problem type, constraint form, dimension to method via a knowledge-based strategy pattern) (Nasution, 2012).
• Machine Learning–Driven Performance Optimization: Semantics-rich knowledge graphs inform embedding and learning strategies in systems like OntoTune, supporting performance-driven arm selection and context-aware learning policies (Yue et al., 10 Nov 2025).
• Low-Density Parity-Check Codes: Ontology-driven enumeration and elimination of cycle patterns in Tanner graphs systematically improves minimum bit-distance and spectrum estimation for non-binary LDPC codes (Chen, 2014).
• Benchmarking and Interoperability: The OPTION ontology formalizes entities, relations, and measures central to optimization benchmarking, enabling semantic integration, cross-platform data harmonization, and SPARQL-powered querying (Kostovska et al., 2021).

6. Evaluation, Complexity, and Scalability

Empirical studies have validated that ontology-driven optimization architectures yield significant performance improvements over ontology-agnostic or baseline workflows. For instance, schema optimization for knowledge graphs yields $7\times$ to $176\times$ speedups in end-to-end query workloads, with both concept-centric and relation-centric heuristics delivering optimal or near-optimal solutions under practical resource constraints, and all transformation pipelines completing in under 200 ms on large ontologies (Lei et al., 2020).

For ontology-driven query rewriting, optimized rewriting algorithms with atom-coverage elimination exhibit quadratic time overhead in CQ size per elimination, yet exponentially reduce the output query set size and join arity, remaining in $\mathrm{AC}^0$ data complexity for linear TGD classes (Gottlob et al., 2011, Gottlob et al., 2014). In machine learning configurations, ontology-driven feature extraction underpins accurate prediction of optimal heuristic configurations, with SVM classifiers achieving F1 scores of 70%–100% for heuristic selection across diverse ontology corpora (Mehri et al., 2018).

These scalability and correctness properties are ensured by careful orchestration of ontological reasoning (offering termination and correctness guarantees per logic fragment), efficient heuristics or approximation schemes (e.g., FPTAS for knapsack subproblems), and empirical validation on large, real-world or synthetic benchmarks.

7. Generalization, Interoperability, and Future Directions

Ontology-driven optimization generalizes across problem domains wherever domain knowledge admits formal, machine-readable ontological modeling. It facilitates integration of disparate data models (as in OPTION (Kostovska et al., 2021)), systematic feature construction for both symbolic and sub-symbolic learning, and the extension of rule- or transformation-based optimization into areas such as LLM prompt engineering (Palagin et al., 2023) or self-training for domain-specialized LLMs (Liu et al., 8 Feb 2025).

A robust trend is the movement from purely symbolic reasoning to hybrid, ontology-informed learning architectures, as exemplified by semantic-knowledge-augmented reinforcement learning for query and system optimization (Yue et al., 10 Nov 2025), as well as iterative, ontology-guided alignment for LLMs (Liu et al., 8 Feb 2025). The underlying principle remains the explicit, formal encoding of domain structure to ground and systematically drive the optimization process, ensuring reproducibility, interoperability, and performance guarantees unattainable by black-box or ad hoc approaches. Extensions to richer description logics, integration of additional domain ontologies, and pairing with advanced learning or statistical estimation frameworks are active areas of ongoing research.