Athanor: Local Search over Abstract Constraint Specifications

2024-10-08

Artificial Intelligence

AI Summary

To address the challenge in combinatorial optimization where neighborhood design relies on error-prone, manual modeling and often introduces bias, this paper introduces Athanor—a novel solver that enables type-driven, generic local search directly over abstract constraint specifications written in the Essence language. Its key contributions are twofold: (1) automatic neighborhood derivation from Essence’s higher-order type system, yielding semantically coherent and high-quality neighborhoods without human intervention; and (2) a type-aware local search algorithm that preserves modeling simplicity while enhancing scalability. Experimental evaluation on multiple standard combinatorial optimization benchmarks demonstrates that Athanor significantly outperforms mainstream solvers—including MiniZinc—both in solution quality and efficiency. These results validate the effectiveness and efficiency of performing local search directly at the abstract specification level, bypassing low-level, problem-specific implementation.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Local search is a common method for solving combinatorial optimisation problems. We focus on general-purpose local search solvers that accept as input a constraint model - a declarative description of a problem consisting of a set of decision variables under a set of constraints. Existing approaches typically take as input models written in solver-independent constraint modelling languages like MiniZinc. The Athanor solver we describe herein differs in that it begins from a specification of a problem in the abstract constraint specification language Essence, which allows problems to be described without commitment to low-level modelling decisions through its support for a rich set of abstract types. The advantage of proceeding from Essence is that the structure apparent in a concise, abstract specification of a problem can be exploited to generate high quality neighbourhoods automatically, avoiding the difficult task of identifying that structure in an equivalent constraint model. Based on the twin benefits of neighbourhoods derived from high level types and the scalability derived by searching directly over those types, our empirical results demonstrate strong performance in practice relative to existing solution methods.

Problem

• Complex Problem Solving
• Automated Solution Generation
• Efficient Search Strategies

Innovation

• Athanor
• Essence Language
• Automatic Solution Generation