Learning Size Independent Constraint Models from Input Data and Positive and Negative Example Solutions

Helmut Simonis

cs.AIOct 9, 2026

Learning Size Independent Constraint Models from Input Data and Positive and Negative Example Solutions

Authors: Helmut Simonis

Organizations: School of Computer Science and Information Technology, University College Cork, Ireland

Abstract

In this paper we describe a Constraint Acquisition Tool that generates size independent constraint programs from input data and positive and negative example solutions of multiple problem instances. The system finds size specific models based on typical constraint patterns over global and binary constraints, then generalizes the models to a size independent model that can be run on unseen input data. The system produces MiniZinc code as well as a textual description of the model. We evaluate the tool on the example problems of the PTHG21 Challenge and show the feasibility of the approach.

Figures & tables

Panel of Figure 1 — Figure 1: Intended Use Case

Positive Example	Input Parameters
⬇ 1 "inputData" : { 2 "lambda" : 2 , 3 "v" : 6 , 4 "k" : 3 5 },

Table 1: Example Problem Instance (Problem 12, BIBD)

Panel of Figure 2 — Figure 2: System Architecture and Evaluation Methodology

Panel of Figure 3 — Figure 3: Pattern Generator for Matrix

Input Parameters			Variable Definition			Symbolic Values
$\lambda$	v	k	domain	rows	columns	rowsum	colsum	scalarproduct
2	6	3	0..1	6	10	5	3	2
1	7	3	0..1	7	7	3	3	1
4	6	3	0..1	6	20	10	3	4
1	9	3	0..1	9	12	4	3	1
2	7	3	0..1	7	14	6	3	2

Figure 4: Input Samples for Formula Generator

Panel of Figure 5 — Figure 5: Graph Representation of Generic Model

Type	Problem	Source	Features
1	Graph Coloring	ALICE, CHIP	graph as data, optimization
2	N-Queens	CSPlib 054
3	Warehouse Location	CSPlib 034	cost matrix/vector as data, implicit cost variables
4	Golomb Ruler	CSPlib 006	implicit decision variables, optimization
5	Sudoku	Pre-assignment	pre-assignment as data, single solution
6	Sudoku	No pre-assignment	many solutions

Table 2: PTHG21 Problems

Problem	Description	Instances	Positive Samples	Negative Samples	Tests	Note
			Classified Correctly
1	Graph Coloring	10	100.00	100.00	100.00
2	N-Queens	10	100.00	100.00	100.00
3	Warehouse Location	10	100.00	100.00	100.00
4	Golomb Ruler	8	100.00	100.00	100.00	1
5	Sudoku (with Hints)	10	100.00	100.00	100.00

Table 3: Results on PTHG21 Benchmarks

Constraint Programming

Constraint programming models combinatorial problems as variables and constraints, using propagation and search to find feasible or optimal solutions.

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May 25, 2026J/K move · Enter open · S save

MPMMine: Better Benchmarks for Constraint Acquisition

Rafał Stachowiak, Tomasz P. Pawlak

Institute of Computing Science, Poznan Univeristy of Technology, Piotrowo 2, Poznań, Poland

Benchmark Construction Benchmark Design Natural Language to Optimization Modeling Operations Research

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Constraint Acquisition (CA) and related research on the validation and enhancement of Mathematical Programming (MP) models using domain knowledge artifacts are currently limited by inadequate benchmarks. The existing benchmarks are loosely organized, provide inconsistent types and formats of artifacts for individual problems, are designed for benchmarking solvers rather than CA algorithms, include narrow classes of problems, or omit crucial details for the reproducibility of experiments and fair comparison of CA methods. We develop a benchmark dataset, a supporting software package, and a benchmarking tool crafted for the consistent, systematic, and comprehensive assessment of CA algorithms, bridging the gap in algorithmic development and experimental infrastructure. This work presents MPMMine, a benchmark suite designed to assess algorithms that discover, validate, and enhance MP models using diverse artifacts. The development of MPMMine is guided by design rules supporting consistency, standardization, completeness, extensibility, openness, and version control. It adopts a uniform structure and relies on open formats. It provides alternative formulations of MP models per problem, tens of parameter instantiations per MP model, and thousands of exemplary solutions and non-solutions in discrete, continuous, and mixed domains, alongside natural-language descriptions to support text-to-model methods. The mpmmine-py Python package provides an application programming interface for accessing the dataset artifacts. The MPMMine Leaderboard is a~tool that systematically evaluates existing CA algorithms using MPMMine under consistent conditions. It leverages open source implementations, runs them in isolated containers adapting input/output to their needs to build an extensive, interactive scoreboard.

Abstract

Constraint Programming

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