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DOI: 10.4230/LIPIcs.CP.2026.56

Constraint Solving and Particle Swarm Optimization for Fixture Layout Optimization

Authors: Anna Vitali, Roberto Amadini, Vittorio Maniezzo, and Maurizio Gabbrielli

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

Abstract

In the wood industry, ensuring the stability and immobility of a workpiece during machining is essential. Vacuum suction cups are commonly used as fixtures, as they can rotate to better conform to the workpiece perimeter. However, this rotational capability introduces additional complexity into fixture placement. This paper addresses the problem of optimally positioning rotatable fixtures by combining two complementary techniques. First, we solve a restricted version of the problem that neglects rotations using a constraint solver, yielding an initial feasible solution. This solution is then refined using a Particle Swarm Optimization algorithm that accounts for rotation. Experimental results show that the quality of the initial solution significantly influences the final placement, and that the proposed approach can effectively support expert operators in making improved decisions.

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Anna Vitali, Roberto Amadini, Vittorio Maniezzo, and Maurizio Gabbrielli. Constraint Solving and Particle Swarm Optimization for Fixture Layout Optimization. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 56:1-56:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{vitali_et_al:LIPIcs.CP.2026.56,
  author =	{Vitali, Anna and Amadini, Roberto and Maniezzo, Vittorio and Gabbrielli, Maurizio},
  title =	{{Constraint Solving and Particle Swarm Optimization for Fixture Layout Optimization}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{56:1--56:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.56},
  URN =		{urn:nbn:de:0030-drops-266897},
  doi =		{10.4230/LIPIcs.CP.2026.56},
  annote =	{Keywords: Constraint Programming, Mixed-Integer Programming, Particle Swarm Optimization, Fixture Layout Optimization, Industrial Application}
}

Document

DOI: 10.4230/OASIcs.Gabbrielli.7

Abstract Interpretation, Symbolic Execution and Constraints

Authors: Roberto Amadini, Graeme Gange, Peter Schachte, Harald Søndergaard, and Peter J. Stuckey

Published in: OASIcs, Volume 86, Recent Developments in the Design and Implementation of Programming Languages (2020)

Abstract

Abstract interpretation is a static analysis framework for sound over-approximation of all possible runtime states of a program. Symbolic execution is a framework for reachability analysis which tries to explore all possible execution paths of a program. A shared feature between abstract interpretation and symbolic execution is that each - implicitly or explicitly - maintains constraints during execution, in the form of invariants or path conditions. We investigate the relations between the worlds of abstract interpretation, symbolic execution and constraint solving, to expose potential synergies.

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Roberto Amadini, Graeme Gange, Peter Schachte, Harald Søndergaard, and Peter J. Stuckey. Abstract Interpretation, Symbolic Execution and Constraints. In Recent Developments in the Design and Implementation of Programming Languages. Open Access Series in Informatics (OASIcs), Volume 86, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{amadini_et_al:OASIcs.Gabbrielli.7,
  author =	{Amadini, Roberto and Gange, Graeme and Schachte, Peter and S{\o}ndergaard, Harald and Stuckey, Peter J.},
  title =	{{Abstract Interpretation, Symbolic Execution and Constraints}},
  booktitle =	{Recent Developments in the Design and Implementation of Programming Languages},
  pages =	{7:1--7:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-171-9},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{86},
  editor =	{de Boer, Frank S. and Mauro, Jacopo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Gabbrielli.7},
  URN =		{urn:nbn:de:0030-drops-132294},
  doi =		{10.4230/OASIcs.Gabbrielli.7},
  annote =	{Keywords: Abstract interpretation, symbolic execution, constraint solving, dynamic analysis, static analysis}
}

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Constraint Solving and Particle Swarm Optimization for Fixture Layout Optimization

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Abstract Interpretation, Symbolic Execution and Constraints

Abstract

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