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<p>Assigning feeders and nozzles is an important step in the setup of pick-and-place machines. We study this feeder and nozzle assignment problem (FNAP) for a representative machine from Kulicke &amp; Soffa (K&amp;S). The goal is to assign nozzles and feeders so that a given set of printed circuit boards can be produced while minimizing cycle time. The heuristic currently used by K&amp;S reliably finds feasible assignments but performs poorly regarding nozzle exchanges, which are strongly correlated with cycle time. To address this, we propose a novel algorithm that tries to find <i>k</i> feasible assignments that are as diverse as possible, for some parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k&gt;1\)</EquationSource> </InlineEquation>. By maximizing solution diversity, our approach increases the likelihood of finding initial solutions that can yield shorter cycle times after further optimization. On real-world instances, our algorithm achieves at least half the theoretical maximum diversity in over 70% of cases for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k \le 10\)</EquationSource> </InlineEquation>. It also produces assignments with estimated nozzle exchanges roughly half those of the current heuristic in 95% of cases, while reducing the number of instances incorrectly classified as infeasible at only a small cost in runtime.</p>

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Using diversity for optimizing cycle time for a pick-and-place machine

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月16日

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  • Mark de Berg,
  • Ugnė Laima Čižiūtė,
  • Dirk Gerrits,
  • Andrés López Martínez,
  • Frits Spieksma

摘要

Assigning feeders and nozzles is an important step in the setup of pick-and-place machines. We study this feeder and nozzle assignment problem (FNAP) for a representative machine from Kulicke & Soffa (K&S). The goal is to assign nozzles and feeders so that a given set of printed circuit boards can be produced while minimizing cycle time. The heuristic currently used by K&S reliably finds feasible assignments but performs poorly regarding nozzle exchanges, which are strongly correlated with cycle time. To address this, we propose a novel algorithm that tries to find k feasible assignments that are as diverse as possible, for some parameter \(k>1\) . By maximizing solution diversity, our approach increases the likelihood of finding initial solutions that can yield shorter cycle times after further optimization. On real-world instances, our algorithm achieves at least half the theoretical maximum diversity in over 70% of cases for \(k \le 10\) . It also produces assignments with estimated nozzle exchanges roughly half those of the current heuristic in 95% of cases, while reducing the number of instances incorrectly classified as infeasible at only a small cost in runtime.