Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

Volume 7874 of the series Lecture Notes in Computer Science pp 128-143

An MDD Approach to Multidimensional Bin Packing

  • Brian KellAffiliated withLancaster UniversityDepartment of Mathematical Sciences, Carnegie Mellon University
  • , Willem-Jan van HoeveAffiliated withLancaster UniversityTepper School of Business, Carnegie Mellon University

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We investigate the application of multivalued decision diagrams (MDDs) to multidimensional bin packing problems. In these problems, each bin has a multidimensional capacity and each item has an associated multidimensional size. We develop several MDD representations for this problem, and explore different MDD construction methods including a new heuristic-driven depth-first compilation scheme. We also derive MDD restrictions and relaxations, using a novel application of a clustering algorithm to identify approximate equivalence classes among MDD nodes. Our experimental results show that these techniques can significantly outperform current CP and MIP solvers.