Object-oriented interaction in resource constrained scheduling
Information Processing Letters
Exhaustive approaches to 2D rectangular perfect packings
Information Processing Letters
A new constraint programming approach for the orthogonal packing problem
Computers and Operations Research
Edge Finding for Cumulative Scheduling
INFORMS Journal on Computing
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Search Strategies for Rectangle Packing
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
New improvements in optimal rectangle packing
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A resource cost aware cumulative
CSCLP'09 Proceedings of the 14th Annual ERCIM international conference on Constraint solving and constraint logic programming
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
LP bounds in various constraint programming approaches for orthogonal packing
Computers and Operations Research
Consecutive Ones Matrices for Multi-dimensional Orthogonal Packing Problems
Journal of Mathematical Modelling and Algorithms
Conservative scales in packing problems
OR Spectrum
Optimal rectangle packing: an absolute placement approach
Journal of Artificial Intelligence Research
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This paper describes new filtering methods for the cumulative constraint. The first method introduces bounds for the so called longest cumulative hole problem and shows how to use these bounds in the context of the non-overlapping constraint. The second method introduces balancing knapsack constraints which relate the total height of the tasks that end at a specific timepoint with the total height of the tasks that start at the same time-point. Experiments on tight rectangle packing problems show that these methods drastically reduce both the time and the number of backtracks for finding all solutions as well as for finding the first solution. For example, we found without backtracking all solutions to 66 perfect square instances of order 23-25 and sizes ranging from 332 × 332 to 661 × 661.