Algorithms on Discrete Near Optimal Partitions
Applications in Higher Dimensional Domain Decomposition, Intensity Modulated Radiation Therapy (IMRT) including Arc Therapy (IMAT)
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In practice, many NP-hard combinatorial optimization problems can be formulated as partitioning problems.In such a formulation, each component in thepartition is assigned with a numerical objectivevalue and the objective function is defined as afunction on the numerical values assigned. Theoptimization problem is to minimize or maximize the objective function on all possible partitionsthat satisfy certain constraints. A feasiblepartition (i.e., a partition that satisfy all theconstraints) with the optimal objective value iscalled an optimal partition. A near-optimal partitionis a partition wit...
In practice, many NP-hard combinatorial optimization
problems can be formulated as partitioning problems.
In such a formulation, each component in the
partition is assigned with a numerical objective
value and the objective function is defined as a
function on the numerical values assigned. The
optimization problem is to minimize or maximize
the objective function on all possible partitions
that satisfy certain constraints. A feasible
partition (i.e., a partition that satisfy all the
constraints) with the optimal objective value is
called an optimal partition. A near-optimal partition
is a partition with an objective value close to the
optimal value. In a partitioning problem, by
exploiting the properties of the underlying
domain, one may be able to construct efficient
heuristic algorithms to produce near-optimal
partitions. We present algorithms for applications in
Higher Dimensional Domain Decomposition, Intensity
Modulated Radiation Therapy (IMRT) including
Intensity Modulated Arc Therapy (IMAT)
problems can be formulated as partitioning problems.
In such a formulation, each component in the
partition is assigned with a numerical objective
value and the objective function is defined as a
function on the numerical values assigned. The
optimization problem is to minimize or maximize
the objective function on all possible partitions
that satisfy certain constraints. A feasible
partition (i.e., a partition that satisfy all the
constraints) with the optimal objective value is
called an optimal partition. A near-optimal partition
is a partition with an objective value close to the
optimal value. In a partitioning problem, by
exploiting the properties of the underlying
domain, one may be able to construct efficient
heuristic algorithms to produce near-optimal
partitions. We present algorithms for applications in
Higher Dimensional Domain Decomposition, Intensity
Modulated Radiation Therapy (IMRT) including
Intensity Modulated Arc Therapy (IMAT)
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