Optimization Task Decomposition
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A Optimization Task Decomposition is an optimization task that involves breaking down a complex optimization problem into smaller, more manageable sub-tasks that can be solved independently or in a coordinated manner.
- Context:
- It can (typically) be utilized to make large-scale optimization problems more tractable.
- It can (often) leverage the structure of an optimization problem to enable efficient, parallelizable, or distributed solution methods.
- It can include various decomposition strategies, such as Primal Decomposition, Dual Decomposition, and Decomposition with Constraints, tailored to the specific characteristics of the optimization problem.
- It can apply to a wide range of domains, including network flow optimization, rate control in networks, and large-scale linear programming.
- It can lead to decentralized solution methods, where sub-tasks are solved independently by different agents or processors, followed by a coordination mechanism to achieve a solution to the original problem.
- It can involve the formulation of a Master Problem and one or more Sub-problems, with the master problem coordinating the overall solution process based on the solutions to the sub-problems.
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- Example(s):
- The decomposition of a network flow optimization task into sub-tasks, each representing the flow optimization for a subset of the network, coordinated through dual variables representing the prices for using network links.
- The division of a large-scale linear programming problem into smaller linear programming problems that can be solved in parallel, with a master problem coordinating the solutions to ensure consistency across the decomposed tasks.
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- Counter-Example(s):
- A direct approach to solving an optimization problem without breaking it down into sub-tasks, often applicable to small-scale or less complex optimization problems.
- Heuristic methods that do not explicitly decompose the optimization task but instead search for a good enough solution through other means, such as genetic algorithms or simulated annealing.
- See: Optimization Problem, Parallel Computing, Distributed Computing, Linear Programming, Network Optimization.