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A DDLM-based Method for Solving Distributed Problems

This paper presents a Distributed Discrete Lagrange Method (DDLM) for solving distributed constraint satisfaction problems (CSPs). The method extends traditional continuous Lagrange multiplier techniques by employing a discrete approach, leveraging a SAT Solver for the main iteration. We demonstrate the effectiveness of the DDLM through 2000 experimental runs on benchmark problems, including updates to iterations and transformed problems. Our findings indicate that while the method works efficiently, additional mathematical theories are required to enhance performance and address the challenge of local minima.

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A DDLM-based Method for Solving Distributed Problems

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  1. A DDLM-based Method for Solving Distributed Problems Tang Yi

  2. Lagrange Multiplier Method • Lagrange Multiplier min f(x) subject to g(x) = 0 Lagrange Function: L(x, ) = f(x) +  g(x) • Traditional method is continuous • Discrete method : DLM

  3. DDLM: Distributed discrete Lagrange Method • An extension to DLM • Main iteration

  4. DDLM based SAT Solver • Transformed problems: • Update the iteration

  5. Experimental Results • 2000 runs in uf100-430 :

  6. Conclusion • A method to solve distributed CSPs with some mathematics equations. • More mathematics theory can be added to improve performance • Also exists local minimum, need other methods to escape from a local minimum.

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