آرشیو پست ها و اخبار آپتیم‌یار

 

• 𝐂𝐨𝐥𝐮𝐦𝐧 𝐆𝐞𝐧𝐞𝐫𝐚𝐭𝐢𝐨𝐧 (𝐂𝐆) 𝐚𝐧𝐝 𝐁𝐫𝐚𝐧𝐜𝐡-&-𝐏𝐫𝐢𝐜𝐞 (𝐁&𝐏) 𝐓𝐞𝐜𝐡𝐧𝐢𝐪𝐮𝐞𝐬 𝐟𝐨𝐫 𝐋𝐚𝐫𝐠𝐞-𝐬𝐜𝐚𝐥𝐞 𝐄𝐱𝐚𝐜𝐭 𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐚𝐭𝐢𝐨𝐧

  Recently, a priceless book that covers advanced algorithms, including column generation and branch-and-price techniques, for solving mathematical programming models (LP, IP, MIP), was provided by Prof. Uchoa and colleagues.Over the past few days, I have been studying the book's content, which is organized exceptionally well. I believe this book will be beneficial for many academics and researchers in operations research, analytics, and mathematical optimization, so I decided to share it with my inspiring and engaging networks.

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  from my POV, the methodological content thoroughly encompasses the following aspects ( 𝕄𝕒𝕚𝕟 ℂ𝕠𝕟𝕥𝕖𝕟𝕥𝕤 ⤵ )

  🔵 Dantzig-Wolf (DW) Decomposition

  🔵DW Reformulation of LPs

  🔵Column Generation (CG) Technique

  🔵Branch-and-Bound (B&B) and Cutting Plane (CP) Algorithms

  🔵Branch-and-Cut (B&C):Combining B&B and CP

  🔵DW + CG + B&B + CP for Efficient Optimizing Ips

  🔵Branch-and-Price (B&P)

  🔵Branch-and-Price-and-Cut (B&P&C)

  🔵Branch-and-Cut-and-Price (B&C&P)

  🔵Robust and Non Robust Cuts

  🔵Benders Decomposition and Branch-and-Benders-Cut (B&BC)

  🔵Lagrangian Relaxation (LR) + CG + CP + Subgradient for Ips

  🔵Convergence Analysis and Assessment of CG, B&P, etc. Algorithms

  🔵Additional Topics in CG and B&P (coming soon)

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  The content of these types of books not only improves methodological skills for advanced decision optimization problem-solving but also has applications in a variety of domains, including transportation and network flow/design, supply chain, healthcare systems, finance, and beyond.

  
  

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