201. Distributed optimization algorithm for multi-agent optimization problems using consensus control
- Author
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Tatsushi NISHI, Naoto DEBUCHI, and Ziang LIU
- Subjects
distributed optimization ,unit commitment ,supply chain planning ,subgradient method ,lagrangian decomposition and coordination approach ,Engineering machinery, tools, and implements ,TA213-215 ,Mechanical engineering and machinery ,TJ1-1570 - Abstract
The distributed optimization algorithms using consensus control are proposed for solving multi-agent optimization problems. The multi-agent optimization problem has discrete and continuous decision variables to minimize the sum of local cost functions with local and global constraints. The problem is formulated as a mixed integer programming problem. In this study, we propose two distributed optimization algorithms to solve the problem. A feasible solution is obtained by solving the continuous optimization problem using an existing distributed optimization method with consensus control and solving the discrete optimization problem by fixing 0-1 variables. In the proposed method 1, all possible combinations of a binary variables are searched. Since all combinations are searched, the exact optimal solution can be obtained. However, it is difficult to apply to large-scale problems. In the proposed method 2, we derive the solution of binary variables by using Lagrangian decomposition and coordination approach. The proposed method 2 can provide approximate solutions for more complex problems within a practical computation time. These methods are successfully implemented to obtain near-optimal solutions in a distributed environment for supply chain planning problems for multiple companies and multi-agent unit commitment problem. The number of information exchanges in the two proposed methods is evaluated. The information exchange for these methods can significantly reduce the data exchange compared with the conventional centralized optimization method. Computational experiments for the multi-agent unit commitment problems and supply chain planning problems for multiple companies demonstrate the effectiveness of the proposed methods.
- Published
- 2024
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