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A decentralized coordination algorithm for multi-objective linear programming with block angular structure

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posted on 18.12.2019 by Evans Sowah Okpoti, In-Jae Jeong

This article considers linear multi-objective programming problems with block angular structure, which are analogous to multi-disciplinary optimization environments where disciplines must collaborate to achieve a common overall goal. In this decentralized environment, a mechanism to guide locally optimized decision makers’ solutions to a Pareto-optimal solution without sharing the entire local information is developed. The mechanism is based on an augmented Lagrangian approach to generate a solution and is separated into two phases: phase I determines an ideal point for each of the single objectives and phase II searches for a compromise solution starting from a single ideal point. Theoretical results show that the algorithm converges and the solution generated is Pareto optimal. The algorithm’s effectiveness is demonstrated via an illustrative example and a real-world bi-objective re-entrant flow-shop production planning problem. The real-world experimental results showed that the decentralized method had an average 50% better performance compared to other centralized methods.

Funding

This work was supported by the Basic Science Research Program through the National Research Foundation of Korea, funded by the Ministry of Education [grant number 2014R1A1A2058147] and the Ministry of Science, ICT and Future Planning (grant number 2017R1E1A1A03070435).

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