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

ABSTRACT

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.

KEYWORDS:

• Collaborative optimization
• decentralized coordination
• multi-objective linear programming
• block angular structure
• multi-agent

View correction statement:

Correction

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Evans Sowah Okpoti http://orcid.org/0000-0002-7776-7950

In-Jae Jeong http://orcid.org/0000-0001-7824-6391

Additional information

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).