A Distributed Algorithm for Large-Scale Multi-Agent MINLPs

In this paper, we focus on the optimization of large-scale multi-agent systems, where agents collaboratively optimize the sum of local objective functions through their own continuous and/or discrete decision variables, subject to global coupling constraints and local constraints. The resulting Mixe...

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Published in:Proceedings of the IEEE Conference on Decision & Control pp. 3266 - 3271
Main Authors: Dong, Sheng, Xia, Weiguo
Format: Conference Proceeding
Language:English
Published: IEEE 16.12.2024
Subjects:
Consensus protocol
Couplings
Distributed algorithms
Linear programming
Mixed integer linear programming
Multi-agent systems
Numerical simulation
Optimization
Programming
ISSN:2576-2370
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Abstract In this paper, we focus on the optimization of large-scale multi-agent systems, where agents collaboratively optimize the sum of local objective functions through their own continuous and/or discrete decision variables, subject to global coupling constraints and local constraints. The resulting Mixed-Integer Nonlinear Programmings (MINLPs) are NP-hard, non-convex, and large-scale. Therefore, this paper aims to design distributed algorithms to find feasible suboptimal solutions with a guaranteed bound. To this end, considering dual decomposition as an effective method to decompose large-scale constraint-coupled optimization problems, we first show, based on the convexification effects of large-scale MINLPs, that the primal solutions from the dual are near-optimal under certain conditions. This expands recent results in Mixed-Integer Linear Programmings (MILPs) to the nonlinear case but requires additional efforts on the proof. Utilizing this result to tighten the coupling constraints, we develop a fully distributed algorithm for the tightened problem, based on dual decomposition and consensus protocols. The algorithm is guaranteed to provide feasible solutions for the original MINLP. Moreover, asymptotic suboptimality bounds are established for the obtained solution. Finally, the efficacy of the method is verified through numerical simulations.
AbstractList In this paper, we focus on the optimization of large-scale multi-agent systems, where agents collaboratively optimize the sum of local objective functions through their own continuous and/or discrete decision variables, subject to global coupling constraints and local constraints. The resulting Mixed-Integer Nonlinear Programmings (MINLPs) are NP-hard, non-convex, and large-scale. Therefore, this paper aims to design distributed algorithms to find feasible suboptimal solutions with a guaranteed bound. To this end, considering dual decomposition as an effective method to decompose large-scale constraint-coupled optimization problems, we first show, based on the convexification effects of large-scale MINLPs, that the primal solutions from the dual are near-optimal under certain conditions. This expands recent results in Mixed-Integer Linear Programmings (MILPs) to the nonlinear case but requires additional efforts on the proof. Utilizing this result to tighten the coupling constraints, we develop a fully distributed algorithm for the tightened problem, based on dual decomposition and consensus protocols. The algorithm is guaranteed to provide feasible solutions for the original MINLP. Moreover, asymptotic suboptimality bounds are established for the obtained solution. Finally, the efficacy of the method is verified through numerical simulations.
Author Dong, Sheng
Xia, Weiguo
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  givenname: Weiguo
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  email: wgxiaseu@dlut.edu.cn
  organization: Dalian University of Technology,Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education and School of Control Science and Engineering,China
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Snippet In this paper, we focus on the optimization of large-scale multi-agent systems, where agents collaboratively optimize the sum of local objective functions...
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StartPage 3266
SubjectTerms Consensus protocol
Couplings
Distributed algorithms
Linear programming
Mixed integer linear programming
Multi-agent systems
Numerical simulation
Optimization
Programming
Title A Distributed Algorithm for Large-Scale Multi-Agent MINLPs
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