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\begin{document}

\title{Data-driven coordination of expensive subproblems in enterprise-wide
optimization}



\author[1]{Damien van de Berg}%
\author[1]{Panagiotis Petsagkourakis}%
\author[2]{Nilay Shah}%
\author[1]{Ehecatl  Del Rio-Chanona}%
\affil[1]{Imperial College London}%
\affil[2]{Imperial College}%


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  \date{May 20, 2024}


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\begin{abstract}
While decomposition techniques in mathematical programming are usually
designed for numerical efficiency, coordination problems within
enterprise-wide optimization are often limited by organizational rather
than numerical considerations. We propose a `data-driven' coordination
framework which manages to recover the same optimum as the equivalent
centralized formulation while allowing coordinating agents to retain
autonomy, privacy, and flexibility over their own objectives,
constraints, and variables. This approach updates the coordinated, or
shared, variables based on derivative-free optimization (DFO) using only
coordinated variables to agent-level optimal subproblem evaluation
`data'. We compare the performance of our framework using different DFO
solvers (CUATRO, Py-BOBYQA, DIRECT-L, GPyOpt) against conventional
distributed optimization (ADMM) on three case studies: collaborative
learning, facility location, and multi-objective blending. We show that
in low-dimensional and nonconvex subproblems, the
exploration-exploitation trade-offs of DFO solvers can be leveraged to
converge faster and to a better solution than in distributed
optimization%
\end{abstract}%



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