Distributed and Asynchronous Coordination of a Mixed-Integer Linear
System via Surrogate Lagrangian Relaxation
Abstract
With the emergence of Internet of Things that allows communications and
local computations, and with the vision of Industry 4.0, a foreseeable
transition is from centralized system planning and operation toward
decentralization with interacting components and subsystems, e.g.,
self-optimizing factories. In this paper, a new “price-based”
decomposition and coordination methodology is developed to efficiently
coordinate subsystems such as machines and parts, which are described by
Mixed-Integer Linear Programming (MILP) formulations, in a distributed
and asynchronous way. To ensure low communication requirements,
exchanges between the “coordinator” and subsystems are limited to
“prices” (Lagrangian multipliers) broadcast by the coordinator, and to
subsystem solutions sent to the coordinator. Asynchronous coordination,
however, may lead to convergence difficulties since the order in which
subsystem solutions arrive at the coordinator is not predefined as a
result of uncertainties in communication and solving times. Under
realistic assumptions of finite communication and solve times,
convergence of our method is proved by innovatively extending Lyapunov
Stability Theory. Numerical testing of generalized assignment problems
through simulation demonstrates that the method converges fast and
provides near-optimal results, paving the way for self-optimizing
factories in the future.