(624b) Data-Driven Coordination in Enterprise-Wide Optimization

Model-based optimization of operations is key for chemical enterprises to remain competitive in an environment of increasingly complex economical, sustainability, and safety considerations [1]. Enterprise-wide optimization (EWO) aims to coordinate previously disconnected decision-making. To this end, optimization models can be integrated into a single model wherein subproblems are coupled via few complicating variables and constraints [2]. When the complicating, also called shared or global, variables are sparse compared to the number of local, or private, subproblem variables, these applications lend themselves well to distributed optimization and decomposition techniques [3]. Examples include the planning and operation of supply chains where regional agents decide on the shared material streams that minimize a private cost. In this work, we show that derivative-free optimization (DFO) solvers present a promising alternative to distributed optimization to coordinate subproblems often arising in EWO.

Distributed optimization is a powerful tool that allows for the solution of large-scale nonlinear problems with potential significant computational savings using only limited information exchange. ADMM and ALADIN have garnered special attention in the chemical engineering literature as distributed optimization techniques [4-7]. Yet, both algorithms display drawbacks that impede practical applicability: ADMM, as a subgradient method, requires many iterations to converge to a high-accuracy solution; ALADIN requires cheap gradient expressions and an approximation of the Hessian of the subproblems. This gradient information might not be available if the optimal solution of the subproblems requires ‘expensive black-box’ evaluations. This is the case in many process systems engineering (PSE) applications: when the subproblems sample the output of proprietary simulation queries; when expressions for the local objectives and constraints are not available for security, privacy, or organisation reasons; when multiple business entities have to coordinate on the design of a supply chain while respecting local constraints and privacy; or when faced with multi-objective optimization, where each objective is given by a black-box simulation or optimization model.

Derivative-free optimization (DFO), also called blackbox or simulation(-based) optimization, is often used to optimize blackboxes, namely systems whose gradient expressions are not readily available [8]. While DFO has been benchmarked on typical process systems engineering problems [9] and bilevel problems [10,11], it has not been used to coordinate sparsely connected distributed subproblems. In this work, we consider the coordination of blackbox subproblems using no model information. We use DFO to find the shared variables that minimize the sum of private subproblem objectives. Four DFO solvers are compared under this data-driven coordination framework to ADMM on three EWO problems: collaborative learning, facility location, and multi-objective coordination. We show that the data-driven coordination scheme allows for convergence to the same optimum achieved with distributed optimization schemes. We highlight under which mathematical and organisational conditions the data-driven scheme is encouraged over ADMM and how these conditions inform the choice of DFO solver. Finally, we point towards further research avenues involving stochasticity and black-box constraints where data-driven strategies might outperform distributed optimization.

References:

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