(52f) Surrogate-Based Derivative-Free Optimization of a Multi-Enterprise Supply Chain Simulation

Simulations are widely used to capture the details of a complex physical or scientific phenomenon. Optimizing over these simulations is thus a problem that is often encountered and is of growing interest. As these simulations are computationally expensive or have no available closed form, this problem is often nontrivial. To address this, a number of derivative-free optimization (DFO) algorithms have been developed in the last couple of decades [1][2]. These algorithms have shown a great potential to be applied for practical problems. Efficient use of surrogate models plays an important role towards the success of many of these algorithms [3]. Some of the algorithms utilize a surrogate model for approximations in small local regions whereas other algorithms use it for global approximation over the entire feasible domain. As the search progresses, quality of the sample set is not maintained globally because of concentrated local searches. As a result, factors such as local variability in the output response may lead to a poor surrogate model that exhibits high variance and poor prediction accuracy. This highlights the need for improved surrogate modeling strategy for DFO.

In this work, an agent-based simulation model is considered for a supply chain network consisting of multiple enterprises. Agent-based models are popular in the area of the supply chain because of their ability to model complex interactions between entities. The problem is to find optimal inventory allocation such that the total cost of the supply chain is minimized. This problem has been shown to be highly nonconvex in the presence of complex interaction mechanisms such as auctions[4]. The problem becomes more difficult as problem size increases with the size of the supply chain. Moreover, the total cost of the supply chain is a combination of several components such as transport cost, inventory cost, production cost, and backorder cost. These individual components display a local variability in the objective function with respect to warehouse capacity. As a result, the output has multiple closely placed local optima. Because of these variations, and because of the quality of sample design, this problem becomes difficult for DFO.

Finally, this work proposes a DFO framework based on Gaussian process regression models with noise variance estimation. The noise variance or nugget parameter is estimated along with other model hyperparameters by maximizing likelihood estimate. Starting from a space filling design, this algorithm relies on expected improvement based adaptive sampling strategy to perform a global search. A model based local search is triggered when promising samples are found during the global search. A comparison of proposed framework with competitive DFO algorithms is presented on test problems and on a large supply chain problem of up to 30 dimensions.

References

[1] A. Conn, K. Scheinberg, and L. Vicente, Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics, 2009.

[2] L. M. Rios and N. V. Sahinidis, “Derivative-free optimization: A review of algorithms and comparison of software implementations,” J. Glob. Optim., vol. 56, no. 3, pp. 1247–1293, 2013.

[3] A. Bhosekar and M. Ierapetritou, “Advances in surrogate based modeling, feasibility analysis, and optimization: A review,” Comput. Chem. Eng., vol. 108, pp. 250–267, 2018.

[4] N. Sahay and M. Ierapetritou, “Multienterprise supply chain: Simulation and optimization,” AIChE J., vol. 62, no. 9, pp. 3392–3403, 2016.