Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

Artificial Intelligence and Its Application in Optimization under Uncertainty

Nowadays, the increase in data acquisition and availability and complexity around optimization make it imperative to jointly use artificial intelligence (AI) and optimization for devising data-driven and intelligent decision support systems (DSS). A DSS can be successful if large amounts of interactive data proceed fast and robustly and extract useful information and knowledge to help decision-making. In this context, the data-driven approach has gained prominence due to its provision of insights for decision-making and easy implementation. The data-driven approach can discover various database patterns without relying on prior knowledge while also handling flexible objectives and multiple scenarios. This chapter reviews recent advances in data-driven optimization, highlighting the promise of data-driven optimization that integrates mathematical programming and machine learning (ML) for decision-making under uncertainty and identifies potential research opportunities. This chapter provides guidelines and implications for researchers, managers, and practitioners in operations research who want to advance their decision-making capabilities under uncertainty concerning data-driven optimization. Then, a comprehensive review and classification of the relevant publications on the data-driven stochastic program, data-driven robust optimization, and data-driven chance-constrained are presented. This chapter also identifies fertile avenues for future research that focus on deep-data-driven optimization, deep data-driven models, as well as online learning-based data-driven optimization. Perspectives on reinforcement learning (RL)-based data-driven optimization and deep RL for solving NP-hard problems are discussed. We investigate the application of data-driven optimization in different case studies to demonstrate improvements in operational performance over conventional optimization methodology. Finally, some managerial implications and some future directions are provided.

Data-Driven Robust Optimization for Steam Systems in Ethylene Plants under Uncertainty

In an ethylene plant, steam system provides shaft power to compressors and pumps and heats the process streams. Modeling and optimization of a steam system is a powerful tool to bring benefits and save energy for ethylene plants. However, the uncertainty of device efficiencies and the fluctuation of the process demands cause great difficulties to traditional mathematical programming methods, which could result in suboptimal or infeasible solution. The growing data-driven optimization approaches offer new techniques to eliminate uncertainty in the process system engineering community. A data-driven robust optimization (DDRO) methodology is proposed to deal with uncertainty in the optimization of steam system in an ethylene plant. A hybrid model of extraction–exhausting steam turbine is developed, and its coefficients are considered as uncertain parameters. A deterministic mixed integer linear programming model of the steam system is formulated based on the model of the components to minimize the operating cost of the ethylene plant. The uncertain parameter set of the proposed model is derived from the historical data, and the Dirichlet process mixture model is employed to capture the features for the construction of the uncertainty set. In combination with the derived uncertainty set, a data-driven conic quadratic mixed-integer programming model is reformulated for the optimization of the steam system under uncertainty. An actual case study is utilized to validate the performance of the proposed DDRO method.

Adjustable Robust Optimization for Planning Logistics Operations in Downstream Oil Networks

The oil industry operates in a very uncertain marketplace, where uncertain conditions can engender oil production fluctuations, order cancellation, transportation delays, etc. Uncertainty may arise from several sources and inexorably affect its management by interfering in the associated decision-making, increasing costs and decreasing margins. In this context, companies often must make fast and precise decisions based on inaccurate information about their operations. The development of mathematical programming techniques in order to manage oil networks under uncertainty is thus a very relevant and timely issue. This paper proposes an adjustable robust optimization approach for the optimization of the refined products distribution in a downstream oil network under uncertainty in market demands. Alternative optimization techniques are studied and employed to tackle this planning problem under uncertainty, which is also cast as a non-adjustable robust optimization problem and a stochastic programing problem. The proposed models are then employed to solve a real case study based on the Portuguese oil industry. The results show minor discrepancies in terms of network profitability and material flows between the three approaches, while the major differences are related to problem sizes and computational effort. Also, the adjustable model shows to be the most adequate one to handle the uncertain distribution problem, because it balances more satisfactorily solution quality, feasibility and computational performance.