Stochastic Cutting Planes for Data-Driven Optimization

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to an $\epsilon$-optimal solution with high probability. Numerical experiments on several problems show that stochastic cutting planes is able to deliver a multiple order-of-magnitude speedup compared to the standard cutting-plane method. We further experimentally explore the lower limits of sampling for stochastic cutting planes and show that for many problems, a sampling size of $O(\sqrt[3]{n})$ appears to be sufficient for high quality solutions

Optimal control of dynamical systems with time-invariant probabilistic parametric uncertainties

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, February 2018.Cataloged from PDF version of thesis. "September 2017." Handwritten on title page "February 2018."Includes bibliographical references (pages 117-121).The importance of taking model uncertainties into account during controller design is well established. Although this theory is well developed and quite mature, the worst-case uncertainty descriptions assumed in robust control formulations are incompatible with the uncertainty descriptions generated by commercial model identification software that produces time-invariant parameter uncertainties typically in the form of probability distribution functions. This doctoral thesis derives rigorous theory and algorithms for the optimal control of dynamical systems with time-invariant probabilistic uncertainties. The main contribution of this thesis is new feedback control design algorithms for linear time-invariant systems with time-invariant probabilistic parametric uncertainties and stochastic noise. The originally stochastic system of equations is transformed into an equivalent deterministic system of equations using polynomial chaos (PC) theory. In addition, the H2- and H[infinity symbol]-norms commonly used to describe the effect of stochastic noise on output are transformed such that the eventual closed-loop performance is insensitive to parametric uncertainties. A robustifying constant is used to enforce the closed-loop stability of the original system of equations. This approach results in the first PC-based feedback control algorithm with proven closed-loop stability, and the first PC-based feedback control formulation that is applicable to the design of fixed-order state and output feedback control designs. The numerical algorithm for the control design is formulated as optimization over bilinear matrix inequality (BMI) constraints, for which commercial software is available. The effectiveness of the approach is demonstrated in two case studies that include a continuous pharmaceutical manufacturing process. In addition to model uncertainties, chemical processes must operate within constraints, such as upper and lower bounds on the magnitude and rate of change of manipulated and/or output variables. The thesis also demonstrates an optimal feedback control formulation that explicitly addresses both constraints and time-invariant probabilistic parameter uncertainties for linear time-invariant systems. The H2-optimal feedback controllers designed using the BMI formulations are incorporated into a fast PC-based model predictive control (MPC) formulation. A numerical case study demonstrates the improved constraint satisfaction compared to past polynomial chaos-based formulations for model predictive control.by Dongying Erin Shen.Ph. D

Advanced methodologies for reliability-based design optimization and structural health prognostics

Failures of engineered systems can lead to significant economic and societal losses. To minimize the losses, reliability must be ensured throughout the system's lifecycle in the presence of manufacturing variability and uncertain operational conditions. Many reliability-based design optimization (RBDO) techniques have been developed to ensure high reliability of engineered system design under manufacturing variability. Schedule-based maintenance, although expensive, has been a popular method to maintain highly reliable engineered systems under uncertain operational conditions. However, so far there is no cost-effective and systematic approach to ensure high reliability of engineered systems throughout their lifecycles while accounting for both the manufacturing variability and uncertain operational conditions. Inspired by an intrinsic ability of systems in ecology, economics, and other fields that is able to proactively adjust their functioning to avoid potential system failures, this dissertation attempts to adaptively manage engineered system reliability during its lifecycle by advancing two essential and co-related research areas: system RBDO and prognostics and health management (PHM). System RBDO ensures high reliability of an engineered system in the early design stage, whereas capitalizing on PHM technology enables the system to proactively avoid failures in its operation stage. Extensive literature reviews in these areas have identified four key research issues: (1) how system failure modes and their interactions can be analyzed in a statistical sense; (2) how limited data for input manufacturing variability can be used for RBDO; (3) how sensor networks can be designed to effectively monitor system health degradation under highly uncertain operational conditions; and (4) how accurate and timely remaining useful lives of systems can be predicted under highly uncertain operational conditions. To properly address these key research issues, this dissertation lays out four research thrusts in the following chapters: Chapter 3 - Complementary Intersection Method for System Reliability Analysis, Chapter 4 - Bayesian Approach to RBDO, Chapter 5 - Sensing Function Design for Structural Health Prognostics, and Chapter 6 - A Generic Framework for Structural Health Prognostics. Multiple engineering case studies are presented to demonstrate the feasibility and effectiveness of the proposed RBDO and PHM techniques for ensuring and improving the reliability of engineered systems within their lifecycles

Operational model for empty container repositioning

Ph.DDOCTOR OF PHILOSOPH

Petroleum Refining and Petrochemical Industry Integration and Coordination under Uncertainty

Petroleum refining and the petrochemical industry account for a major share in the world energy and industrial market. In many situations, they represent the economy back-bone of industrial countries. Today, the volatile environment of the market and the continuous change in customer requirements lead to constant pressure to seek opportunities that properly align and coordinate the different components of the industry. In particular, petroleum refining and petrochemical industry coordination and integration is gaining a great deal of interest. However, previous research in the field either studied the two systems in isolation or assumed limited interactions between them. The aim of this thesis is to provide a framework for the planning, integration and coordination of multisite refinery and petrochemical networks using proper deterministic, stochastic and robust optimization techniques. The contributions of this dissertation fall into three categories; namely, a) Multisite refinery planning, b) Petrochemical industry planning, and c) Integration and coordination of multisite refinery and petrochemical networks. The first part of this thesis tackles the integration and coordination of a multisite refinery network. We first address the design and analysis of multisite integration and coordination strategies within a network of petroleum refineries through a mixed-integer linear programming (MILP) technique. The integrated network design specifically addresses intermediate material transfer between processing units at each site. The proposed model is then extended to account for model uncertainty by means of two-stage stochastic programming. Parameter uncertainty was considered and included coefficients of the objective function and right-hand-side parameters in the inequality constraints. Robustness is analyzed based on both model robustness and solution robustness, where each measure is assigned a scaling factor to analyze the sensitivity of the refinery plan and the integration network due to variations. The proposed technique makes use of the sample average approximation (SAA) method with statistical bounding techniques to give an insight on the sample size required to give adequate approximation of the problem. The second part of the thesis addresses the strategic planning, design and optimization of a network of petrochemical processes. We first set up and give an overview of the deterministic version of the petrochemical industry planning model adopted in this thesis. Then we extend the model to address the strategic planning, design and optimization of a network of petrochemical processes under uncertainty and robust considerations. Similar to the previous part, robustness is analyzed based on both model robustness and solution robustness. Parameter uncertainty considered in this part includes process yield, raw material and product prices, and lower product market demand. The Expected Value of Perfect Information (EVPI) and Value of the Stochastic Solution (VSS) are also investigated to numerically illustrate the value of including the randomness of the different model parameters. The final part of this dissertation addresses the integration between the multisite refinery system and the petrochemical industry. We first develop a framework for the design and analysis of possible integration and coordination strategies of multisite refinery and petrochemical networks to satisfy given petroleum and chemical product demand. The main feature of the work is the development of a methodology for the simultaneous analysis of process network integration within a multisite refinery and petrochemical system. Then we extend the petroleum refinery and petrochemical industry integration problem to consider different sources of uncertainties in model parameters. Parameter uncertainty considered includes imported crude oil price, refinery product price, petrochemical product price, refinery market demand, and petrochemical lower level product demand. We apply the sample average approximation (SAA) method within an iterative scheme to generate the required scenarios and provide solution quality by measuring the optimality gap of the final solution