This dissertation addresses the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second approach is Lagrangean decomposition. We present numerical results for a process network planning problem and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly. To further generalize this work, we also propose a graph-theory algorithm for non-anticipativity constraint reduction in problems with arbitrary scenario sets. Finally, in a break from the rest of the thesis, we present the basics of stochastic programming for non-expert users.
Optimization under uncertainty has been an active area of research for many years. However, its application in Process Synthesis has faced a number of important barriers that have prevented its effective application. Barriers include availability of information on the uncertainty of the data (ad-hoc or historical), determination of the nature of the uncertainties (exogenous vs. endogenous), selection of an appropriate strategy for hedging against uncertainty (robust optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty in the interpretation of the results by non-expert users. In this paper, we describe recent advances that have addressed some of these barriers.
Optimization under uncertainty has been an active area of research for many years. However, its application in Process Systems Engineering has faced a number of important barriers that have prevented its effective application. Barriers include availability of information on the uncertainty of the data (ad-hoc or historical), determination of the nature of the uncertainties (exogenous vs. endogenous), selection of an appropriate strategy for hedging against uncertainty (robust/chance constrained optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty of interpretation of the results by non-expert users. In this paper, we describe recent advances that have addressed some of these barriers for mostly linear models.
This paper presents a tutorial on the state-of-the-art software for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classified according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders decomposition, dual decomposition and progressive hedging, as well as possible improvements and variants. We also present extensive numerical results to underline the properties and performance of each algorithm using software implementations, including DECIS, FORTSP, PySP, and DSP. Finally, we discuss the strengths and weaknesses of each methodology and propose future research directions.
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