Sampling-Based Progressive Hedging Algorithms in Two-Stage Stochastic Programming

نویسندگان

  • Nezir Aydin
  • Alper Murat
  • Boris S. Mordukhovich
چکیده

Abstract Most real-world optimization problems are subject to uncertainties in parameters. In many situations where the uncertainties can be estimated to a certain degree, various stochastic programming (SP) methodologies are used to identify robust plans. Despite substantial advances in SP, it is still a challenge to solve practical SP problems, partially due to the exponentially increasing number of scenarios representing the underlying uncertainties. Two commonly used SP approaches to tackle this complexity are approximation methods, i.e., Sample Average Approximation (SAA), and decomposition methods, i.e., Progressive Hedging Algorithm (PHA). SAA, while effectively used in many applications, can lead to poor solution quality if the selected sample sizes are not sufficiently large. With larger sample sizes, however, SAA becomes computationally impractical. In contrast, PHA---as an exact method for convex problems and a very effective method in terms of finding very good solutions for nonconvex problems--suffers from the need to iteratively solve many scenario subproblems, which is computationally expensive. In this paper, we develop novel SP algorithms integrating SAA and PHA methods. The proposed methods are innovative in that they blend the complementary aspects of PHA and SAA in terms of exactness and computational efficiency, respectively. Further, the developed methods are practical in that they allow the analyst to calibrate the tradeoff between the exactness and speed of attaining a solution. We demonstrate the effectiveness of the developed integrated approaches, Sampling-Based Progressive Hedging Algorithm (SBPHA) and Discarding SBPHA (d-SBPHA), over the pure strategies (i.e., SAA). The validation of the methods is demonstrated through two-stage stochastic Capacitated Reliable Facility Location Problem (CRFLP).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Sampling based progressive hedging algorithms for stochastic programming problems

...............................................................................................138 Autobiographical Statement ................................................................................ 140

متن کامل

Progressive hedging-based metaheuristics for stochastic network design

We consider the stochastic variant of the fixed-charge capacitated multicommodity network design (CMND) problem in which demands are stochastic. We propose a two-stage stochastic programming formulation where design decisions make up the first stage, while a series of recourse decisions are made in the second stage to distribute the commodities according to observed demands. The overall objecti...

متن کامل

Large Margin Classification with the Progressive Hedging Algorithm

Several learning algorithms in classification and structured prediction are formulated as large scale optimization problems. We show that a generic iterative reformulation and resolving strategy based on the progressive hedging algorithm from stochastic programming results in a highly parallel algorithm when applied to the large margin classification problem with nonlinear kernels. We also unde...

متن کامل

Two-stage stochastic programming model for capacitated complete star p-hub network with different fare classes of customers

In this paper, a stochastic programming approach is applied to the airline network revenue management problem. The airline network with the arc capacitated single hub location problem based on complete–star p-hub network is considered. We try to maximize the profit of the transportation company by choosing the best hub locations and network topology, applying revenue management techniques to al...

متن کامل

A Progressive Hedging Based Branch-and-Bound Algorithm for Stochastic Mixed-Integer Programs

Progressive Hedging (PH) is a well-known algorithm for solving multi-stage stochastic convex optimization problems. Most previous extensions of PH for stochastic mixed-integer programs have been implemented without convergence guarantees. In this paper, we present a new framework that shows how PH can be utilized while guaranteeing convergence to globally optimal solutions of stochastic mixed-i...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015