Coalescing Data and Decision Sciences for Analytics

The dream of analytics is to work from common, clean, and consistent data sources in a manner that all of its facets (descriptive, predictive, and prescriptive) are sup- ported via a coherent vision of data and decision sciences. To the extent that data and decisions sciences work within logically/mathematically consistent frameworks, and that these paradigms … Read more

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-integer convex … Read more

Learning Enabled Optimization: Towards a Fusion of Statistical Learning and Stochastic Optimization

Several emerging applications, such as “Analytics of Things” and “Integrative Analytics” call for a fusion of statistical learning (SL) and stochastic optimization (SO). The Learning Enabled Optimization paradigm fuses concepts from these disciplines in a manner which not only enriches both SL and SO, but also provides a framework which supports rapid model updates and … Read more

A State Transition MIP Formulation for the Unit Commitment Problem

In this paper, we present the state-transition formulation for the unit commitment problem. This formulation is based on the definition of new decision variables, which, instead of indicating the on/off statuses of a generator, captures its state transitions between consecutive time periods. We show that this new approach produces a formulation which naturally includes valid … Read more

Mitigating Uncertainty via Compromise Decisions in Two-stage Stochastic Linear Programming

Stochastic Programming (SP) has long been considered as a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines … Read more

Ancestral Benders’ Cuts and Multi-term Disjunctions for Mixed-Integer Recourse Decisions in Stochastic Programming

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely … Read more

Decomposition Algorithms with Parametric Gomory Cuts for Two-Stage Stochastic Integer Programs

We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage. We develop decomposition algorithms akin to the L-shaped or Benders methods by utilizing Gomory cuts to obtain iteratively tighter approximations of the second-stage integer programs. We show that the proposed methodology … Read more

A Computational Study of the Cutting Plane Tree Algorithm for General Mixed-Integer Linear Programs

The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obtain the solution of general mixed-integer linear programs (MILP) with bounded integer variables. In this paper, we present our computational experience with variants of the CPT algorithm. Because the CPT algorithm is based on discovering multi-term disjunctions, this paper is the first … Read more

Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard … Read more