Algorithmic Approach for Improved Mixed-Integer Reformulations of Convex Generalized Disjunctive Programs
نویسندگان
چکیده
In this work, we propose an algorithmic approach to improve mixed-integer models that are originally formulated as convex Generalized Disjunctive Programs (GDP). The algorithm seeks to obtain an improved continuous relaxation of the MILP/MINLP reformulation of the GDP, while limiting the growth in the problem size. There are three main stages that form the basis of the algorithm. The first one is a pre-solve, consequence of the logic nature of GDP, which allows us to reduce the problem size, find good relaxation bounds and identify properties that help us determine where to apply a basic step. The second stage is the iterative application of basic steps, selecting where to apply them, and monitoring the improvement of the formulation. Finally, we use a hybrid reformulation of GDP that seeks to exploit both of the advantages attributed to the two common GDP-to-MILP/MINLP transformations, the Big-M and Hull reformulation. We illustrate the application of this algorithm with several examples. The results show the improvement in the problem formulations by generating models with improved relaxed solutions and relatively small growth in the number of continuous variables and constraints. The algorithm generally leads to reduction in the solution times.
منابع مشابه
Improved Formulations and Computational Strategies for the Solution and Nonconvex Generalized Disjunctive Programs
Many optimization problems require the modelling of discrete and continuous variables, giving rise to mixed-integer linear and mixed-integer nonlinear programming (MILP / MINLP). An alternative representation of MINLP is Generalized Disjunctive Programming (GDP)1. GDP models are represented through continuous and Boolean variables, and involve algebraic equations, disjunctions, and logic propos...
متن کاملA hierarchy of relaxations for nonlinear convex generalized disjunctive programming
We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of th...
متن کاملGeneralized Disjunctive Programming as a Systematic Modeling Framework to Derive Scheduling Formulations
We propose generalized disjunctive programming models for the short-term scheduling problem of single stage batch plants with parallel units. Three different concepts of continuous-time representation are explored, immediate and general precedence, as well as multiple time grids. The GDP models are then reformulated using both big-M and convex hull reformulations, and the resulting mixed-intege...
متن کاملPerspective Reformulation and Applications
In this paper we survey recent work on the perspective reformulation approach that generates tight, tractable relaxations for convex mixed integer nonlinear programs (MINLP)s. This preprocessing technique is applicable to cases where the MINLP contains binary indicator variables that force continuous decision variables to take the value 0, or to belong to a convex set. We derive from first prin...
متن کاملReview of Nonlinear Mixed-Integer and Disjunctive Programming Techniques
This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented firs...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- INFORMS Journal on Computing
دوره 27 شماره
صفحات -
تاریخ انتشار 2015