Branch-and-Cut for Separable Piecewise Linear Optimization: New Inequalities and Intersection with Semi-Continuous Constraints
نویسندگان
چکیده
We give new facets and valid inequalities for the separable piecewise linear optimization knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. In a companion paper [12] we demonstrate the efficiency of the inequalities when used as cuts in a branch-and-cut scheme.
منابع مشابه
Nonconvex, lower semicontinuous piecewise linear optimization
A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et. al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulati...
متن کاملLinear optimization on the intersection of two fuzzy relational inequalities defined with Yager family of t-norms
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Yager family of t-norms is considered as fuzzy composition. Yager family of t-norms is a parametric family of continuous nilpotent t-norms which is also one of the most frequently appli...
متن کاملLinear optimization on Hamacher-fuzzy relational inequalities
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Hamacher family of t-norms is considered as fuzzy composition. Hamacher family of t-norms is a parametric family of continuous strict t-norms, whose members are decreasing functions of ...
متن کاملOn the use of intersection cuts for bilevel optimization
We address a generic Mixed-Integer Bilevel Linear Program (MIBLP), i.e., a bilevel optimization problem where all objective functions and constraints are linear, and some/all variables are required to take integer values. We first propose necessary modifications needed to turn a standard branch-and-bound MILP solver into an exact and finitely-convergent MIBLP solver, also addressing MIBLP unbou...
متن کاملSemi-continuous Cuts for Mixed-Integer Programming
We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general mixed-integer programming. We show how strong inequalities valid for the semi-continuous knapsack polyhedron can be derived and used in a branch...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010