The benefits of transmission line switching are well-known in terms reducing operational cost and improving system reliability power systems. However, finding the optimal network configuration is a challenging task due to combinatorial nature underlying optimization problem. In this work, we identify certain "node-based" set that appears as substructure problem then conduct polyhedral study set...

The network design problem with connectivity requirements (NDC) models a wide variety of celebrated combinatorial optimization problems including the minimum spanning tree, Steiner tree, and survivable network design problems. We develop strong formulations for two versions of the edge-connectivity NDC problem: unitary problems requiring connected network designs, and nonunitary problems permit...

In this paper, we present procedures to obtain facet-defining inequalities for the independence system polytope. These procedures are defined for inequalities which are not necessarily rank inequalities. We illustrate the use of these procedures by deriving strong valid inequalities for the acyclic induced subgraph, triangle free induced subgraph, bipartite induced subgraph, and knapsack polyto...

In this paper, we propose the inclusion of a set of valid inequalities derived using a lifting procedure into a lot scheduling model applied to the soft-drink production. The set of valid inequalities is derived from constraints associated with the scheduling decisions. A computational study conducted to evaluate the quality of the proposed reformulation and how the lifted inequalities relate t...

We study the facial structure of a polyhedron associated with the single node relaxation of network ow problems with additive variable upper bounds. This type of structure arises for example in network design/expansion problems, in production planning problems with setup times. We rst derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet...

Non-Convex Quadratic Programming with Box Constraints is a fundamental NP-hard global optimisation problem. Recently, some authors have studied a certain family of convex sets associated with this problem. We prove several fundamental results concerned with these convex sets: we determine their dimension, characterise their extreme points and vertices, show their invariance under certain affine...

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation...

Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving Mixed Integer Nonlinear Programming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use “discarded” information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizati...

Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid inequalities. As an extension to this work, we study the following “less idealized” questions in this paper: (1) Are there integer programs, such that sparse ine...