This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startup and shutdown processes are also … Read more
This paper provides the convex hull description for the following basic operating constraints of a single power generation unit in Unit Commitment (UC) problems: 1) generation limits, 2) startup and shutdown capabilities, and 3) minimum up and down times. Although the model does not consider some crucial constraints, such as ramping, the proposed constraints can … Read more
This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more
Despite the significant attention they have drawn, big bucket lot-sizing problems remain notoriously difficult to solve. Previous work of Akartunali and Miller (2012) presented results (computational and theoretical) indicating that what makes these problems difficult are the embedded single-machine, single-level, multi-period submodels. We therefore consider the simplest such submodel, a multi-item, two-period capacitated relaxation that … Read more
In this paper, we introduce a generalization of the continuous mixing set (which we refer to as the continuous n-mixing set). This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. We develop new classes of valid inequalities for this set, referred to as n’-step cycle inequalities, … Read more
We present a parallel local search approach for obtaining high quality solutions to the Fixed Charge Multi-commodity Network Flow problem (FCMNF). The approach proceeds by improving a given feasible solution by solving restricted instances of the problem where flows of certain commodities are fixed to those in the solution while the other commodities are locally … Read more
This paper provides a study of integer linear programming formulations for the diameter constrained spanning tree problem (DMSTP) in the natural space of edge design variables. After presenting a straightforward model based on the well known jump inequalities a new stronger family of circular-jump inequalities is introduced. These inequalities are further generalized in two ways: … Read more
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however … Read more
This paper introduces a new vehicle routing problem transferring one commodity between customers with a capacitated vehicle that can visit a customer more than once,although a maximum number of visits must be respected. It generalizes the capacitated vehicle routing problem with split demands and some other variants recently addressed in the literature. We model the … Read more
In this paper we provide a unified treatment of general two-term disjunctions on cross-sections of the second-order cone. We derive a closed-form expression for a convex inequality that is valid for such a disjunctive set and show that this inequality is sufficient to characterize the closed convex hull of all two-term disjunctions on ellipsoids and … Read more