Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N – k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. We present theoretical results and computation … Read more
We prove that the subset sum problem has a polynomial time computable certificate of infeasibility for all $a$ weight vectors with density at most $1/(2n)$ and for almost all integer right hand sides. The certificate is branching on a hyperplane, i.e. by a methodology dual to the one explored by Lagarias and Odlyzko; Frieze; Furst … Read more
We address optimization of nonlinear functions of the form $f(Wx)$~, where $f:\R^d\rightarrow \R$ is a nonlinear function, $W$ is a $d\times n$ matrix, and feasible $x$ are in some large finite set $\calF$ of integer points in $\R^n$~. Generally, such problems are intractable, so we obtain positive algorithmic results by looking at broad natural classes … Read more
We extend work on generating relaxations of simple sets with guaranteed bounds. Citation Unpublished. Columbia University, July 2008. Article Download View Tightening simple mixed-integer sets with guaranteed bounds
GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this … Read more
GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. An intensification … Read more
GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution … Read more
Experience has shown that a crafted combination of concepts of different metaheuristics can result in robust combinatorial optimization schemes and produce higher solution quality than the individual metaheuristics themselves, especially when solving difficult real-world combinatorial optimization problems. This chapter gives an overview of different ways to hybridize GRASP (Greedy Randomized Adaptive Search Procedures) to create … Read more
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in Kaibel and Pfetsch (Math. Program. 114 (1), 2008, 1-36). These polytopes are the convex hulls of all 0/1-matrices with lexicographically sorted columns and at most, resp. exactly, one 1-entry per row. They are … Read more
We investigate the problem of simultaneously determining the location of facilities and the design of vehicle routes to serve customer demands under vehicle and facility capacity restrictions. We present a set-partitioning-based formulation of the problem and study the relationship between his formulation and the graph-based formulations that have been used in previous studies of this … Read more