A Simple Clique Camouflaging Against Greedy Maximum Clique Heuristics

Taking a small graph, on which the randomized New-Best-In maximum clique heuristic fails to find the maximum clique, we construct on its basis a class of graphs exemplifying the inefficiency of SM greedy heuristics considered by Brockington and Culberson. We show that a 7(k+1)-vertex graph from this class is enough to provide a counterexample for … Read more

A globally convergent linearly constrained Lagrangian method for nonlinear optimization

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints”. Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. The well known software package MINOS has proven effective on many … Read more

A Global Convergence Theory of a Filter Line Search Method for Nonlinear Programming

A framework for proving global convergence for a class of line search filter type methods for nonlinear programming is presented. The underlying method is based on the dominance concept of multiobjective optimization where trial points are accepted provided there is a sufficient decrease in the objective function or constraints violation function. The proposed methods solve … Read more

Iterative algorithms with seminorm-induced oblique projections

A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility … Read more

Robust Option Modelling

This paper considers robust optimization to cope with uncertainty about the stock return process in one period portfolio selection problems involving options. The ro- bust approach relates portfolio choice to uncertainty, making more cautious portfolios when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlyings and show that … Read more

Selected Topics in Column Generation

Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not found in textbooks, yet. We emphasize on the growing understanding of the dual point of view, which brought considerable progress to the column generation theory … Read more

Socially optimal location of facilities with fixed servers, stochastic demand and congestion

We present two capacity choice scenarios for the socially optimal location of facilities with fixed servers, stochastic demand and congestion. Walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems are motivating examples of such facilities. The choice of locations for such facilities influences not only distances for users traveling … Read more

A spring-embedding approach for the facility layout problem

The facility layout problem is concerned with finding the most efficient arrangement of a given number of departments with unequal area requirements within a facility. The facility layout problem is a hard problem, and therefore, exact solution methods are only feasible for small or greatly restricted problems. In this paper, we propose a spring-embedding approach … Read more

Integrating design and production planning considerations in multi-bay manufacturing facility layout

This paper develops a new mathematical model that integrates layout design and production planning to prescribe efficient multi-bay manufacturing facilities. The model addresses the need to distribute department replicas throughout the facility and extends the use of product and process requirements as problem parameters in order to increase process routing flexibility. In addition, the model … Read more

An extended distance-based facility layout problem

The distance-based facility layout problem with unequal-area departments has been studied by many researchers for over 30 years. Still, current approaches require certain assumptions that limit the type of solutions obtained. In this paper, we consider manufacturing systems in which replicates of the same machine type may exist in the facility and propose an extended … Read more