Statistical inference and hypotheses testing of risk averse stochastic programs

We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the stochastic program is expressed in terms of a law invariant coherent risk measure. The obtained results are applied … Read more

Matroid Optimisation Problems with Nested Non-linear Monomials in the Objective Function

Recently, Buchheim and Klein suggested to study polynomial-time solvable optimisation problems with linear objective functions combined with exactly one additional quadratic monomial. They concentrated on special quadratic spanning tree or forest problems. We extend their results to general matroid optimisation problems with a set of nested monomials in the objective function. The monomials are linearised … Read more

A Two-Stage Stochastic Program for Multi-shift, Multi-analyst, Workforce Optimization with Multiple On Call Options

Motivated by a cybersecurity workforce optimization problem, this paper investigates optimizing staffing and shift scheduling decisions given unknown demand and multiple on call staffing options at a 24/7 firm with three shifts per day, three analyst types, and several staffing and scheduling constraints. We model this problem as a two-stage stochastic program and solve it … Read more

Nonlinear Regression Analysis by Global Optimization: A Case Study in Space Engineering

The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniques have been applied to solve nonlinear (as well as linear) model calibration problems numerically: the limitations of such approaches in the nonlinear … Read more

Monoidal Cut Strengthening and Generalized Mixed-Integer Rounding for Disjunctions and Complementarity Constraints

In the early 1980s, Balas and Jeroslow presented monoidal disjunctive cuts exploiting the integrality of variables. This article investigates the relation of monoidal cut strengthening to other classes of cutting planes for general two-term disjunctions. We introduce a generalization of mixed-integer rounding cuts and show equivalence to monoidal disjunctive cuts. Moreover, we demonstrate the effectiveness … Read more

Minimization and Maximization Versions of the Quadratic Traveling Salesman Problem

The traveling salesman problem (TSP) asks for a shortest tour through all vertices of a graph with respect to the weights of the edges. The symmetric quadratic traveling salesman problem (SQTSP) associates a weight with every three vertices traversed in succession. If these weights correspond to the turning angles of the tour, we speak of … Read more

Computational study of valid inequalities for the maximum hBccut problem

We consider the maximum k-cut problem that consists in partitioning the vertex set of a graph into k subsets such that the sum of the weights of edges joining vertices in different subsets is maximized. We focus on identifying effective classes of inequalities to tighten the semidefinite programming relaxation. We carry out an experimental study … Read more

An Adaptive Partition-based Level Decomposition for Solving Two-stage Stochastic Programs with Fixed Recourse

We present a computational study of several strategies to solve two-stage stochastic linear programs by integrating the adaptive partition-based approach with level decomposition. A partition-based formulation is a relaxation of the original stochastic program, obtained by aggregating variables and constraints according to a scenario partition. Partition refinements are guided by the optimal second-stage dual vectors … Read more

A polyhedral study of the cardinality constrained multi-cycle and multi-chain problem on directed graphs

In this paper, we study the Cardinality Constrained Multi-cycle Problem (CCMcP) and the Car- dinality Constrained Cycle and Chain Problem (CCCCP). A feasible solution allows one or more cardinality-constrained cycles to exist on the digraph. A vertex can only be involved in at most one cycle, and there may be vertices not involved in any … Read more

Solving Large Aircraft Landing Problems on Multiple Runways by Applying a Constraint Programming Approach

Aircraft Landing Problem is to assign an airport’s runways to the arrival aircraft as well as to schedule the landing time of these aircraft. In this paper, due to the complexity of the problem, which is NP-hard, we develop an iterative-based heuristic by exploiting special characteristics of the problem. Computational results show the developed approach … Read more