Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Human performance and strategies while solving an aircraft routing and sequencing problem: an experimental approach

As airport resources are stretched to meet increasing demand for services, effective use of ground infrastructure is increasingly critical for ensuring operational efficiency. Work in operations research has produced algorithms providing airport tower controllers with guidance on optimal timings and sequences for flight arrivals, departures, and ground movement. While such decision support systems have the potential to improve operational efficiency, they may also affect users’ mental workload, situation awareness, and task performance. This work sought to identify performance outcomes and strategies employed by human decision makers during an experimental airport ground movement control task with the goal of identifying opportunities for enhancing user-centered tower control decision support systems. To address this challenge, thirty novice participants solved a set of vehicle routing problems presented in the format of a game representing the airport ground movement task practiced by runway controllers. The games varied across two independent variables, network map layout (representing task complexity) and gameplay objective (representing task flexibility), and verbal protocol, visual protocol, task performance, workload, and task duration were collected as dependent variables. A logistic regression analysis revealed that gameplay objective and task duration significantly affected the likelihood of a participant identifying the optimal solution to a game, with the likelihood of an optimal solution increasing with longer task duration and in the less flexible objective condition. In addition, workload appeared unaffected by either independent variable, but verbal protocols and visual observations indicated that high-performing participants demonstrated a greater degree of planning and situation awareness. Through identifying human behavior during optimization problem solving, the work of tower control can be better understood, which, in turn, provides insights for developing decision support systems for ground movement management

Extended formulations for column constrained orbitopes

In the literature, packing and partitioning orbitopes were discussed to handle symmetries that act on variable matrices in certain binary programs. In this paper, we extend this concept by restrictions on the number of $1$-entries in each column. We develop extended formulations of the resulting polytopes and present numerical results that show their effect on the LP relaxation of a graph partitioning problem

The Quadratic Assignment Problem

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds