Gerhard F. Post

An algorithm-based topographical biomaterials library to instruct cell fate

It is increasingly recognized that material surface topography is able to evoke specific cellular responses, endowing materials with instructive properties that were formerly reserved for growth factors. This opens the window to improve upon, in a cost-effective manner, biological performance of any surface used in the human body. Unfortunately, the interplay between surface topographies and cell behavior is complex and still incompletely understood. Rational approaches to search for bioactive surfaces will therefore omit previously unperceived interactions. Hence, in the present study, we use mathematical algorithms to design nonbiased, random surface features and produce chips of poly(lactic acid) with 2,176 different topographies. With human mesenchymal stromal cells (hMSCs) grown on the chips and using high-content imaging, we reveal unique, formerly unknown, surface topographies that are able to induce MSC proliferation or osteogenic differentiation. Moreover, we correlate parameters of the mathematical algorithms to cellular responses, which yield novel design criteria for these particular parameters. In conclusion, we demonstrate that randomized libraries of surface topographies can be broadly applied to unravel the interplay between cells and surface topography and to find improved material surfaces.

A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem

This paper is concerned with the development of intelligent decision support methodologies for nurse rostering problems in large modern hospital environments. We present an approach which hybridises heuristic ordering with variable neighbourhood search. We show that the search can be extended and the solution quality can be significantly improved by the careful combination and repeated use of heuristic ordering, variable neighbourhood search and backtracking. The amount of computational time that is allowed plays a significant role and we analyse and discuss this. The algorithms are evaluated against a commercial Genetic Algorithm on commercial data. We demonstrate that this methodology can significantly outperform the commercial algorithm. This paper is one of the few in the scientific nurse rostering literature which deal with commercial data and which compare against a commercially implemented algorithms.

An XML format for benchmarks in High School Timetabling

The High School Timetabling Problem is amongst the most widely used timetabling problems. This problem has varying structures in different high schools even within the same country or educational system. Due to lack of standard benchmarks and data formats this problem has been studied less than other timetabling problems in the literature. In this paper we describe the High School Timetabling Problem in several countries in order to find a common set of constraints and objectives. Our main goal is to provide exchangeable benchmarks for this problem. To achieve this we propose a standard data format suitable for different countries and educational systems, defined by an XML schema. The schema and datasets are available online.

XHSTT: an XML archive for high school timetabling problems in different countries

We present the progress on the benchmarking project for high school timetabling that was introduced at PATAT 2008. In particular, we announce the High School Timetabling Archive XHSTT-2011 with 21 instances from 8 countries and an evaluator capable of checking the syntax of instances and evaluating the solutions.

A case study for timetabling in a dutch secondary school

This paper describes a case study for constructing the yearly schedule of a secondary school in the Netherlands. This construction is divided in three steps. In the first step we create cluster schemes containing the optional subjects. A cluster scheme consists of cluster lines, and a cluster line contains classes which will be taught simultaneously. Part of the problem is that the students are not yet assigned to the classes. Once the cluster schemes are fixed, it remains to schedule the lessons to time slots and rooms. We first schedule the lessons to day-parts, and once this is completed we schedule the lessons to time slots within the day-parts. Thanks to consistency checks in the day-part phase, going from day-parts to time slots is possible. Finally, in the third step, we improve the previously found schedule by a tabu search using ejection chains. Compared to hand-made schedules, the results are very promising.

Sports tournaments, home-away assignments, and the break minimization problem

We consider the break minimization problem for fixing home-away assignments in round-robin sports tournaments. First, we show that, for an opponent schedule with n teams and n-1 rounds, there always exists a home-away assignment with at most 14n(n-2) breaks. Secondly, for infinitely many n, we construct opponent schedules for which at least 16n(n-1) breaks are necessary. Finally, we prove that break minimization for n teams and a partial opponent schedule with r rounds is an NP-hard problem for r>=3. This is in strong contrast to the case of r=2 rounds, which can be scheduled (in polynomial time) without any breaks.

Progress control in iterated local search for nurse rostering

This paper describes an approach in which a local search technique is alternated with a process which ‘jumps’ to another point in the search space. After each ‘jump’ a (time-intensive) local search is used to obtain a new local optimum. The focus of the paper is in monitoring the progress of this technique on a set of real world nurse rostering problems. We propose a model for estimating the quality of this new local optimum. We can then decide whether to end the local search based on the predicted quality. The fact that we avoid searching these bad neighbourhoods enables us to reach better solutions in the same amount of time. We evaluate the approach on five highly constrained problems in nurse rostering. These problems represent complex and challenging real world rostering situations and the approach described here has been developed during a commercial implementation project by ORTEC bv.

Constructing fair round robin tournaments with a minimum number of breaks

Given n clubs with two teams each, we show that, if n is even, it is possible to construct a schedule for a single round robin tournament satisfying the following properties: the number of breaks is 2n-2, teams of the same club never play at home simultaneously, and they play against each other in the first round. We also consider a fairness constraint related to different playing strengths of teams competing in the tournament.

A class of graded Lie algebras of vector fields and first order differential operators

Finite‐dimensional Lie algebras of polynomial vector fields on Rn, that contain the elements ∂/∂xi and xi(∂/∂xi) for i=1...n were studied. To any Lie algebra L of this class, an N‐valued n×n matrix A and a set of special elements S⊆{1,...,n} are associated. It is proven that the pair (A,S) necessarily satisfies two properties. Conversely, to any pair (A,S) satisfying those two properties is associated a Lie algebra L(A,S), such that L(A,S) is maximal in the class of all L with matrix A and special elements S. For the Lie algebras L(A,S) the possible extensions to first order differential operators, and its modules of C∞ functions are discussed.

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers.