http://www3.eng.cam.ac.uk/~hj231/Papers/rostering.pdf

Staff scheduling and rostering: A review of applications, methods and models

Simulated annealing is a popular local search meta-heuristic used to address discrete and, to a lesser extent, continuous optimization problems. The key feature of simulated annealing is that it provides a means to escape local optima by allowing hill-climbing moves (i.e., moves which worsen the objective function value) in hopes of finding a global optimum. A brief history of simulated annealing is presented, including a review of its application to discrete and continuous optimization problems. Convergence theory for simulated annealing is reviewed, as well as recent advances in the analysis of finite time performance. Other local search algorithms are discussed in terms of their relationship to simulated annealing. The chapter also presents practical guidelines for the implementation of simulated annealing in terms of cooling schedules, neighborhood functions, and appropriate applications.

The Theory and Practice of Simulated Annealing

Computational methods for rostering and personnel scheduling has been a subject of continued research and commercial interest since the 1950s. This annotated bibliography puts together a comprehensive collection of some 700 references in this area, focusing mainly on algorithms for generating rosters and personnel schedules but also covering related areas such as workforce planning and estimating staffing requirements. We classify these papers according to the type of problem addressed, the application areas covered and the methods used. In addition, a short summary is provided for each paper.

http://www3.eng.cam.ac.uk/~hj231/Papers/AORRosteringPaper.pdf

An Annotated Bibliography of Personnel Scheduling and Rostering

This paper investigates a genetic algorithm based hyperheuristic (hyper-GA) for scheduling geographically distributed training staff and courses. The aim of the hyper-GA is to evolve a good-quality heuristic for each given instance of the problem and use this to find a solution by applying a suitable ordering from a set of low-level heuristics. Since the user only supplies a number of low-level problem-specific heuristics and an evaluation function, the hyperheuristic can easily be reimplemented for a different type of problem, and we would expect it to be robust across a wide range of problem instances. We show that the problem can be solved successfully by a hyper-GA, presenting results for four versions of the hyper-GA as well as a range of simpler heuristics and applying them to five test data set.

/pdf/an-investigation-of-a-hyperheuristic-genetic-algorithm-znovj8oamy.pdf

An investigation of a hyperheuristic genetic algorithm applied to a trainer scheduling problem

For a positive integer k, a k-coloring of a graph inline image is a mapping inline image such that inline image whenever inline image. The COLORING problem is to decide, for a given G and k, whether a k-coloring of G exists. If k is fixed (i.e., it is not part of the input), we have the decision problem k-COLORING instead. We survey known results on the computational complexity of COLORING and k-COLORING for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial coloring, or where lists of permissible colors are given for each vertex.

/pdf/a-survey-on-the-computational-complexity-of-coloring-graphs-290lv8e457.pdf

A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs

For any integer k, we prove the existence of a uniquely k-colourable graph of girth at least g on at most k12(g+1) vertices whose maximal degree is at most 5k13. From this we deduce that, unless NP=RP, no polynomial time algorithm for k-Colourability on graphs G of girth g(G)≥log∣G∣/13logk and maximum degree Δ(G)≤6k13 can exist. We also study several related problems.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0963548398003678

Uniquely Colourable Graphs and the Hardness of Colouring Graphs of Large Girth

We report about a study of a simulated annealing algorithm for the airline crew pairing problem based on a run-cutting formulation. Computational results are reported for some real-world short- to medium-haul test problems with up to 4600 flights per month. Furthermore we find that run time can be saved and solution quality can be improved by using a problem specific initial solution, by relaxing constraints “as far as possible”, by combining simulated annealing with a problem specific local improvement heuristic and by multiple independent runs.

Best Practice Simulated Annealing for the Airline Crew Scheduling Problem

We study the complexity of the problems of bounded maximum degree and large girth. All results are essentially best possible. We also construct regular class-one graphs of large girth and small order. Finally, we point out how vertex resp. edge feedback sets of size O(log n) can be used to solve Max Cut, Independent Set, Node Cover, Dominating Set, Vertex Feedback Set and Steiner Tree in polynomial time.

Thomas Emden-Weinert

Papers

Uniquely Colourable Graphs and the Hardness of Colouring Graphs of Large Girth

Best Practice Simulated Annealing for the Airline Crew Scheduling Problem

The Complexity of Some Problems on Very Sparse Graphs