A wide-ranging computational comparison of high-performance graph colouring algorithms

This paper reviews the current state of the literature surrounding methods for the general graph colouring problem and presents a broad comparison of six high-performance algorithms, each belonging to one of the main algorithmic schemes identified. Unlike many previous computational studies in graph colouring, a large range of both artificially generated and real-world graphs are considered, culminating in over 40,000 individual trials that have consumed more than a decade of computation time in total. The picture painted by the comparison is complex, with each method outperforming all others on at least one occasion; however, general patterns are also observed, particularly with regards to the advantages of hybridising local-search techniques with global-based operators

A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure

Creating seating plans: A practical application

© 2016 Operational Research Society Ltd. All rights reserved. 0160-5682/16. This paper examines the interesting problem of designing seating plans for large events such as weddings and gala dinners where, among other things, the aim is to construct solutions where guests are sat on the same tables as friends and family, but, perhaps more importantly, are kept away from those they dislike. This problem is seen to be N P-complete from a number of different perspectives. We describe the problem model and heuristic algorithm that is used on the commercial website www.weddingseatplanner.com. We present results on the performance of this algorithm, demonstrating the factors that can influence run time and solution quality, and also present a comparison with an equivalent IP model used in conjunction with a commercial solver

Tackling the edge dynamic graph colouring problem with and without future adjacency information

Many real world operational research problems, such as frequency assignment and exam timetabling, can be reformulated as graph colouring problems (GCPs). Most algorithms for the GCP operate under the assumption that its constraints are fixed, allowing us to model the problem using a static graph. However, in many real-world cases this does not hold and it is more appropriate to model problems with constraints that change over time using an edge dynamic graph. Although exploring methods for colouring dynamic graphs has been identified as an area of interest with many real-world applications, to date, very little literature exists regarding such methods. In this paper we present several heuristic methods for modifying a feasible colouring at time-step t into an initial, but not necessarily feasible, colouring for a “similar” graph at time-step t+1t+1 . We will discuss two cases; (1) where changes occur at random, and (2) where probabilistic information about future changes is provided. Experimental results are also presented and the benefits of applying these particular modification methods are investigated