Vertex Descent is a local search algorithm which forms the basis of a wide spectrum of tabu search, simulated annealing and hybrid evolutionary algorithms for graph colouring. These algorithms are usually treated as experimental and provide strong results on established benchmarks. As a step towards studying these heuristics analytically, an analysis of the behaviour of Vertex Descent is provided. It is shown that Vertex Descent is able to find feasible colourings for several types of instances in expected polynomial time. This includes 2-colouring of paths and 3-colouring of graphs with maximum degree 3. The same also holds for 3-colouring of a subset of 3-colourable graphs with maximum degree 4. As a consequence, Vertex Descent finds a 3-colouring in expected polynomial time for the smallest graph for which Br 'elaz's heuristic DSATUR needs 4 colours. On the other hand, Vertex Descent may fail for forests with maximum degree 3 with high probability.
Tabu search techniques are used for moving step by step towards the minimum value of a function. A tabu list of forbidden movements is updated during the iterations to avoid cycling and being trapped in local minima. Such techniques are adapted to graph coloring problems. We show that they provide almost optimal colorings of graphs having up to 1000 nodes and their efficiency is shown to be significantly superior to the famous simulated annealing. This paper examines the best current algorithm for solving the Chromatic Number Problem, due to Galinier and Hao (Journal of Combinatorial Optimization,1999, 3(4), pp 379-397). The algorithm combines a Genetic Algorithm with Tabu Search. We show that the algorithm remains powerful even if the Tabu Search component is eliminated, and explore the reasons for its success where other Genetic Algorithms have failed. In addition we propose a generalized algorithm for the Frequency Assignment Problem. A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a well-known tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of state-of-the-art algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement. The evaluation or fitness function is a key component ofany heuristic search algorithm. This paper introduces a new evaluationfunction for the well-known graph K-coloring problem. This functiontakes into account not only the number of conflicting vertices, but alsoinherent information related to the structure of the graph. To assessthe effectiveness of this new evaluation function, we carry out a numberof experiments using a set of DIMACS benchmark graphs. Based onstatistic data obtained with a parameter free steepest descent, we showan improvement of the new evaluation function over the classical one.