Graph vertex colouring can be defined in such a way where colour assignments are substituted by vertex contractions. We present various hyper-graph representations for the graph colouring problem all based on the approach where vertices are merged into groups. In this paper, we show this provides a uniform and compact way to define algorithms, both of a complete or a heuristic nature. Moreover, the representation provides information useful to guide algorithms during their search. In this paper we focus on the quality of solutions obtained by graph colouring heuristics that make use of higher order properties derived during the search. An evolutionary algorithm is used to search permutations of possible merge orderings.

In this paper we demonstrate how evolutionary computation can be used to acquire difficult to solve combinatorial problem instances, thereby stress-testing the corresponding algorithms used to solve these instances. The technique is applied in three important domains of combinatorial optimisation, binary constraint satisfaction, Boolean satisfiability, and the travelling salesman problem. Problem instances acquired through this technique are more difficult than ones found in popular benchmarks. We analyse these evolved instances with the aim to explain their difficulty in terms of structural properties, thereby exposing the weaknesses of corresponding algorithms.

We introduce a novel representation for the graph colouring problem, called the Integer Merge Model, which aims to reduce the time complexity of graph colouring algorithms. Moreover, this model provides useful information to aid in the creation of heuristics that can make the colouring process even faster. It also serves as a compact definition for the description of graph colouring algorithms. To verify the potential of the model, we use it in the complete algorithm DSATUR, and in two version of an incomplete approximation algorithm; an evolutionary algorithm and the same evolutionary algorithm extended with guiding heuristics. Both theoretical and empirical results are provided investigation is performed to show an increase in the efficiency of solving graph colouring problems. Two problem suites were used for the empirical evidence: a set of practical problem instances and a set of hard problem instances from the phase transition.

We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony optimisation (ACO).We compare the performance in terms of effectiveness between these three hybrid methods on a suite f popular benchmark instances, which contains instances too large to solve by current exact methods. Our results show that the EA and the ACO outperform the VNS on almost all used benchmark instances. Furthermore, the ACO yields most of the time better solutions than the EA in long-term runs, whereas the EA dominates when the computation time is strongly restricted.

We introduce a novel representation for the graph colouring problem, called the Integer Merge Model, which aims to reduce the time complexity of an algorithm. Moreover, our model provides useful information for guiding heuristics as well as a compact description for algorithms. To verify the potential of the model, we use it in dsatur, in an evolutionary algorithm, and in the same evolutionary algorithm extended with heuristics. An empiricial investigation is performed to show an increase in efficiency on two problem suites , a set of practical problem instances and a set of hard problem instances from the phase transition.

This paper proposes a computational model for solving optimisation problems that mimics the principle of evolutionary transitions in individual complexity. More specifically it incorporates mechanisms for the emergence of increasingly complex individuals from the interaction of more simple ones. The biological principles for transition are outlined and mapped onto an evolutionary computation context. The class of binary constraint satisfaction problems is used to illustrate the transition mechanism.

This paper proposes an evolutionary approach for the composition of solutions in an incremental way. The approach is based on the metaphor of transitions in complexity discussed in the context of evolutionary biology. Partially defined solutions interact and evolve into aggregations until a full solution for the problem at hand is found. The impact of the initial population on the outcome and the dynamics of the process is evaluated using the domain of binary constraint satisfaction problems.

This paper proposes an incremental approach for building solutions using evolutionary computation. It presents a simple evolutionary model called a Transition model. It lets building units of a solution interact and then uses an evolutionary process to merge these units toward a full solution for the problem at hand. The paper provides a preliminary study on the evolutionary dynamics of this model as well as an empirical comparison with other evolutionary techniques on binary constraint satisfaction.

In this paper, we combine a powerful representation for graph colouring problems with different heuristic strategies for colour assignment. Our novel strategies employ heuristics that exploit information about the partial colouring in an aim to improve performance. An evolutionary algorithm is used to drive the search. We compare the different strategies to each other on several very hard benchmarks and on generated problem instances, and show where the novel strategies improve the efficiency.

In this article, we try to provide insight into the consequence of mutation and crossover rates when solving binary constraint satisfaction problems. This insight is based on a measurement of the space searched by an evolutionary algorithm. From data empirically acquired we describe the relation between the success ratio and the searched space. This is achieved using the resampling ratio, which is a measure for the amount of points revisited by a search algorithm. This relation is based on combinations of parameter settings for the variation operators. We then show that the resampling ratio is useful for identifying the quality of parameter settings, and provide a range that corresponds to robust parameter settings.

We compare two heuristic approaches, evolutionary computation and ant colony optimisation, and a complete tree-search approach, constraint programming, for solving binary constraint satisfaction problems. We experimentally show that, if evolutionary computation is far from being able to compete with the two other approaches, ant colony optimisation nearly always succeeds in finding a solution, so that it can actually compete with constraint programming. The resampling ratio is used to provide insight into heuristic algorithms performances. Regarding efficiency, we show that if constraint programming is the fastest when instances have a low number of variables, ant colony optimisation becomes faster when increasing the number of variables.

This paper describes a novel representation and ordering model that aided by an evolutionary algorithm, is used in solving the graph k-colouring problem. Its strength lies in reducing the search space by breaking symmetry. An empirical comparison is made with two other algorithms on a standard suit of problem instances and on a suit of instances in the phase transition where it shows promising results.

We present a study on the difficulty of solving binary constraint satisfaction problems where an evolutionary algorithm is used to explore the space of problem instances. By directly altering the structure of problem instances and by evaluating the effort it takes to solve them using a complete algorithm we show that the evolutionary algorithm is able to detect problem instances that are harder to solve than those produced with conventional methods. Results from the search of the evolutionary algorithm confirm conjectures about where the most difficult to solve problem instances can be found with respect to the tightness.

Constraint handling is not straightforward in evolutionary algorithms (EA) since the usual search operators, mutation and recombination, are `blind' to constraints. Nevertheless, the issue is highly relevant, for many challenging problems involve constraints. Over the last decade numerous EAs for solving constraint satisfaction problems (CSP) have been introduced and studied on various problems. The diversity of approaches and the variety of problems used to study the resulting algorithms prevents a fair and accurate comparison of these algorithms. This paper aligns related work by presenting a concise overview and an extensive performance comparison of all these EAs on a systematically generated test suite of random binary CSPs. The random problem instance generator is based on a theoretical model that fixes deficiencies of models and respective generators that have been formerly used in the Evolutionary Computing (EC) field.

This paper describes a novel representation and ordering model, that is aided by an evolutionary algorithm, is used in solving the graph k-coloring. A comparison is made between the new representation and an improved version of the traditional graph coloring technique DSATUR on an extensive list of graph k-coloring problem instances with different properties. The results show that our model outperforms the improved DSATUR on most of the problem instances.

A limited number of hardcopies is available for those who are interested, drop me an e-mail. Contents (chapter level):

• 1. Introduction
• 2. Evolutionary Computation
• Part I: Constraint Satisfaction
• 3. Constraint Satisfaction problems
• 4. Solving Constraint Satisfaction Problems
• 5. Empirical Research on Constraint Satisfaction
• 6. Measuring the Resampling Ratio
• 7. Constraint Satisfaction: Conclusions
• Part II: Data Mining
• 8. Introduction
• 9. Classification
• 10. Symbolic Regression
• 11. Data Mining Conclusions
• 12. Dynamic Behaviour
• 13. Bridging the Gap
• A. RandomCSP Library
• B. Library for Evolutionary Algorithm Programming
• C. Case Study: Scheduling a Telescope

In this paper we present a new tool to measure the efficiency of evolutionary algorithms by storing the whole searched space of a run, a process whereby we gain insight into the number of distinct points in the state space an algorithm has visited as opposed to the number of function evaluations done within the run. This investigation demonstrates a certain inefficiency of the classical mutation operator with mutation-rate 1/l, where l is the dimension of the state space. Furthermore we present a model for predicting this inefficiency and verify it empirically using the new tool on binary constraint satisfaction problems.

Constraint Satisfaction Problems form a class of problems that are generally computationally difficult and have been addressed with many complete and heuristic algorithms. We present two complete algorithms, as well as two evolutionary algorithms, and compare them on randomly generated instances of binary constraint satisfaction prob-lems. We find that the evolutionary algorithms are less effective than the classical techniques.

LOFAR, a new radio telescope, will be designed to observe with up to 8 independent beams, thus allowing several simultaneous observations. Scheduling of multiple observations parallel in time, each having their own constraints, requires a more intelligent and flexible scheduling function then operated before. In support of the LOFAR radio telescope project, and in co-operation with Leiden University, Fokker Space has started a study to investigate the suitability of the use of evolutionary algorithms applied to complex scheduling problems. After a positive familiarisation phase, we now examine the potential use of evolutionary algorithms via a demonstration project. Results of the familiarisation phase, and the first results of the demonstration project are presented in this paper.

Supervised by van Hemert, J.I. and W.A. Kosters

Supervised by van Hemert, J.I., H. de Wolf and W.A. Kosters

Constraint satisfaction has been the subject of many studies. Different areas of research have tried to solve all kind of constraint problems. Here we will look at a general model for constraint satisfaction problems in the form of binary constraint satisfaction. The problems generated from this model are studied in the research area of constraint programming and in the research area of evolutionary computation. This paper provides an empirical comparison of two techniques from each area. Basically, this is a check on how well both areas are doing. It turns out that, although evolutionary algorithms are doing well, classic approaches are still more successful.

In this chapter we describe a problem independent method for treating constrain ts in an evolutionary algorithm. Technically, this method amounts to changing the defini tion of the fitness function during a run of an EA, based on feedback from the search pr ocess. Obviously, redefining the fitness function means redefining the problem to be sol ved. On the short term this deceives the algorithm making the fitness values deteriorate , but as experiments clearly indicate, on the long run it is beneficial. We illustrate t he power of the method on different constraint satisfaction problems and point out other application areas of this technique.

This paper presents a comparative study of Evolutionary Algorithms (EAs) for Constraint Satisfaction Problems (CSPs). We focus on EAs where fitness is based on penalization of constraint violations and the penalties are adapted during the execution. Three different EAs based on this approach are implemented. For highly connected constraint networks, the results provide further empirical support to the theoretical prediction of the phase transition in binary CSPs.

Supervised by A.E. Eiben and E. Marchiori

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EA). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping GA on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping GA and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.