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The Single-Track Railway Scheduling Problem can be modelled as a special case of the Job-Shop Scheduling Problem. This can be achieved by considering the train trips as jobs, which will be scheduled on tracks regarded as resources. A train trip may have many tasks that consist of traversing from one point to another on a track. Each of these distinct points can be a station or a signal placed along the track. Conicts may occur when the desired timetable would result in two trains occupying the same section of the track at the same time. The mapping of the problem we have proposed in this thesis is a more realistic approach when modelling the physical representation of a track railway. This is because we take into account the actual signals placed along the track delimiting each track segment. These signals control whether a train can or cannot go on that particular track segment, avoiding thus the possibility of trains running into each other. Previous authors adopted an approximation to what is found in practice by adding minimum headway constraints between trains into their model. Two strategies for resolving the conicts in a desired timetable are presented. The two strategies have their applicability in practice. For instance, resolving a conict in the rst strategy stems from the observed practice of train operators: in the rst strategy a conict is resolved by re-timing one of the trips at its departure time up to the point the conict is resolved. Train operating companies do not typically want to plan for passenger trains being delayed after their departure. On the other hand, the second strategy resolves a conict by delaying only the conicting piece of one of the two trips (and subsequent pieces of that trip). In this way, the section of the trip before...

We are interested in defining a general evolutionary algorithm to solve Constraint Satisfaction Problems, which take into account both advantages of the systematic and traditional methods and of characteristics of the CSP. In this context knowledge about properties of the constraint network has allowed us to define a fitness function, for Evaluation, [15]. We introduce here two new operators which look at the constraint network during the evolution. The first one is a bisexual operator like crossover denominated arc-crossover, for Exploitation. The second one is an operator like mutation called arc-mutation, for Exploration. These operators are used to improve the stochastic search.

Currently there is a growing interest in the evolutionary algorithm paradigm, as it promises a robust and general search technique. Still, in spite of much research, for many people the question remains how good evolutionary algorithms really are. Therefore, in this research, a successful class of evolutionary algorithms, Steady State evolutionary algorithms, is thoroughly examined to find optimal settings on two NP-complete problems: Graph 3-Coloring and 3-Satisfiability. Several versions of the evolutionary algorithm are tested and evaluated and the best version for each NP-complete problem is compared to a good existing algorithm for each problem. Then extensions for the evolutionary algorithm are presented that make the evolutionary algorithms perform better than the more traditional algorithms on the hardest problem instances. i Preface This research was done as a Master's Thesis for graduating in Computer Science at Leiden University. It is about evolutionary algorithms, searc...

Case combination is a difficult problem in Case Based Reasoning, as sub-cases often exhibit conflicts when merged together. In our previous work we formalized case combination by representing each case as a constraint satisfaction problem, and used the minimum conflicts algorithm to systematically synthesize the global solution. However, we also found instances of the problem in which the minimum conflicts algorithm does not perform case combination efficiently. In this paper we describe those situations in which initially retrieved cases are not easily adaptable, and propose a method by which to improve case adaptability with a genetic algorithm. We introduce a fitness function that maintains as much retrieved case information as possible, while also perturbing a sub-solution to allow subsequent case combination to proceed more efficiently.

The Processor Configuration Problem (PCP) is a Constraint Optimization Problem. The task is to link up a finite set of processors into a network, while minimizing the maximum distance between these processors. Since each processor has a limited number of communication channels, a carefully planned layout could minimize the overhead for message switching. In this paper, we present a Genetic Algorithm (GA) approach to the PCP. Our technique uses a mutation based GA, a function that produces schemata by analyzing previous solutions, and an effective data representation. Our approach has been shown to out-pegorm other published techniques in this problem.

In this paper we discuss the possibilities of applying genetic algorithms (GA) for solving constraint satisfaction problems (CSP). We point out how the greediness of deterministic classical CSP solving techniques can be counterbalanced by the random mechanisms of GAs. We tested our ideas by running experiments on four different CSPs: N-queens, graph 3-colouring, the traffic lights and the Zebra problem. Three of the problems have proven to be GA-easy, and even for the GA-hard one the performance of the GA could be boosted by techniques familiar in classical methods. Thus GAs are promising tools for solving CSPs. In the discussion, we address the issues of non-solvable CSPs and the generation of all the solutions. 1.1 Introduction In this paper we consider genetic algorithms (GA) for solving constraint satisfaction problems (CSP) with finite domains. The majority of CSP solving algorithms, which we will refer to as classical ones, are deterministic and constructive search algorithms....

A constraint satisfaction problem (CSP) involves a set of variables, a domain of potential values for each variable, and a set of constraints, which specifies the acceptable combinations of values. One popular approach is to represent the original problem as a constraint network where nodes represent variables and arcs represent constraints between variables. Node consistency and arc consistency techniques are first applied to prune the domains of variables. Constraint propagation techniques are then applied to solve the problem. Many AI and engineering problems can be formulated as CSPs and solved by various CSP algorithms such as constraint propagation, backtracking, forward checking, and hybrids. This paper gives an overview of these algorithms. In particular, we present a review of the interval constraint satisfaction problems (ICSP). Real intervals or sets of discrete values label the variables. The constraints can be binary relationships or n-ary mathematical operations. The tech...

We are interested on defining a general evolutionary algorithm that repairs to solve Constraint Satisfaction Problems and which takes into account both advantages of the systematic and traditional methods and of a characteristics of the CSP. We use the knowledge about properties of the constraint network to define a fitness function, and three operators arc-mutation, arc-crossover and constraint dynamic adaptive crossover. The number of constraint checks has also taken into consideration for designing the operators. The algorithm has been tested by running experiments on randomly generated 3-coloring graphs. The results suggest that the technique may be successfully applied to solve CSP.

Local search is one of the fundamental paradigms for solving computationally hard combinatorial problems, including the constraint satisfaction problem (CSP). It provides the basis for some of the most successful and versatile methods for solving the large and difficult problem instances encountered in many real-life applications. Despite impressive advances in systematic, complete search algorithms, local search methods in many cases represent the only feasible way for solving these large and complex instances. Local search algorithms are also naturally suited for dealing with the optimisation criteria arising in many practical applications. The basic idea underlying local search is to start with a randomly or heuristically generated candidate solution of a given problem instance, which may be infeasible, sub-optimal or incomplete, and to iteratively improve this candidate solution by means of typically minor modifications. Different local search methods vary in the way in which improvements are achieved, and in particular, in the way in which situations are handled in which no direct improvement is possible. Most local search methods use randomisation to ensure that the search process does not