Michael Sampels

A MAX-MIN Ant System for the University Course Timetabling Problem

We consider a simplification of a typical university course timetabling problem involving three types of hard and three types of soft constraints. A MAX-MIN Ant System, which makes use of a separate local search routine, is proposed for tackling this problem. We devise an appropriate construction graph and pheromone matrix representation after considering alternatives. The resulting algorithm is tested over a set of eleven instances from three classes of the problem. The results demonstrate that the ant system is able to construct significantly better timetables than an algorithm that iterates the local search procedure from random starting solutions.

An Ant Colony Optimization Algorithm for Shop Scheduling Problems

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure derived by Nowicki and Smutnicki for the job shop scheduling problem. Then, we develop an ant colony optimization approach, which uses a strong non-delay guidance for constructing solutions and which employs black-box local search procedures to improve the constructed solutions. We compare this algorithm to an adaptation of the tabu search by Nowicki and Smutnicki to group shop scheduling. Despite its general nature, our algorithm works particularly well when applied to open shop scheduling instances, where it improves the best known solutions for 15 of the 28 tested instances. Moreover, our algorithm is the first competitive ant colony optimization approach for job shop scheduling instances.

Ant algorithms for the university course timetabling problem with regard to the state-of-the-art

Two ant algorithms solving a simplified version of a typical university course timetabling problem are presented -Ant Colony System and MAX-MIN Ant System. The algorithms are tested over a set of instances from three classes of the problem. Results are compared with recent results obtained with several metaheuristics using the same local search routine (or neighborhood definition), and a reference random restart local search algorithm. Further, both ant algorithms are compared on an additional set of instances. Conclusions are drawn about the performance of ant algorithms on timetabling problems in comparison to other metaheuristics. Also the design, implementation, and parameters of ant algorithms solving the university course timetabling problem are discussed. It is shown that the particular implementation of an ant algorithm has significant influence on the observed algorithm performance.

When Model Bias Is Stronger than Selection Pressure

We investigate the influence of model bias in model-based search. As an example we choose Ant Colony Optimization as a well-known model-based search algorithm. We present the effect of two different pheromone models for an Ant Colony Optimization algorithm to tackle a general scheduling problem. The results show that a pheromone model can introduce a strong bias toward certain regions of the search space, stronger than the selection pressure introduced by the updating rule for the model. This potentially leads to an algorithm where over time the probability to produce good quality solutions decreases.

Metaheuristics for Group Shop Scheduling

The Group Shop Scheduling Problem (GSP) is a generalization of the classical Job Shop and Open Shop Scheduling Problems. In the GSP there are m machines and n jobs. Each job consists of a set of operations, which must be processed on specified machines without preemption. The operations of each job are partitioned into groups on which a total precedence order is given. The problem is to order the operations on the machines and on the groups such that the maximal completion time (makespan) of all operations is minimized. The main goal of this paper is to provide a fair comparison of five metaheuristic approaches (i.e., Ant Colony Optimization, Evolutionary Algorithm, Iterated Local Search, Simulated Annealing, and Tabu Search) to tackle the GSP. We guarantee a fair comparison by a common definition of neighborhood in the search space, by using the same data structure, programming language and compiler, and by running the algorithms on the same hardware.

Large Networks with Small Diameter

The construction of large networks with small diameter D for a given maximal degree Δ is a major goal in combinatorial network theory. Using genetic algorithms, together with Cayley graph techniques, new results for this degree/diameter problem can be obtained. A modification of the Todd-Coxeter algorithm yields further results and allows, with Sabidussis representation theorem, a uniform representation of vertex-symmetric graphs. The paper contains an updated table of the best known (Δ, D)-graphs and a table with the largest known graphs for a given Δ and maximum average distance µ between the nodes.

On generalized Moore digraphs

The transmission of a strongly connected digraph D is defined as the sum of all distances in D. A lower bound for the transmission in terms of the order n and the maximal outdegree Δ + of D can be regarded as a generalization of the Moore bound for digraphs. Bridges and Toueg showed that Moore digraphs in the strong sense exist only for the trivial cases Δ + =1 or Δ + =n-1. Using techniques founded on Cayley digraphs, we constructed vertex-symmetric generalized Moore digraphs. Such graphs are applicable to interconnection networks of parallel computers, routers, switches, backbones, etc.

Visualization of Automorphisms and Vertex-Symmetry

A heuristic for the visualization of arbitrary automorphisms of a graph by two-dimensional drawings is presented. The restriction of the drawing to a subgraph induced by an orbit of the automorphism is according to a symmetry of the plane. For a vertex-symmetric graph, a collection of drawings for a set of automorphisms which generate a transitive group on the vertices shows this symmetry property.