How Much Forcing is Necessary to Let the Results of Particle Swarms Converge? - Bassimir, Bernd; Schmitt, Manuel; Wanka, Rolf (Proc. Int. Conf. on Swarm Intelligence Based Optimization (ICSIBO), 2014)
In order to improve the behavior of Particle Swarm Optimization (PSO), the classical method is often extended by additional operations. Here, we are interested in how much ``PSO" remains in this case, and how often the extension takes over the computation. We study the variant of PSO that applies random velocities (then called forced moves) as soon as the so-called potential of the swarm falls below a certain bound. We show experimentally that the number of iterations the swarm actually deviates from the classical PSO behavior is small as long as the particles are sufficiently far away from any local optimum. As soon as the swarm comes close to a local optimum, the number of forced moves increases significantly and approaches a value that depends on the swarm size and the problem dimension, but not on the actual fitness function, an observation that can be used as a stopping criterion. Additionally, we provide an explanation for the observed phenomenon in terms of the swarms potential.

On the Computation of Robust Examination Timetables: Methods and Experimental Results - Bassimir, Bernd; Wanka, Rolf (Journal of Scheduling, 2024)
With ever rising student numbers and an increasing shift towards more interdisciplinary study programs the requirements for finding schedules for courses and exams become ever more complex. In real world scenarios the models used in calculating solutions to the course and the examination timetabling problem are often required to be provided to the students at the time of registrations. In course timetabling this lead to the field of curriculum based course timetabling (CB-CTTP) where timetables are calculated based on the structure of the study programs. For the examination timetabling problem (ETTP) only a few papers focus on scheduling exams without registration data as the requirements for exams are often more strict or partial information is known from course registrations. In this paper we show that, using robustness techniques, we can also define the examination timetabling problem based on curricula. We introduce three robustness soft constraints that address the inherent uncertainty when using the curriculum-based model. These soft criteria are analyzed using a multi-objective simulated annealing algorithm and the results are compared on the found Pareto front approximations. We give experiments that show that without a significant loss in solution quality the chance of rescheduling after the exact numbers for the model are known is significantly reduced.<br
Keywords: Curriculum-Based Examination Timetabling; Simulated Annealing; Multi-objective Optimization; Robustness

Probabilistic Curriculum-based Examination Timetabling - Bassimir, Bernd; Wanka, Rolf (Proc 12th International Conference on the Practice and Theory of Automated Timetabling (PATAT), 2018)
In the literature, the examination timetabling problem (ETTP) is mostly described as a post enrollment problem (PE-ETTP). As such, it is known at optimization time how many students will take an exam and consequently how big a room is needed and which exams should not be held at the same time because of overlapping student lists. To compute a timetable using this approach, students need to register for exams before the timetable is generated. A direct consequence is that at registration time students have no idea when their exams are being held. Furthermore as timetables are often released at the end of the semester, it is hard for lecturers to plan their other responsibilities accordingly. This leads to a negative reaction from both the student body and the staff holding the exams. In this paper, we describe a curriculum-based examination timetabling variant that is similar to the curriculum-based examination timetabling problem model (CB-ETTP) introduced by Cataldo et al. 2017. The aim of the model introduced in this work is to combine the positive aspects of PE-ETTP and CB-ETTP by the use of machine learning while reducing the problems of the CB-ETTP, namely the overestimation in the number of students taking an exam. We describe an approach to calculate the number of students taking an exam by using old planning data. Furthermore we give an example for integrating the knowledge from past experience as a new soft constraint. Through the addition of this new soft constraint, we get a measure for the robustness of the timetable in respect to the uncertainty in the data. Finally, we present experiments based on real world data from the University of Erlangen-Nuremberg (FAU) showing that the approach gives a good estimation for the number of students with only slight deviations from the actual numbers. <br
Keywords: Examination Timetabling; Curriculum-based Timetabling; Machine Learning

Robustness Approaches for the Examination Timetabling Problem under Data Uncertainty - Bassimir, Bernd; Wanka, Rolf (Proc. 9th Multidisciplinary International Conference on Scheduling: Theory and Applications, 2019)
In the literature the examination timetabling problem (ETTP) is often considered a post-enrollment problem (PE-ETTP). In the real world, universities often schedule their exams before students register using information from previous terms. A direct consequence of this approach is the uncertainty present in the resulting models. In this work we discuss several approaches available in the robust optimization literature. We consider the implications of each approach in respect to the examination timetabling problem and present how the most favorable approaches can be applied to the ETTP. Afterwards we analyze the impact of some possible implementations of the given robustness approaches on two real world instances and several random instances generated by our instance generation framework which we introduce in this work. <br
Keywords: Examination Timetabling; Robust Optimization; Test Instance Genera- tion

Self-adaptive potential-based stopping criteria for Particle Swarm Optimization with forced moves - Bassimir, Bernd; Schmitt, Manuel; Wanka, Rolf (Swarm Intelligence, 2020)
We study the variant of Particle Swarm Optimization that applies random velocities in a dimension instead of the regular velocity update equations as soon as the so-called potential of the swarm falls below a certain small bound in this dimension, arbitrarily set by the user. In this case, the swarm performs a forced move. In this paper, we are interested in how, by counting the forced moves, the swarm can decide for itself to stop its movement because it is improbable to find better candidate solutions than the already-found best solution. We formally prove that when the swarm is close to a (local) optimum, it behaves like a blind-searching cloud and that the frequency of forced moves exceeds a certain, objective function-independent value. Based on this observation, we define stopping criteria and evaluate them experimentally showing that good candidate solutions can be found much faster than setting upper bounds on the iterations and better solutions compared to applying other solutions from the literature.<br
Keywords: Particle Swarm Optimization; Stopping criterion; Heuristics

Theory of particle swarm optimization: A survey of the power of the swarm’s potential - Bassimir, Bernd; Raß, Alexander; Schmitt, Manuel (it - Information Technology, 2019)
This paper presents a survey on different showcases for potential measures on particle swarm optimization (PSO). First, a potential is analyzed to prove convergence to non-optimal points. Second, one can apply a minor modification to PSO to prevent convergence to non-optimal points by using an easy potential measure. Finally, analyzing this potential measure yields a reliable stopping criterion for the modified PS
Keywords: Particle swarm optimization; potential; meta-heuristics