Framework for Scheduling Problems

Abstract

Scheduling problems form an important subclass of combinatorial optimisation problems with many applications in manufacturing and logistics. Predominately these problems are NP-complete (decision based) and NP-hard (optimisation based), hence the main course of research in solving them concentrates on the design of efficient heuristic algorithms. Two main categories of these algorithms exist: deterministic algorithms and evolutionary metaheuristics. The deterministic algorithms comprise local improvement techniques, such as k-opt algorithm, which try to improve existing feasible solution, and constructive heuristics, such as NEH, which build a solution starting from scratch, adding one job at a time. Evolutionary metaheuristics have prospered in the past decades, owing to their efficiency and flexibility. Drawing inspiration from the theory of natural evolution or swarm behavioural patterns, the most popular of these algorithms in practice include for instance Genetic Algorithms, Differential Evolution, Particle Swarm Optimisation, amongst others.

However, even though these heuristics provide in most cases close to optimal solution at reasonable execution time, this time is still impractically long for many applications. Therefore much effort has been dedicated to accelerating these algorithms. Since the development of hardware turns away from increasing the clock speed towards the parallel processing units, owing to reaching the limits of technology due to the increased power consumption and heat dissipation, this effort goes into parallelisation of the existing algorithms, to enable exploitation of the computing power of multi-core or many-core platforms. This is the goal of the first part of the thesis, accelerating two of the deterministic algorithms, NEH and 2-opt, with interesting results.

Another approach has been taken in the second part, with the core premise of exploring the influence of stochasticity on the performance of an evolutionary algorithm, selecting the relatively recent and promising Discrete Artificial Bee Colony algorithm. The pseudo-random number generator has been replaced with the different types of dissipative chaos maps, with some of them improving the algorithm significantly.

It has been shown that the population based evolutionary algorithms often form complex networks, taken from the point of view of the information exchange between individual solutions during the course of population development. The final part of this thesis puts this observation into practice by embedding the complex network analysis based self-adaptive mechanism into the ABC algorithm, a continuous optimisation problems solving evolutionary algorithm, which is however the basis for the afore mentioned DABC algorithm, and proving the effectiveness for some of the developed versions, currently on the standard continuous optimisation test functions, with the possibility to extend this modification to the combinatorial optimisations problems in the future being discussed in the conclusion.