Using a Parallel Ensemble of Sequence-Based Selection Hyper-Heuristics for Electric Bus Scheduling

Abstract

A Sequence-based Selection Hyper-Heuristic (SSHH) utilises a hidden Markov model (HMM) to generate sequences of low-level heuristics to apply to a given problem. The HMM represents learnt probabilistic relationships in transitioning from one heuristic to the next for generating good sequences. However, a single HMM will only represent one learnt behaviour pattern which may not be ideal. Furthermore, using a single HMM to generate sequences is sequential in manner but most processors are parallel in nature. Consequently, this paper proposes that the effectiveness and speed of SSHH can be improved by using multiple SSHH, an ensemble. These will be able to operate in parallel exploiting multi-core processor resources facilitating faster optimisation. Two methods of parallel ensemble SSHH are investigated, sharing the best found solution amongst SSHH instantiations or combining HMM information between SSHH models. The effectiveness of the methods are assessed using a real-world electric bus scheduling optimisation problem. Sharing best found solutions between ensembles of SSHH models that have differing sequence behaviours significantly improved upon sequential SSHH results with much lower run-times.