This paper aims to produce classifiers that are not only accurate but also interpretable to decision makers. The classifiers are represented in the form of risk scores, i.e. simple linear classifiers where coefficient vectors are sparse and bounded integer vectors which are then optimised by a novel and scalable discrete particle swarm optimisation algorithm. In contrast to past studies which usually use particle swarm optimisation as a pre-processing step, the proposed algorithm incorporates particle swarm optimisation into the classification process. A penalty-based fitness function and a local search heuristic based on symmetric uncertainty are developed to efficiently identify classifiers with high classification performance and a preferred model size or complexity. Experiments with 10 benchmark datasets show that the proposed swarm-based algorithm is a strong candidate to develop effective linear classifiers. Comparisons with other interpretable machine learning algorithms that produce rule-based and tree-based classifiers also demonstrate the competitiveness of the proposed algorithm. Further analyses also confirm the interpretability of the produced classifiers. Finally, the proposed algorithm shows excellent speed-up via parallelisation, which gives it a great advantage when coping with large scale problems.