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PurposeThe purpose of this paper is to present a new particle swarm optimization (PSO) algorithm called HelixPSO for finding ribonucleic acid (RNA) secondary structures that have a low energy and are similar to the native structure.Design/methodology/approachTwo variants of HelixPSO are described and compared to the recent algorithms Rna‐Predict, SARNA‐Predict, SetPSO and RNAfold. Furthermore, a parallel version of the HelixPSO is proposed.FindingsFor a set of standard RNA test sequences it is shown experimentally that HelixPSO obtains a better average sensitivity than SARNA‐Predict and SetPSO and is as good as RNA‐Predict and RNAfold. When best values for different measures (e.g. number of correctly predicted base pairs, false positives and sensitivity) over several runs are compared, HelixPSO performs better than RNAfold, similar to RNA‐Predict, and is outperformed by SARNA‐Predict. It is shown that HelixPSO complements RNA‐Predict and SARNA‐Predict well since the algorithms show often very different behavior on the same sequence. For the parallel version of HelixPSO it is shown that good speedup values can be obtained for small to medium size PC clusters.Originality/valueThe new PSO algorithm HelixPSO for finding RNA secondary structures uses different algorithmic ideas than the other existing PSO algorithm SetPSO. HelixPSO uses thermodynamic information as well as the centroid as a reference structure and is based on a multiple swarm approach.

PurposeThe purpose of this paper is to propose an algorithm that is based on the ant colony optimization (ACO) metaheuristic for producing harmonized melodies. ACO is a nature inspired metaheuristic where a colony of ants searches for an optimum of a function. The algorithm works in two stages. In the first stage it creates a melody. The obtained melody is then harmonized according to the rules of baroque harmony in the second stage. A multi‐objective version of the algorithm is also proposed, where each tier is optimized as a separate objective.Design/methodology/approachThe ACO metaheuristic is adapted to graphs representing notes and chords. Desirability of a sequence of notes is measured by conformance to compositional rules. The fitness of a melody is evaluated with five equally weighted rules governing smoothness of the melody curve, its contour, tendency tone resolution, tone colors and the pitch of the final note. Harmonization is guided by six rules, grouped into three tiers of two rules each. These rules cover chord arrangement, voice distance, voice leading, harmonic progression, smoothness, and chord resolution. Rules of a tier do not score unless those of the previous tier yield high values.FindingsThe proposed algorithm improves on the only other existing musical ACO by adding the notion of harmony and by evolving voices codependently. The output is comparable to different types of other existing algorithms (genetic algorithm, rule‐based search algorithm) in the field. The multi‐objective variant significantly enhances solution quality and convergence speed, which makes extensions of the system for real time performance realistic.Originality/valueThis algorithm is the first ACO algorithm proposed for the problem of melody creation and harmonization.