Abstract: The firefly algorithm is a recent nature-inspired algorithm that is receiving increasing attention from the scientific community during the last few years. One of its most promising variants is given by the memetic self-adaptive firefly algorithm (MSA-FFA), recently introduced to solve combinatorial problems. In this paper we propose a modification of the original MSA-FFA for continuous optimisation problems. The most important features of our method are: the problem-dependent selection of control parameters for self-adaptation, a simple population model providing an adequate trade-off between exploration and exploitation, and the use of an adaptive-size Luus-Jaakola random local search. This new method is applied to solve a very difficult real-world continuous optimisation problem arising in geometric modelling and manufacturing. The paper also provides the first reliable, standardised benchmark for this optimisation problem. This benchmark is used for a comparative analysis of our method with respect to some of the most popular nature-inspired algorithms. Our results show that the proposed method outperforms previous approaches (including the standard firefly algorithm) for most of the instances in the benchmark.

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