Memetic algorithms with continuous local search methods have arisen as effective tools to address the difficulty of obtaining reliable solutions of high precision for complex continuous optimisation problems. There exists a group of continuous local search algorithms that stand out as exceptional local search optimisers. However, on some occasions, they may become very expensive, because of the way they exploit local information to guide the search process. In this paper, they are called intensive continuous local search methods. Given the potential of this type of local optimisation methods, it is interesting to build prospective memetic algorithm models with them.

This paper presents the concept of local search chain as a springboard to design memetic algorithm approaches that can effectively use intense continuous local search methods as local search operators. Local search chain concerns the idea that, at one stage, the local search operator may continue the operation of a previous invocation, starting from the final configuration (initial solution, strategy parameter values, internal variables, etc.) reached by this one. The proposed memetic algorithm favours the formation of local search chains during the memetic algorithm run with the aim of concentrating local tuning in search regions showing promise. In order to study the performance of the new memetic algorithm model, an instance is implemented with CMA-ES as an intense local search method. The benefits of the proposal in comparison to other kinds of memetic algorithms and evolutionary algorithms proposed in the literature to deal with continuous optimisation problems are experimentally shown. Concretely, the empirical study reveals a clear superiority when tackling high-dimensional problems.

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