Improving (1+1) covariance matrix adaptation evolution strategy: A simple yet efficient approach

Abstract

In recent years, part of the meta-heuristic optimisation research community has called for a simplification of the algorithmic design: indeed, while most of the state-of-the-art algorithms are characterised by a high level of complexity, complex algorithms are hard to understand and therefore tune for specific real-world applications. Here, we follow this reductionist approach by combining straightforwardly two methods recently proposed in the literature, namely the Re-sampling Inheritance Search (RIS) and the (1+1) Covariance Matrix Adaptation Evolution Strategy (CMA-ES). We propose an RI-(1+1)-CMA-ES algorithm that on the one hand improves upon the original (1+1)-CMA-ES, on the other it keeps the original spirit of simplicity at the basis of RIS. We show with an extensive experimental campaign that the proposed algorithm efficiently solves a large number of benchmark functions and is competitive with several modern optimisation algorithms much more complex in terms of algorithmic design.

The SOS Platform: Designing, Tuning and Statistically Benchmarking Optimisation Algorithms

“…In particular, the possibility of declaring variables of the kind Algorithm, to initiate and execute optimisation processes inside another algorithm, lead to the implementation of complex algorithms by writing very neat code. This is evident from figure 3, where the code of the iterated local search algorithm proposed in [66] is shown. At first glance, one can observe that the source code is clear and resembles pseudocode.…”

“…More examples are available in the extended results files stored in the repository [92]. In (b), some results from the study in [66] obtained over the functions of the SOS implementation of the CEC 2014 [2] benchmark suite. Extended results tables for this study are available in the repository [91].…”

“…H 0 : A = B cannot be rejected), the symbol = is placed next to B; • if the reference algorithm A statistically outperforms a comparison algorithm B, the symbol + is placed next to B; • if the reference algorithm A is statistically outperformed by a comparison algorithm B, the symbol − is placed next to B. respectively. In (a), some results from the study in [66] obtained over the functions of the SOS implementation of the CEC 2014 [2] benchmark suite. In (b), some from the study in [23] obtained over three real-world problems of the CEC 2011 [77] bechmakr suite implemented in SOS.…”

A Clustering System for Dynamic Data Streams Based on Metaheuristic Optimisation

“…Second, since the proposed methods do not benefit from preceding optimisation processes (as shown in Figure 8), probably because of the dynamic nature of the problem, the optimisation algorithm employing "restart" mechanisms will be implemented and tested. These algorithms usually work on a very short computational budget and handle dynamic domains better than others by simply re-sampling the initial point where a local search routine is applied, as, e.g., [54], or by also adding to it information from the previous past solution with the "inheritance" method [55][56][57].…”

Can Single Solution Optimisation Methods Be Structurally Biased?

“…Several methods, such as Rosenbrock, Powell, Solis-Wets and SPSA, are designed to be global optimisers but are currently mainly used for local search [41]- [43]. Also metaheuristics such as (1+1)-CMAES have been proven to show better results when equipped with a re-start mechanism, to move upon exploration, and run multiple times with a short budget to refine promising candidate solutions [44]. Finally, it has bee reported previously that NMA and RM are free of SB [15].…”