## 3 The CRO-SL: A Low-Level Ensemble Evolutionary Algorithm
### Substrate Layers Defined in the CRO-SL  
Very different search strategies can be defined in the CRO-SL as part of the multi-method approach. They are usually defined at the practitioner's discretion. In previous approaches, it has been shown that combinations of well-known traditional operators with novel search techniques provide the best set of techniques (substrates) in the CRO-SL. Some of the most used traditional operators in previous applications of the CRO-SL are Harmony Search (HS), Differential Evolution (DE), classical two-points crossover (2 Px), classical multi-points crossover (MPx), and Gaussian-based mutation (GM). In this paper, we combine these traditional search strategies with two new operators for search and optimization, recently proposed: the Firefly algorithm (Fa) and the Water Wave Optimization (WWo) approach. Previous simulations were developed considering each substrate individually. All the functional values for both cases analyzed in the paper were above the functional value obtained using a combination of all the substrates. Thus, demonstrating a worst performance when they work independently than when working assembled in the CRO-SL. We provide here a short definition of these substrates for the CRO-SL ensemble. 1. HS: Mutation from the Harmony Search algorithm. Harmony Search [52] is a population-based meta-heuristic that mimics the improvisation of a music orchestra while it is composing a melody. HS controls how new larvae are generated in one of the following ways: (i) with a probability HMCR\(\in[0,1]\) (Harmony Memory Considering Rate), the value of a component of the new larva is drawn uniformly from the same values of the component in the other corals, and (ii) with a probability PAR\(\in[0,1]\) (Pitch Adjusting Rate), subtle adjustments are applied to the values of the current larva, replaced by any of its neighboring values (upper or lower, with equal probability). 2. DE: Mutation from Differential Evolution algorithm (with \(F=0.6\)). This operator is based on the evolutionary algorithm with the same name [53], a method with powerful global search capabilities. DE introduces a differential mechanism for exploringthe search space. Therefore, new larvae are generated by perturbing the population members using vector differences of individuals. Perturbations are introduced by applying \(x^{\prime}_{i}=x^{1}_{i}+F(x^{2}_{i}-x^{3}_{i})\) (where \(F\) determines the evolution factor weighting the perturbation amplitude) for each encoded parameter on a random basis. After this perturbation, final perturbed vector \(x^{\prime}\) is combined with an alternative coral in the reef following a classical 2-points crossover, as defined next. 3. 2 Px: Classical 2-points crossover. The crossover operator is the most classical exploration mechanism in genetic and evolutionary algorithms [54]. It consists of coupling to individuals at random, choosing two points for the crossover, and interchanging the genetic material in-between both points. In the CRO-SL, one individual to be crossed is from the 2 Px substrate, whereas the couple can be chosen from any part of the reef. 4. MPx: Multi-points crossover. Similar to the 2-points crossover, but in this case a number \(k\) of crossover points are selected, and a binary template decides whether parts of the individuals are interchanged. 5. GM: Gaussian Mutation, with a \(\sigma\) value linearly decreasing during the run, from \(0.2\cdot(A-B)\) to \(0.02\cdot(A-B)\), where \([B,A]\) is the domain search. Specifically, the Gaussian probability density function is \[f_{G(0,\sigma^{2})}(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{x^{2}}{2\sigma^{2} }}.\] The reason of adapting the value of \(\sigma\) along the generations is to provide a stronger mutation in the beginning of the optimization, while fine-tuning with smaller displacements nearing the end. The mutated larva is thus calculated as \(x^{\prime}_{i}=x_{i}+\delta N_{i}(0,1)\), where \(N_{i}(0,1)\) is a random number following the Gaussian distribution. 6.