# Evolutionary Systems

### Training Neural Networks with PSO - Vortarus Technologies LLC

In this article we are going to discuss training neural networks using particle swarm optimization (PSO). Training a neural network is an optimization problem so the optimization algorithm is of primary importance. When training MLPs we are adjusting weights between neurons using an error function as our optimization objective. PNNs and GRNNs use a smoothing factor, σ to define the network. The objective is to find sigmas that minimize error.

### Adaptive Intelligent Secondary Control of Microgrids Using a Biologically-Inspired Reinforcement Learning

In this paper, a biologically-inspired adaptive intelligent secondary controller is developed for microgrids to tackle system dynamics uncertainties, faults, and/or disturbances. The developed adaptive biologically-inspired controller adopts a novel computational model of emotional learning in mammalian limbic system. The learning capability of the proposed biologically-inspired intelligent controller makes it a promising approach to deal with the power system non-linear and volatile dynamics without increasing the controller complexity, and maintain the voltage and frequency stabilities by using an efficient reference tracking mechanism. The performance of the proposed intelligent secondary controller is validated in terms of the voltage and frequency absolute errors in the simulated microgrid. Simulation results highlight the efficiency and robustness of the proposed intelligent controller under the fault conditions and different system uncertainties compared to other benchmark controllers.

### Hierarchical Genetic Algorithms with evolving objective functions

We propose a framework of genetic algorithms which use multi-level hierarchies to solve an optimization problem by searching over the space of simpler objective functions. We solve a variant of Travelling Salesman Problem called \texttt{soft-TSP} and show that when the constraints on the overall objective function are changed the algorithm adapts to churn out solutions for the changed objective. We use this idea to speed up learning by systematically altering the constraints to find a more globally optimal solution. We also use this framework to solve polynomial regression where the actual objective function is unknown but searching over space of available objective functions yields a good approximate solution.

### Towards Automation of Creativity: A Machine Intelligence Approach

Abstract: This paper demonstrates emergence of computational creativity in the field of music. Different aspects of creativity such as producer, process, product and press are studied and formulated. Different notions of computational creativity such as novelty, quality and typicality of compositions as products are studied and evaluated. We formulate an algorithmic perception on human creativity and propose a prototype that is capable of demonstrating human-level creativity. We then validate the proposed prototype by applying various creativity benchmarks with the results obtained and compare the proposed prototype with the other existing computational creative systems. I. INTRODUCTION Computational creativity is the modeling or replicating human creativity computationally. Traditionally computational creativity has focused more on creative systems' products or processes, though this focus has widened recently. Research on creativity offers four Ps of creativity (Rhodes, 1961; MacKinnon, 1970; Jordanous, 2016). These four P's are: 1. Person/Producer: a creative agent 2. Process: an activity done by the creative agent 3. Product: the product of the creative process 4. Press/Environment: the overall environment of creativity 110 The proposed methodology addresses all the four P's of creativity unlike most of recent works, which focus on these individually (Saunders, 2012; Gervas & Leon, 2014; Misztal & Indurkhya, 2014; Sosa & Gero, 2015; Besold & Plaza, 2015; Harmon, 2015). Figure 1 gives a simplified view of proposed computational creative system in the context of four P's of creativity.

### Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms

In the field of multi-objective optimization algorithms, multi-objective Bayesian Global Optimization (MOBGO) is an important branch, in addition to evolutionary multi-objective optimization algorithms (EMOAs). MOBGO utilizes Gaussian Process Models learned from previous objective function evaluations to decide the next evaluation site by maximizing or minimizing an infill criterion. A common criterion in MOBGO is the Expected Hypervolume Improvement (EHVI), which shows a good performance on a wide range of problems, with respect to exploration and exploitation. However, so far it has been a challenge to calculate exact EHVI values efficiently. In this paper, an efficient algorithm for the computation of the exact EHVI for a generic case is proposed. This efficient algorithm is based on partitioning the integration volume into a set of axis-parallel slices. Theoretically, the upper bound time complexities are improved from previously $O (n^2)$ and $O(n^3)$, for two- and three-objective problems respectively, to $\Theta(n\log n)$, which is asymptotically optimal. This article generalizes the scheme in higher dimensional case by utilizing a new hyperbox decomposition technique, which was proposed by D{\"a}chert et al, EJOR, 2017. It also utilizes a generalization of the multilayered integration scheme that scales linearly in the number of hyperboxes of the decomposition. The speed comparison shows that the proposed algorithm in this paper significantly reduces computation time. Finally, this decomposition technique is applied in the calculation of the Probability of Improvement (PoI).

### A Bayesian Approach for the Robust Optimisation of Expensive-To-Evaluate Functions

Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single, possible fragile, optimal design. Expensive black-box functions can be optimised effectively with Bayesian optimisation, where a Gaussian process is a popular choice as a prior over the expensive function. We propose a method for robust optimisation using Bayesian optimisation to find a region of design space in which the expensive function's performance is insensitive to the inputs whilst retaining a good quality. This is achieved by sampling realisations from a Gaussian process modelling the expensive function and evaluating the improvement for each realisation. The expectation of these improvements can be optimised cheaply with an evolutionary algorithm to determine the next location at which to evaluate the expensive function. We describe an efficient process to locate the optimum expected improvement. We show empirically that evaluating the expensive function at the location in the candidate sweet spot about which the model is most uncertain or at random yield the best convergence in contrast to exploitative schemes. We illustrate our method on six test functions in two, five, and ten dimensions, and demonstrate that it is able to outperform a state-of-the-art approach from the literature.

### Towards a framework for the evolution of artificial general intelligence

In this work, a novel framework for the emergence of general intelligence is proposed, where agents evolve through environmental rewards and learn throughout their lifetime without supervision, i.e., self-supervised learning through embodiment. The chosen control mechanism for agents is a biologically plausible neuron model based on spiking neural networks. Network topologies become more complex through evolution, i.e., the topology is not fixed, while the synaptic weights of the networks cannot be inherited, i.e., newborn brains are not trained and have no innate knowledge of the environment. What is subject to the evolutionary process is the network topology, the type of neurons, and the type of learning. This process ensures that controllers that are passed through the generations have the intrinsic ability to learn and adapt during their lifetime in mutable environments. We envision that the described approach may lead to the emergence of the simplest form of artificial general intelligence.

### Optimal initialization of K-means using Particle Swarm Optimization

This paper proposes the use of an optimization algorithm, namely PSO to decide the initial centroids in K-means, to eventually get better accuracy. The vectorized notation of the optimal centroids can be thought of as entities in an optimization space, where the accuracy of K-means over a random subset of the data could act as a fitness measure. The resultant optimal vector can be used as the initial centroids for K-means.

### Derivative-Free Global Optimization Algorithms: Population based Methods and Random Search Approaches

In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation algorithm, which updates the model variables layers by layers with the gradient descent algorithm or its variants. However, the objective functions of deep learning models to be optimized are usually non-convex and the gradient descent algorithms based on the first-order derivative can get stuck into the local optima very easily. To resolve such a problem, various local or global optimization algorithms have been proposed, which can help improve the training of deep learning models greatly. The representative examples include the Bayesian methods, Shubert-Piyavskii algorithm, Direct, LIPO, MCS, GA, SCE, DE, PSO, ES, CMA-ES, hill climbing and simulated annealing, etc. This is a follow-up paper of [18], and we will introduce the population based optimization algorithms, e.g., GA, SCE, DE, PSO, ES and CMA-ES, and random search algorithms, e.g., hill climbing and simulated annealing, in this paper. For the introduction to the other derivative-free optimization algorithms, please refer to [18] for more information.

### Runtime Analysis of the Univariate Marginal Distribution Algorithm under Low Selective Pressure and Prior Noise

We perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between decision variables. For a problem instance of size $n$, the currently best known upper bound on the expected runtime is $\mathcal{O}(n\lambda\log\lambda+n^2)$ (Dang and Lehre, GECCO 2015), while a lower bound necessary to understand how the algorithm copes with variable dependencies is still missing. Motivated by this, we show that the algorithm requires a $e^{\Omega(\mu)}$ runtime with high probability and in expectation if the selective pressure is low; otherwise, we obtain a lower bound of $\Omega(\frac{n\lambda}{\log(\lambda-\mu)})$ on the expected runtime. Furthermore, we for the first time consider the algorithm on the function under a prior noise model and obtain an $\mathcal{O}(n^2)$ expected runtime for the optimal parameter settings. In the end, our theoretical results are accompanied by empirical findings, not only matching with rigorous analyses but also providing new insights into the behaviour of the algorithm.