Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be observed in genealogical networks, but we still can not satisfactorily describe its dynamics or its relation to population evolution over time. In this paper, we use an algorithm to measure the impact of individuals in several numerical populations and study its dynamics of evolution through nonextensive statistics. Like this, we show evidence that the observed emergence of power law has a dynamic behavior over time. This dynamic development can be described using a family of q-exponential distributions whose parameters are time-dependent and follow a specific pattern. We also show evidence that elitism significantly influences the power law scaling factors observed. These results imply that the different power law shapes and deviations observed in genealogical networks are static images of a time-dependent dynamic development that can be satisfactorily described using q-exponential distributions.
Epidemiologists model the dynamics of epidemics in order to propose control strategies based on pharmaceutical and non-pharmaceutical interventions (contact limitation, lock down, vaccination, etc). Hand-designing such strategies is not trivial because of the number of possible interventions and the difficulty to predict long-term effects. This task can be cast as an optimization problem where state-of-the-art machine learning algorithms such as deep reinforcement learning, might bring significant value. However, the specificity of each domain -- epidemic modelling or solving optimization problem -- requires strong collaborations between researchers from different fields of expertise. This is why we introduce EpidemiOptim, a Python toolbox that facilitates collaborations between researchers in epidemiology and optimization. EpidemiOptim turns epidemiological models and cost functions into optimization problems via a standard interface commonly used by optimization practitioners (OpenAI Gym). Reinforcement learning algorithms based on Q-Learning with deep neural networks (DQN) and evolutionary algorithms (NSGA-II) are already implemented. We illustrate the use of EpidemiOptim to find optimal policies for dynamical on-off lock-down control under the optimization of death toll and economic recess using a Susceptible-Exposed-Infectious-Removed (SEIR) model for COVID-19. Using EpidemiOptim and its interactive visualization platform in Jupyter notebooks, epidemiologists, optimization practitioners and others (e.g. economists) can easily compare epidemiological models, costs functions and optimization algorithms to address important choices to be made by health decision-makers.
An unbounded external archive (UEA), which stores all nondominated solutions found during the search process, is frequently used to evaluate the performance of multi-objective evolutionary algorithms (MOEAs) in recent studies. A recent benchmarking study also shows that decomposition-based MOEA (MOEA/D) is competitive with state-of-the-art MOEAs when the UEA is incorporated into MOEA/D. However, a parameter study of MOEA/D using the UEA has not yet been performed. Thus, it is unclear how control parameter settings influence the performance of MOEA/D with the UEA. In this paper, we present an analysis of control parameters of MOEA/D under two performance evaluation scenarios. One is a final population scenario where the performance assessment of MOEAs is performed based on all nondominated solutions in the final population, and the other is a reduced UEA scenario where it is based on a pre-specified number of selected nondominated solutions from the UEA. Control parameters of MOEA/D investigated in this paper include the population size, scalarizing functions, and the penalty parameter of the penalty-based boundary intersection (PBI) function. Experimental results indicate that suitable settings of the three control parameters significantly depend on the choice of an optimization scenario. We also analyze the reason why the best parameter setting is totally different for each scenario.
We consider how an (almost) optimal parameter adaptation process for an adaptive DE might behave, and compare the behavior and performance of this approximately optimal process to that of existing, adaptive mechanisms for DE. An optimal parameter adaptation process is an useful notion for analyzing the parameter adaptation methods in adaptive DE as well as other adaptive evolutionary algorithms, but it cannot be known generally. Thus, we propose a Greedy Approximate Oracle method (GAO) which approximates an optimal parameter adaptation process. We compare the behavior of GAODE, a DE algorithm with GAO, to typical adaptive DEs on six benchmark functions and the BBOB benchmarks, and show that GAO can be used to (1) explore how much room for improvement there is in the performance of the adaptive DEs, and (2) obtain hints for developing future, effective parameter adaptation methods for adaptive DEs.
Multimodality is one of the biggest difficulties for optimization as local optima are often preventing algorithms from making progress. This does not only challenge local strategies that can get stuck. It also hinders meta-heuristics like evolutionary algorithms in convergence to the global optimum. In this paper we present a new concept of gradient descent, which is able to escape local traps. It relies on multiobjectivization of the original problem and applies the recently proposed and here slightly modified multi-objective local search mechanism MOGSA. We use a sophisticated visualization technique for multi-objective problems to prove the working principle of our idea. As such, this work highlights the transfer of new insights from the multi-objective to the single-objective domain and provides first visual evidence that multiobjectivization can link single-objective local optima in multimodal landscapes.
Computational modeling is becoming a widely used methodology in modern neuroscience. However, as the complexity of the phenomena under study increases, the analysis of the results emerging from the simulations concomitantly becomes more challenging. In particular, the configuration and validation of brain circuits involving learning often require the processing of large amounts of action potentials and their comparison to the stimulation being presented to the input of the system. In this study we present a systematic work-flow for the configuration of spiking-neuronal-network-based learning systems including evolutionary algorithms for information transmission optimization, advanced visualization tools for the validation of the best suitable configuration and customized scripts for final quantitative evaluation of the learning capabilities. By integrating both grouped action potential information and stimulation-related events, the proposed visualization framework provides qualitatively assessment of the evolution of the learning process in the simulation under study. The proposed work-flow has been used to study how receptive fields emerge in a network of inhibitory interneurons with excitatory and inhibitory spike-timing dependent plasticity when it is exposed to repetitive and partially overlapped stimulation patterns. According to our results, the output population reliably detected the presence of the stimulation patterns, even when the fan-in ratio of the interneurons was considerably restricted.
Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionary algorithms for multi-modal multi-objective optimization have been proposed in the literature. However, there is no efficient method for multi-modal many-objective optimization, where the number of objectives is more than three. To address this issue, this paper proposes a niching indicator-based multi-modal multi- and many-objective optimization algorithm. In the proposed method, the fitness calculation is performed among a child and its closest individuals in the solution space to maintain the diversity. The performance of the proposed method is evaluated on multi-modal multi-objective test problems with up to 15 objectives. Results show that the proposed method can handle a large number of objectives and find a good approximation of multiple equivalent Pareto optimal solutions. The results also show that the proposed method performs significantly better than eight multi-objective evolutionary algorithms.
Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multi-objective optimization, they are likely to perform poorly for multi-modal multi-objective optimization due to the lack of mechanisms to maintain the solution space diversity. To address this issue, this paper proposes a framework to improve the performance of decomposition-based evolutionary algorithms for multi-modal multi-objective optimization. Our framework is based on three operations: assignment, deletion, and addition operations. One or more individuals can be assigned to the same subproblem to handle multiple equivalent solutions. In each iteration, a child is assigned to a subproblem based on its objective vector, i.e., its location in the objective space. The child is compared with its neighbors in the solution space assigned to the same subproblem. The performance of improved versions of six decomposition-based evolutionary algorithms by our framework is evaluated on various test problems regarding the number of objectives, decision variables, and equivalent Pareto optimal solution sets. Results show that the improved versions perform clearly better than their original algorithms.
Deep facial expression recognition faces two challenges that both stem from the large number of trainable parameters: long training times and a lack of interpretability. We propose a novel method based on evolutionary algorithms, that deals with both challenges by massively reducing the number of trainable parameters, whilst simultaneously retaining classification performance, and in some cases achieving superior performance. We are robustly able to reduce the number of parameters on average by 95% (e.g. from 2M to 100k parameters) with no loss in classification accuracy. The algorithm learns to choose small patches from the image, relative to the nose, which carry the most important information about emotion, and which coincide with typical human choices of important features. Our work implements a novel form attention and shows that evolutionary algorithms are a valuable addition to machine learning in the deep learning era, both for reducing the number of parameters for facial expression recognition and for providing interpretable features that can help reduce bias.
C++ code snippets from a multi-core parallel memory-efficient crossover for genetic programming are given. They may be adapted for separate generation evolutionary algorithms where large chromosomes or small RAM require no more than M + (2 times nthreads) simultaneously active individuals.
Weight initialization is critical in being able to successfully train artificial neural networks (ANNs), and even more so for recurrent neural networks (RNNs) which can easily suffer from vanishing and exploding gradients. In neuroevolution, where evolutionary algorithms are applied to neural architecture search, weights typically need to be initialized at three different times: when initial genomes (ANN architectures) are created at the beginning of the search, when offspring genomes are generated by crossover, and when new nodes or edges are created during mutation. This work explores the difference between using Xavier, Kaiming, and uniform random weight initialization methods, as well as novel Lamarckian weight inheritance methods for initializing new weights during crossover and mutation operations. These are examined using the Evolutionary eXploration of Augmenting Memory Models (EXAMM) neuroevolution algorithm, which is capable of evolving RNNs with a variety of modern memory cells (e.g., LSTM, GRU, MGU, UGRNN and Delta-RNN cells) as well recurrent connections with varying time skips through a high performance island based distributed evolutionary algorithm. Results show that with statistical significance, utilizing the Lamarckian strategies outperforms Kaiming, Xavier and uniform random weight initialization, and can speed neuroevolution by requiring less backpropagation epochs to be evaluated for each generated RNN.
We propose PESA, a novel approach combining Particle Swarm Optimisation (PSO), Evolution Strategy (ES), and Simulated Annealing (SA) in a hybrid Algorithm, inspired from reinforcement learning. PESA hybridizes the three algorithms by storing their solutions in a shared replay memory. Next, PESA applies prioritized replay to redistribute data between the three algorithms in frequent form based on their fitness and priority values, which significantly enhances sample diversity and algorithm exploration. Additionally, greedy replay is used implicitly within SA to improve PESA exploitation close to the end of evolution. The validation against 12 high-dimensional continuous benchmark functions shows superior performance by PESA against standalone ES, PSO, and SA, under similar initial starting points, hyperparameters, and number of generations. PESA shows much better exploration behaviour, faster convergence, and ability to find the global optima compared to its standalone counterparts. Given the promising performance, PESA can offer an efficient optimisation option, especially after it goes through additional multiprocessing improvements to handle complex and expensive fitness functions.
The increasing importance of robots and automation creates a demand for learnable controllers which can be obtained through various approaches such as Evolutionary Algorithms (EAs) or Reinforcement Learning (RL). Unfortunately, these two families of algorithms have mainly developed independently and there are only a few works comparing modern EAs with deep RL algorithms. We show that Multidimensional Archive of Phenotypic Elites (MAP-Elites), which is a modern EA, can deliver better-performing solutions than one of the state-of-the-art RL methods, Proximal Policy Optimization (PPO) in the generation of locomotion controllers for a simulated hexapod robot. Additionally, extensive hyper-parameter tuning shows that MAP-Elites displays greater robustness across seeds and hyper-parameter sets. Generally, this paper demonstrates that EAs combined with modern computational resources display promising characteristics and have the potential to contribute to the state-of-the-art in controller learning.
This paper presents an experimental comparison among four Automated Machine Learning (AutoML) methods for recommending the best classification algorithm for a given input dataset. Three of these methods are based on Evolutionary Algorithms (EAs), and the other is Auto-WEKA, a well-known AutoML method based on the Combined Algorithm Selection and Hyper-parameter optimisation (CASH) approach. The EA-based methods build classification algorithms from a single machine learning paradigm: either decision-tree induction, rule induction, or Bayesian network classification. Auto-WEKA combines algorithm selection and hyper-parameter optimisation to recommend classification algorithms from multiple paradigms. We performed controlled experiments where these four AutoML methods were given the same runtime limit for different values of this limit. In general, the difference in predictive accuracy of the three best AutoML methods was not statistically significant. However, the EA evolving decision-tree induction algorithms has the advantage of producing algorithms that generate interpretable classification models and that are more scalable to large datasets, by comparison with many algorithms from other learning paradigms that can be recommended by Auto-WEKA. We also observed that Auto-WEKA has shown meta-overfitting, a form of overfitting at the meta-learning level, rather than at the base-learning level.
Evolutionary algorithms (EAs) have been successfully applied to optimize the policies for Reinforcement Learning (RL) tasks due to their exploration ability. The recently proposed Negatively Correlated Search (NCS) provides a distinct parallel exploration search behavior and is expected to facilitate RL more effectively. Considering that the commonly adopted neural policies usually involves millions of parameters to be optimized, the direct application of NCS to RL may face a great challenge of the large-scale search space. To address this issue, this paper presents an NCS-friendly Cooperative Coevolution (CC) framework to scale-up NCS while largely preserving its parallel exploration search behavior. The issue of traditional CC that can deteriorate NCS is also discussed. Empirical studies on 10 popular Atari games show that the proposed method can significantly outperform three state-of-the-art deep RL methods with 50% less computational time by effectively exploring a 1.7 million-dimensional search space.
Various studies have shown that immune system inspired hypermutation operators can allow artificial immune systems (AIS) to be very efficient at escaping local optima of multimodal optimisation problems. However, this efficiency comes at the expense of considerably slower runtimes during the exploitation phase compared to standard evolutionary algorithms. We propose modifications to the traditional `hypermutations with mutation potential' (HMP) that allow them to be efficient at exploitation as well as maintaining their effective explorative characteristics. Rather than deterministically evaluating fitness after each bit-flip of a hypermutation, we sample the fitness function stochastically with a `parabolic' distribution which allows the `stop at first constructive mutation' (FCM) variant of HMP to reduce the linear amount of wasted function evaluations when no improvement is found to a constant. The stochastic distribution also allows the removal of the FCM mechanism altogether as originally desired in the design of the HMP operators. We rigorously prove the effectiveness of the proposed operators for all the benchmark functions where the performance of HMP is rigorously understood in the literature and validating the gained insights to show linear speed-ups for the identification of high quality approximate solutions to classical NP-Hard problems from combinatorial optimisation. We then show the superiority of the HMP operators to the traditional ones in an analysis of the complete standard Opt-IA AIS, where the stochastic evaluation scheme allows HMP and ageing operators to work in harmony. Through a comparative performance study of other `fast mutation' operators from the literature, we conclude that a power-law distribution for the parabolic evaluation scheme is the best compromise in black box scenarios where little problem knowledge is available.
Multiple Artificial Intelligence (AI) methods have been proposed over recent years to create controllers to play multiple video games of different nature and complexity without revealing the specific mechanics of each of these games to the AI methods. In recent years, Evolutionary Algorithms (EAs) employing rolling horizon mechanisms have achieved extraordinary results in these type of problems. However, some limitations are present in Rolling Horizon EAs making it a grand challenge of AI. These limitations include the wasteful mechanism of creating a population and evolving it over a fraction of a second to propose an action to be executed by the game agent. Another limitation is to use a scalar value (fitness value) to direct evolutionary search instead of accounting for a mechanism that informs us how a particular agent behaves during the rolling horizon simulation. In this work, we address both of these issues. We introduce the use of a statistical tree that tackles the latter limitation. Furthermore, we tackle the former limitation by employing a mechanism that allows us to seed part of the population using Monte Carlo Tree Search, a method that has dominated multiple General Video Game AI competitions. We show how the proposed novel mechanism, called Statistical Tree-based Population Seeding, achieves better results compared to vanilla Rolling Horizon EAs in a set of 20 games, including 10 stochastic and 10 deterministic games.
This paper proposes environment design in the life simulation game The Sims as a novel platform and challenge for testing divergent search algorithms. In this domain, which includes a minimal viability criterion, the goal is to furnish a house with objects that satisfy the physical needs of a simulated agent. Importantly, the large number of objects available to the player (whether human or automated) affords a wide variety of solutions to the underlying design problem. Empirical studies in a novel open source simulator called SimSim investigate the ability of novelty-based evolutionary algorithms to effectively generate viable environment designs.
Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there has been an increased interest from the evolutionary computation community to model bilevel problems due to its applicability in the real-world applications for decision-making problems. In this work, a partial nested evolutionary approach with a local heuristic search has been proposed to solve the benchmark problems and have outstanding results. This approach relies on the concept of intermarriage-crossover in search of feasible regions by exploiting information from the constraints. A new variant has also been proposed to the commonly used convergence approaches, i.e., optimistic and pessimistic. It is called extreme optimistic approach. The experimental results demonstrate the algorithm converges differently to known optimum solutions with the optimistic variants. Optimistic approach also outperforms pessimistic approach. Comparative statistical analysis of our approach with other recently published partial to complete evolutionary approaches demonstrates very competitive results.
In recent years, machine learning has seen an increasing presencein a large variety of fields, especially in health care and bioinformatics.More specifically, the field where machine learning algorithms have found most applications is Genetic Algorithms.The objective of this paper is to conduct a survey of articles published from 2015 onwards that deal with Genetic Algorithms(GA) and how they are used in bioinformatics.To achieve the objective, a scoping review was conducted that utilized Google Scholar alongside Publish or Perish and the Scimago Journal & CountryRank to search for respectable sources. Upon analyzing 31 articles from the field of bioinformatics, it became apparent that genetic algorithms rarely form a full application, instead they rely on other vital algorithms such as support vector machines.Indeed, support vector machines were the most prevalent algorithms used alongside genetic algorithms; however, while the usage of such algorithms contributes to the heavy focus on accuracy by GA programs, it often sidelines computation times in the process. In fact, most applications employing GAs for classification and feature selectionare nearing or at 100% success rate, and the focus of future GA development should be directed elsewhere. Population-based searches, like GA, are often combined with other machine learning algorithms. In this scoping review, genetic algorithms combined with Support Vector Machines were found to perform best. The performance metric that was evaluated most often was accuracy. Measuring the accuracy avoids measuring the main weakness of GAs, which is computational time. The future of genetic algorithms could be open-ended evolutionary algorithms, which attempt to increase complexity and find diverse solutions, rather than optimize a fitness function and converge to a single best solution from the initial population of solutions.