Particle swarm optimization (PSO) is an iterative search method that moves a set of candidate solution around a search-space towards the best known global and local solutions with randomized step lengths. PSO frequently accelerates optimization in practical applications, where gradients are not available and function evaluations expensive. Yet the traditional PSO algorithm ignores the potential knowledge that could have been gained of the objective function from the observations by individual particles. Hence, we draw upon concepts from Bayesian optimization and introduce a stochastic surrogate model of the objective function. That is, we fit a Gaussian process to past evaluations of the objective function, forecast its shape and then adapt the particle movements based on it. Our computational experiments demonstrate that baseline implementations of PSO (i.e., SPSO2011) are outperformed. Furthermore, compared to, state-of-art surrogate-assisted evolutionary algorithms, we achieve substantial performance improvements on several popular benchmark functions. Overall, we find that our algorithm attains desirable properties for exploratory and exploitative behavior.
Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires an unreasonable amount of time using traditional exhaustive search algorithms. The success of these population-based frameworks is mainly due to their flexibility and ease of adaptation to the most different and complex optimisation problems. This paper presents a metaheuristic algorithm called Stochastic Fractal Search, inspired by the natural phenomenon of growth based on a mathematical concept called the fractal, which is shown to be able to explore the search space more efficiently. This paper also focuses on the algorithm steps and some example applications of engineering design optimisation problems commonly used in the literature being applied to the proposed algorithm.
Fuzzy Cognitive Maps (FCMs) is a complex systems modeling technique which, due to its unique advantages, has lately risen in popularity. They are based on graphs that represent the causal relationships among the parameters of the system to be modeled, and they stand out for their interpretability and flexibility. With the late popularity of FCMs, a plethora of research efforts have taken place to develop and optimize the model. One of the most important elements of FCMs is the learning algorithm they use, and their effectiveness is largely determined by it. The learning algorithms learn the node weights of an FCM, with the goal of converging towards the desired behavior. The present study reviews the genetic algorithms used for training FCMs, as well as gives a general overview of the FCM learning algorithms, putting evolutionary computing into the wider context.
Generative Adversarial Networks (GANs) are powerful generative models that achieved strong results, mainly in the image domain. However, the training of GANs is not trivial, presenting some challenges tackled by different strategies. Evolutionary algorithms, such as COEGAN, were recently proposed as a solution to improve the GAN training, overcoming common problems that affect the model, such as vanishing gradient and mode collapse. In this work, we propose an evaluation method based on t-distributed Stochastic Neighbour Embedding (t-SNE) to assess the progress of GANs and visualize the distribution learned by generators in training. We propose the use of the feature space extracted from trained discriminators to evaluate samples produced by generators and from the input dataset. A metric based on the resulting t-SNE maps and the Jaccard index is proposed to represent the model quality. Experiments were conducted to assess the progress of GANs when trained using COEGAN. The results show both by visual inspection and metrics that the Evolutionary Algorithm gradually improves discriminators and generators through generations, avoiding problems such as mode collapse.
Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called $SD-(1+1)EA$ introduced by Rajabi and Witt (GECCO 2020) adds stagnation detection to the classical $(1+1)EA$ with standard bit mutation, which flips each bit independently with some mutation rate, and raises the mutation rate when the algorithm is likely to have encountered local optima. In this paper, we investigate stagnation detection in the context of the $k$-bit flip operator of randomized local search that flips $k$ bits chosen uniformly at random and let stagnation detection adjust the parameter $k$. We obtain improved runtime results compared to the $SD-(1+1)EA$ amounting to a speed-up of up to $e=2.71\dots$ Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of $k$ due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the local $k$-bit flip with stagnation detection.
There is a growing interest in automated neural architecture search (NAS) methods. They are employed to routinely deliver high-quality neural network architectures for various challenging data sets and reduce the designer's effort. The NAS methods utilizing multi-objective evolutionary algorithms are especially useful when the objective is not only to minimize the network error but also to minimize the number of parameters (weights) or power consumption of the inference phase. We propose a multi-objective NAS method based on Cartesian genetic programming for evolving convolutional neural networks (CNN). The method allows approximate operations to be used in CNNs to reduce the power consumption of a target hardware implementation. During the NAS process, a suitable CNN architecture is evolved together with approximate multipliers to deliver the best trade-offs between the accuracy, network size, and power consumption. The most suitable approximate multipliers are automatically selected from a library of approximate multipliers. Evolved CNNs are compared with common human-created CNNs of a similar complexity on the CIFAR-10 benchmark problem.
The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature. While particle swarm optimizers share such advantages, they outperform evolutionary algorithms in that they require lower computational cost and easier implementation, involving no operator design and few coefficients to be tuned. However, even marginal variations in the settings of these coefficients greatly influence the dynamics of the swarm. Since this paper does not intend to study their tuning, general-purpose settings are taken from previous studies, and virtually the same algorithm is used to optimize a variety of notably different problems. Thus, following a review of the paradigm, the algorithm is tested on a set of benchmark functions and engineering problems taken from the literature. Later, complementary lines of code are incorporated to adapt the method to combinatorial optimization as it occurs in scheduling problems, and a real case is solved using the same optimizer with the same settings. The aim is to show the flexibility and robustness of the approach, which can handle a wide variety of problems.
The range of applications of traditional optimization methods are limited by the features of the object variables, and of both the objective and the constraint functions. In contrast, population-based algorithms whose optimization capabilities are emergent properties, such as evolutionary algorithms and particle swarm optimization, present almost no restriction on those features and can handle different optimization problems with few or no adaptations. Their main drawbacks consist of their comparatively higher computational cost and difficulty in handling equality constraints. The particle swarm optimization method is sometimes viewed as an evolutionary algorithm because of their many similarities, despite not being inspired by the same metaphor: they evolve a population of individuals taking into account previous experiences and using stochastic operators to introduce new responses. The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature for decades. While the particle swarm optimizers share such advantages, their main desirable features when compared to evolutionary algorithms are their lower computational cost and easier implementation, involving no operator design and few parameters to be tuned. However, even slight modifications of these parameters greatly influence the dynamics of the swarm. This paper deals with the effect of the settings of the parameters of the particles' velocity update equation on the behaviour of the system.
Traditional methods present a very restrictive range of applications, mainly limited by the features of the function to be optimized and of the constraint functions. In contrast, evolutionary algorithms present almost no restriction to the features of these functions, although the most appropriate constraint-handling technique is still an open question. The particle swarm optimization (PSO) method is sometimes viewed as another evolutionary algorithm because of their many similarities, despite not being inspired by the same metaphor. Namely, they evolve a population of individuals taking into consideration previous experiences and using stochastic operators to introduce new responses. The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature for decades. While all such advantages are valid when comparing the PSO paradigm to traditional methods, its main advantages with respect to evolutionary algorithms consist of its noticeably lower computational cost and easier implementation. In fact, the plain version can be programmed in a few lines of code, involving no operator design and few parameters to be tuned. This paper deals with three important aspects of the method: the influence of the parameters' tuning on the behaviour of the system; the design of stopping criteria so that the reliability of the solution found can be somehow estimated and computational cost can be saved; and the development of appropriate techniques to handle constraints, given that the original method is designed for unconstrained optimization problems.
Safe learning and optimization deals with learning and optimization problems that avoid, as much as possible, the evaluation of non-safe input points, which are solutions, policies, or strategies that cause an irrecoverable loss (e.g., breakage of a machine or equipment, or life threat). Although a comprehensive survey of safe reinforcement learning algorithms was published in 2015, a number of new algorithms have been proposed thereafter, and related works in active learning and in optimization were not considered. This paper reviews those algorithms from a number of domains including reinforcement learning, Gaussian process regression and classification, evolutionary algorithms, and active learning. We provide the fundamental concepts on which the reviewed algorithms are based and a characterization of the individual algorithms. We conclude by explaining how the algorithms are connected and suggestions for future research.
Variable division and optimization (D\&O) is a frequently utilized algorithm design paradigm in Evolutionary Algorithms (EAs). A D\&O EA divides a variable into partial variables and then optimize them respectively. A complicated problem is thus divided into simple subtasks. For example, a variable of portfolio problem can be divided into two partial variables, i.e. the selection of assets and the allocation of capital. Thereby, we optimize these two partial variables respectively. There is no formal discussion about how are the partial variables iteratively optimized and why can it work for both single- and multi-objective problems in D\&O. In this paper, this gap is filled. According to the discussion, an elitist selection method for partial variables in multiobjective problems is developed. Then this method is incorporated into the Decomposition-Based Multiobjective Evolutionary Algorithm (D\&O-MOEA/D). With the help of a mathematical programming optimizer, it is achieved on the constrained multiobjective portfolio problems. In the empirical study, D\&O-MOEA/D is implemented for 20 instances and recent Chinese stock markets. The results show the superiority and versatility of D\&O-MOEA/D on large-scale instances while the performance of it on small-scale problems is also not bad. The former targets convergence towards the Pareto front and the latter helps promote diversity among the non-dominated solutions during the search process.
Bacteria have been a source of inspiration for the design of evolutionary algorithms. At the beginning of the 20th century synthetic biology was born, a discipline whose goal is the design of biological systems that do not exist in nature, for example, programmable synthetic bacteria. In this paper, we introduce as a novelty the designing of evolutionary algorithms where all the steps are conducted by synthetic bacteria. To this end, we designed a genetic algorithm, which we have named BAGA, illustrating its utility solving simple instances of optimization problems such as function optimization, 0/1 knapsack problem, Hamiltonian path problem. The results obtained open the possibility of conceiving evolutionary algorithms inspired by principles, mechanisms and genetic circuits from synthetic biology. In summary, we can conclude that synthetic biology is a source of inspiration either for the design of evolutionary algorithms or for some of their steps, as shown by the results obtained in our simulation experiments.
In this paper, we approach the problem of optimizing blackbox functions over large hybrid search spaces consisting of both combinatorial and continuous parameters. We demonstrate that previous evolutionary algorithms which rely on mutation-based approaches, while flexible over combinatorial spaces, suffer from a curse of dimensionality in high dimensional continuous spaces both theoretically and empirically, which thus limits their scope over hybrid search spaces as well. In order to combat this curse, we propose ES-ENAS, a simple and modular joint optimization procedure combining the class of sample-efficient smoothed gradient techniques, commonly known as Evolutionary Strategies (ES), with combinatorial optimizers in a highly scalable and intuitive way, inspired by the one-shot or supernet paradigm introduced in Efficient Neural Architecture Search (ENAS). By doing so, we achieve significantly more sample efficiency, which we empirically demonstrate over synthetic benchmarks, and are further able to apply ES-ENAS for architecture search over popular RL benchmarks.
Large-scale multiobjective optimization problems (LSMOPs) are characterized as involving hundreds or even thousands of decision variables and multiple conflicting objectives. An excellent algorithm for solving LSMOPs should find Pareto-optimal solutions with diversity and escape from local optima in the large-scale search space. Previous research has shown that these optimal solutions are uniformly distributed on the manifold structure in the low-dimensional space. However, traditional evolutionary algorithms for solving LSMOPs have some deficiencies in dealing with this structural manifold, resulting in poor diversity, local optima, and inefficient searches. In this work, a generative adversarial network (GAN)-based manifold interpolation framework is proposed to learn the manifold and generate high-quality solutions on this manifold, thereby improving the performance of evolutionary algorithms. We compare the proposed algorithm with several state-of-the-art algorithms on large-scale multiobjective benchmark functions. Experimental results have demonstrated the significant improvements achieved by this framework in solving LSMOPs.
Neural Architecture Search (NAS) has gained significant popularity as an effective tool for designing high performance deep neural networks (DNNs). NAS can be performed via policy gradient, evolutionary algorithms, differentiable architecture search or tree-search methods. While significant progress has been made for both policy gradient and differentiable architecture search, tree-search methods have so far failed to achieve comparable accuracy or search efficiency. In this paper, we formulate NAS as a Combinatorial Multi-Armed Bandit (CMAB) problem (CMAB-NAS). This allows the decomposition of a large search space into smaller blocks where tree-search methods can be applied more effectively and efficiently. We further leverage a tree-based method called Nested Monte-Carlo Search to tackle the CMAB-NAS problem. On CIFAR-10, our approach discovers a cell structure that achieves a low error rate that is comparable to the state-of-the-art, using only 0.58 GPU days, which is 20 times faster than current tree-search methods. Moreover, the discovered structure transfers well to large-scale datasets such as ImageNet.
Robot gait optimization is the task of generating an optimal control trajectory under various internal and external constraints. Given the high dimensions of control space, this problem is particularly challenging for multi-legged robots walking in complex and unknown environments. Existing literatures often regard the gait generation as an optimization problem and solve the gait optimization from scratch for robots walking in a specific environment. However, such approaches do not consider the use of pre-acquired knowledge which can be useful in improving the quality and speed of motion generation in complex environments. To address the issue, this paper proposes a transfer learning-based evolutionary framework for multi-objective gait optimization, named Tr-GO. The idea is to initialize a high-quality population by using the technique of transfer learning, so any kind of population-based optimization algorithms can be seamlessly integrated into this framework. The advantage is that the generated gait can not only dynamically adapt to different environments and tasks, but also simultaneously satisfy multiple design specifications (e.g., speed, stability). The experimental results show the effectiveness of the proposed framework for the gait optimization problem based on three multi-objective evolutionary algorithms: NSGA-II, RM-MEDA and MOPSO. When transferring the pre-acquired knowledge from the plain terrain to various inclined and rugged ones, the proposed Tr-GO framework accelerates the evolution process by a minimum of 3-4 times compared with non-transferred scenarios.
We combine two popular optimization approaches to derive learning algorithms for generative models: variational optimization and evolutionary algorithms. The combination is realized for generative models with discrete latents by using truncated posteriors as the family of variational distributions. The variational parameters of truncated posteriors are sets of latent states. By interpreting these states as genomes of individuals and by using the variational lower bound to define a fitness, we can apply evolutionary algorithms to realize the variational loop. The used variational distributions are very flexible and we show that evolutionary algorithms can effectively and efficiently optimize the variational bound. Furthermore, the variational loop is generally applicable ("black box") with no analytical derivations required. To show general applicability, we apply the approach to three generative models (we use noisy-OR Bayes Nets, Binary Sparse Coding, and Spike-and-Slab Sparse Coding). To demonstrate effectiveness and efficiency of the novel variational approach, we use the standard competitive benchmarks of image denoising and inpainting. The benchmarks allow quantitative comparisons to a wide range of methods including probabilistic approaches, deep deterministic and generative networks, and non-local image processing methods. In the category of "zero-shot" learning (when only the corrupted image is used for training), we observed the evolutionary variational algorithm to significantly improve the state-of-the-art in many benchmark settings. For one well-known inpainting benchmark, we also observed state-of-the-art performance across all categories of algorithms although we only train on the corrupted image. In general, our investigations highlight the importance of research on optimization methods for generative models to achieve performance improvements.
In this paper, a genetic algorithm, one of the evolutionary algorithms optimization methods, is used for the first time for the problem of finding extremal binary self-dual codes. We present a comparison of the computational times between a genetic algorithm and a linear search for different size search spaces and show that the genetic algorithm is capable of finding binary self-dual codes significantly faster than the linear search. Moreover, by employing a known matrix construction together with the genetic algorithm, we are able to obtain new binary self-dual codes of lengths 68 and 72 in a significantly short time. In particular, we obtain 11 new extremal binary self-dual codes of length 68 and 17 new binary self-dual codes of length 72.
To handle different types of Many-Objective Optimization Problems (MaOPs), Many-Objective Evolutionary Algorithms (MaOEAs) need to simultaneously maintain convergence and population diversity in the high-dimensional objective space. In order to balance the relationship between diversity and convergence, we introduce a Kernel Matrix and probability model called Determinantal Point Processes (DPPs). Our Many-Objective Evolutionary Algorithm with Determinantal Point Processes (MaOEADPPs) is presented and compared with several state-of-the-art algorithms on various types of MaOPs \textcolor{blue}{with different numbers of objectives}. The experimental results demonstrate that MaOEADPPs is competitive.
Reinforcement learning techniques achieved human-level performance in several tasks in the last decade. However, in recent years, the need for interpretability emerged: we want to be able to understand how a system works and the reasons behind its decisions. Not only we need interpretability to assess the safety of the produced systems, we also need it to extract knowledge about unknown problems. While some techniques that optimize decision trees for reinforcement learning do exist, they usually employ greedy algorithms or they do not exploit the rewards given by the environment. This means that these techniques may easily get stuck in local optima. In this work, we propose a novel approach to interpretable reinforcement learning that uses decision trees. We present a two-level optimization scheme that combines the advantages of evolutionary algorithms with the advantages of Q-learning. This way we decompose the problem into two sub-problems: the problem of finding a meaningful and useful decomposition of the state space, and the problem of associating an action to each state. We test the proposed method on three well-known reinforcement learning benchmarks, on which it results competitive with respect to the state-of-the-art in both performance and interpretability. Finally, we perform an ablation study that confirms that using the two-level optimization scheme gives a boost in performance in non-trivial environments with respect to a one-layer optimization technique.