A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation problem, which is often unknown to the user. Non-deterministic parameter control mechanisms adjust parameters using information obtained from the evolutionary process. Self-adaptation -- where parameter settings are encoded in the chromosomes of individuals and evolve through mutation and crossover -- is a popular parameter control mechanism in evolutionary strategies. However, there is little theoretical evidence that self-adaptation is effective, and self-adaptation has largely been ignored by the discrete evolutionary computation community. Here we show through a theoretical runtime analysis that a non-elitist, discrete evolutionary algorithm which self-adapts its mutation rate not only outperforms EAs which use static mutation rates on \leadingones, but also improves asymptotically on an EA using a state-of-the-art control mechanism. The structure of this problem depends on a parameter $k$, which is \emph{a priori} unknown to the algorithm, and which is needed to appropriately set a fixed mutation rate. The self-adaptive EA achieves the same asymptotic runtime as if this parameter was known to the algorithm beforehand, which is an asymptotic speedup for this problem compared to all other EAs previously studied. An experimental study of how the mutation-rates evolve show that they respond adequately to a diverse range of problem structures. These results suggest that self-adaptation should be adopted more broadly as a parameter control mechanism in discrete, non-elitist evolutionary algorithms.
Neural architecture search (NAS) is a promising method for automatically design neural architectures. NAS adopts a search strategy to explore the predefined search space to find outstanding performance architecture with the minimum searching costs. Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement or inefficient exploration ability. In this paper, we propose a neural predictor guided evolutionary algorithm to enhance the exploration ability of EA for NAS (NPENAS) and design two kinds of neural predictors. The first predictor is defined from Bayesian optimization and we propose a graph-based uncertainty estimation network as a surrogate model that is easy to implement and computationally efficient. The second predictor is a graph-based neural network that directly outputs the performance prediction of the input neural architecture. The NPENAS using the two neural predictors are denoted as NPENAS-BO and NPENAS-NP respectively. In addition, we introduce a new random architecture sampling method to overcome the drawbacks of the existing sampling method. Extensive experiments demonstrate the superiority of NPENAS. Quantitative results on three NAS search spaces indicate that both NPENAS-BO and NPENAS-NP outperform most existing NAS algorithms, with NPENAS-BO achieving state-of-the-art performance on NASBench-201 and NPENAS-NP on NASBench-101 and DARTS, respectively.
Generative Adversarial Networks (GANs) are popular tools for generative modeling. The dynamics of their adversarial learning give rise to convergence pathologies during training such as mode and discriminator collapse. In machine learning, ensembles of predictors demonstrate better results than a single predictor for many tasks. In this study, we apply two evolutionary algorithms (EAs) to create ensembles to re-purpose generative models, i.e., given a set of heterogeneous generators that were optimized for one objective (e.g., minimize Frechet Inception Distance), create ensembles of them for optimizing a different objective (e.g., maximize the diversity of the generated samples). The first method is restricted by the exact size of the ensemble and the second method only restricts the upper bound of the ensemble size. Experimental analysis on the MNIST image benchmark demonstrates that both EA ensembles creation methods can re-purpose the models, without reducing their original functionality. The EA-based demonstrate significantly better performance compared to other heuristic-based methods. When comparing both evolutionary, the one with only an upper size bound on the ensemble size is the best.
In evolutionary algorithms, genetic operators iteratively generate new offspring which constitute a potentially valuable set of search history. To boost the performance of crossover in real-coded genetic algorithm (RCGA), in this paper we propose to exploit the search history cached so far in an online style during the iteration. Specifically, survivor individuals over past few generations are collected and stored in the archive to form the search history. We introduce a simple yet effective crossover model driven by the search history (abbreviated as SHX). In particular, the search history is clustered and each cluster is assigned a score for SHX. In essence, the proposed SHX is a data-driven method which exploits the search history to perform offspring selection after the offspring generation. Since no additional fitness evaluations are needed, SHX is favorable for the tasks with limited budget or expensive fitness evaluations. We experimentally verify the effectiveness of SHX over 4 benchmark functions. Quantitative results show that our SHX can significantly enhance the performance of RCGA, in terms of accuracy.
Game-playing Evolutionary Algorithms, specifically Rolling Horizon Evolutionary Algorithms, have recently managed to beat the state of the art in win rate across many video games. However, the best results in a game are highly dependent on the specific configuration of modifications and hybrids introduced over several papers, each adding additional parameters to the core algorithm. Further, the best previously published parameters have been found from only a few human-picked combinations, as the possibility space has grown beyond exhaustive search. This paper presents the state of the art in Rolling Horizon Evolutionary Algorithms, combining all modifications described in literature, as well as new ones, for a large resultant hybrid. We then use a parameter optimiser, the N-Tuple Bandit Evolutionary Algorithm, to find the best combination of parameters in 20 games from the General Video Game AI Framework. Further, we analyse the algorithm's parameters and some interesting combinations revealed through the optimisation process. Lastly, we find new state of the art solutions on several games by automatically exploring the large parameter space of RHEA.
The performance of a deep neural network is heavily dependent on its architecture and various neural architecture search strategies have been developed for automated network architecture design. Recently, evolutionary neural architecture search (ENAS) has received increasing attention due to the attractive global optimization capability of evolutionary algorithms. However, ENAS suffers from extremely high computation costs because a large number of performance evaluations is usually required in evolutionary optimization and training deep neural networks is itself computationally very intensive. To address this issue, this paper proposes a new evolutionary framework for fast ENAS based on directed acyclic graph, in which parents are randomly sampled and trained on each mini-batch of training data. In addition, a node inheritance strategy is adopted to generate offspring individuals and their fitness is directly evaluated without training. To enhance the feature processing capability of the evolved neural networks, we also encode a channel attention mechanism in the search space. We evaluate the proposed algorithm on the widely used datasets, in comparison with 26 state-of-the-art peer algorithms. Our experimental results show the proposed algorithm is not only computationally much more efficiently, but also highly competitive in learning performance.
Wave energy is a fast-developing and promising renewable energy resource. The primary goal of this research is to maximise the total harnessed power of a large wave farm consisting of fully-submerged three-tether wave energy converters (WECs). Energy maximisation for large farms is a challenging search problem due to the costly calculations of the hydrodynamic interactions between WECs in a large wave farm and the high dimensionality of the search space. To address this problem, we propose a new hybrid multi-strategy evolutionary framework combining smart initialisation, binary population-based evolutionary algorithm, discrete local search and continuous global optimisation. For assessing the performance of the proposed hybrid method, we compare it with a wide variety of state-of-the-art optimisation approaches, including six continuous evolutionary algorithms, four discrete search techniques and three hybrid optimisation methods. The results show that the proposed method performs considerably better in terms of convergence speed and farm output.
Portfolio optimization is a financial task which requires the allocation of capital on a set of financial assets to achieve a better trade-off between return and risk. To solve this problem, recent studies applied multi-objective evolutionary algorithms (MOEAs) for its natural bi-objective structure. This paper presents a method injecting a distribution-based mutation method named L\'evy Flight into a decomposition based MOEA named MOEA/D. The proposed algorithm is compared with three MOEA/D-like algorithms, NSGA-II, and other distribution-based mutation methods on five portfolio optimization benchmarks sized from 31 to 225 in OR library without constraints, assessing with six metrics. Numerical results and statistical test indicate that this method can outperform comparison methods in most cases. We analyze how Levy Flight contributes to this improvement by promoting global search early in the optimization. We explain this improvement by considering the interaction between mutation method and the property of the problem.
This paper presents Natural Evolution Strategies (NES), a recent family of algorithms that constitute a more principled approach to black-box optimization than established evolutionary algorithms. NES maintains a parameterized distribution on the set of solution candidates, and the natural gradient is used to update the distribution's parameters in the direction of higher expected fitness. We introduce a collection of techniques that address issues of convergence, robustness, sample complexity, computational complexity and sensitivity to hyperparameters. This paper explores a number of implementations of the NES family, ranging from general-purpose multi-variate normal distributions to heavy-tailed and separable distributions tailored towards global optimization and search in high dimensional spaces, respectively. Experimental results show best published performance on various standard benchmarks, as well as competitive performance on others.
This paper proposes the first-ever algorithmic framework for tuning hyper-parameters of stochastic optimization algorithm based on reinforcement learning. Hyper-parameters impose significant influences on the performance of stochastic optimization algorithms, such as evolutionary algorithms (EAs) and meta-heuristics. Yet, it is very time-consuming to determine optimal hyper-parameters due to the stochastic nature of these algorithms. We propose to model the tuning procedure as a Markov decision process, and resort the policy gradient algorithm to tune the hyper-parameters. Experiments on tuning stochastic algorithms with different kinds of hyper-parameters (continuous and discrete) for different optimization problems (continuous and discrete) show that the proposed hyper-parameter tuning algorithms do not require much less running times of the stochastic algorithms than bayesian optimization method. The proposed framework can be used as a standard tool for hyper-parameter tuning in stochastic algorithms.
Tuning hyper-parameters for evolutionary algorithms is an important issue in computational intelligence. Performance of an evolutionary algorithm depends not only on its operation strategy design, but also on its hyper-parameters. Hyper-parameters can be categorized in two dimensions as structural/numerical and time-invariant/time-variant. Particularly, structural hyper-parameters in existing studies are usually tuned in advance for time-invariant parameters, or with hand-crafted scheduling for time-invariant parameters. In this paper, we make the first attempt to model the tuning of structural hyper-parameters as a reinforcement learning problem, and present to tune the structural hyper-parameter which controls computational resource allocation in the CEC 2018 winner algorithm by Q-learning. Experimental results show favorably against the winner algorithm on the CEC 2018 test functions.
A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as it allows improving training speed for the algorithms and may help human understanding the results. Building on previous works, a novel approach is presented: candidate corsets are iteratively optimized, adding and removing samples. As there is an obvious trade-off between limiting training size and quality of the results, a multi-objective evolutionary algorithm is used to minimize simultaneously the number of points in the set and the classification error. Experimental results on non-trivial benchmarks show that the proposed approach is able to deliver results that allow a classifier to obtain lower error and better ability of generalizing on unseen data than state-of-the-art coreset discovery techniques.
Real-world and complex problems have usually many objective functions that have to be optimized all at once. Over the last decades, Multi-Objective Evolutionary Algorithms (MOEAs) are designed to solve this kind of problems. Nevertheless, some problems have many objectives which lead to a large number of non-dominated solutions obtained by the optimization algorithms. The large set of non-dominated solutions hinders the selection of the most appropriate solution by the decision maker. This paper presents a new algorithm that has been designed to obtain the most significant solutions from the Pareto Optimal Frontier (POF). This approach is based on the cone-domination applied to MOEA, which can find the knee point solutions. In order to obtain the best cone angle, we propose a hypervolume-distribution metric, which is used to self-adapt the angle during the evolving process. This new algorithm has been applied to the real world application in Unmanned Air Vehicle (UAV) Mission Planning Problem. The experimental results show a significant improvement of the algorithm performance in terms of hypervolume, number of solutions, and also the required number of generations to converge.
The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most commonly-used in practice. This paper shows that evolutionary algorithms can discover novel activation functions that outperform ReLU. A tree-based search space of candidate activation functions is defined and explored with mutation, crossover, and exhaustive search. Experiments on training wide residual networks on the CIFAR-10 and CIFAR-100 image datasets show that this approach is effective. Replacing ReLU with evolved activation functions results in statistically significant increases in network accuracy. Optimal performance is achieved when evolution is allowed to customize activation functions to a particular task; however, these novel activation functions are shown to generalize, achieving high performance across tasks. Evolutionary optimization of activation functions is therefore a promising new dimension of metalearning in neural networks.
Recent years have seen an increasing integration of distributed renewable energy resources into existing electric power grids. Due to the uncertain nature of renewable energy resources, network operators are faced with new challenges in balancing load and generation. In order to meet the new requirements, intelligent distributed energy resource plants can be used which provide as virtual power plants e.g. demand side management or flexible generation. However, the calculation of an adequate schedule for the unit commitment of such distributed energy resources is a complex optimization problem which is typically too complex for standard optimization algorithms if large numbers of distributed energy resources are considered. For solving such complex optimization tasks, population-based metaheuristics -- as e.g. evolutionary algorithms -- represent powerful alternatives. Admittedly, evolutionary algorithms do require lots of computational power for solving such problems in a timely manner. One promising solution for this performance problem is the parallelization of the usually time-consuming evaluation of alternative solutions. In the present paper, a new generic and highly scalable parallel method for unit commitment of distributed energy resources using metaheuristic algorithms is presented. It is based on microservices, container virtualization and the publish/subscribe messaging paradigm for scheduling distributed energy resources. Scalability and applicability of the proposed solution are evaluated by performing parallelized optimizations in a big data environment for three distinct distributed energy resource scheduling scenarios. The new method provides cluster or cloud parallelizability and is able to deal with a comparably large number of distributed energy resources. The application of the new proposed method results in very good performance for scaling up optimization speed.
Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach. In this paper, we consider the dynamic chance-constrained knapsack problem where the weight of each item is stochastic, the capacity constraint changes dynamically over time, and the objective is to maximize the total profit subject to the probability that total weight exceeds the capacity. We make use of prominent tail inequalities such as Chebyshev's inequality, and Chernoff bound to approximate the probabilistic constraint. Our key contribution is to introduce an additional objective which estimates the minimal capacity bound for a given stochastic solution that still meets the chance constraint. This objective helps to cater for dynamic changes to the stochastic problem. We apply single- and multi-objective evolutionary algorithms to the problem and show how bi-objective optimization can help to deal with dynamic chance-constrained problems.
Variable selection problems generally present more than a single solution and, sometimes, it is worth to find as many solutions as possible. The use of Evolutionary Algorithms applied to this kind of problem proves to be one of the best methods to find optimal solutions. Moreover, there are variants designed to find all or almost all local optima, known as Niching Genetic Algorithms (NGA). There are several different NGA methods developed in order to achieve this task. The present work compares the behavior of eight different niching techniques, applied to a climatic database of four weather stations distributed in Tucuman, Argentina. The goal is to find different sets of input variables that have been used as the input variable by the estimation method. Final results were evaluated based on low estimation error and low dispersion error, as well as a high number of different results and low computational time. A second experiment was carried out to study the capability of the method to identify critical variables. The best results were obtained with Deterministic Crowding. In contrast, Steady State Worst Among Most Similar and Probabilistic Crowding showed good results but longer processing times and less ability to determine the critical factors.
Building a surrogate model of an objective function has shown to be effective to assist evolutionary algorithms (EAs) to solve real-world complex optimisation problems which involve either computationally expensive numerical simulations or costly physical experiments. However, their effectiveness mostly focuses on small-scale problems with less than 10 decision variables. The scalability of surrogate assisted EAs (SAEAs) have not been well studied yet. In this paper, we propose a Gaussian process surrogate model assisted EA for medium-scale expensive multi-objective optimisation problems with up to 50 decision variables. There are three distinctive features of our proposed SAEA. First, instead of using all decision variables in surrogate model building, we only use those correlated ones to build the surrogate model for each objective function. Second, rather than directly optimising the surrogate objective functions, the original multi-objective optimisation problem is transformed to a new one based on the surrogate models. Last but not the least, a subset selection method is developed to choose a couple of promising candidate solutions for actual objective function evaluations thus to update the training dataset. The effectiveness of our proposed algorithm is validated on benchmark problems with 10, 20, 50 variables, comparing with three state-of-the-art SAEAs.
Many science and engineering applications require finding solutions to planning and optimization problems by satisfying a set of constraints. These constraint problems (CPs) are typically NP-complete and can be formalized as constraint satisfaction problems (CSPs) or constraint optimization problems (COPs). Evolutionary algorithms (EAs) are good solvers for optimization problems ubiquitous in various problem domains, however traditional operators for EAs are 'blind' to constraints or generally use problem dependent objective functions; as they do not exploit information from the constraints in search for solutions. A variation of EA, Intelligent constraint handling evolutionary algorithm (ICHEA), has been demonstrated to be a versatile constraints-guided EA for continuous constrained problems in our earlier works in (Sharma and Sharma, 2012) where it extracts information from constraints and exploits it in the evolutionary search to make the search more efficient. In this paper ICHEA has been demonstrated to solve benchmark exam timetabling problems, a classic COP. The presented approach demonstrates competitive results with other state-of-the-art approaches in EAs in terms of quality of solutions. ICHEA first uses its inter-marriage crossover operator to satisfy all the given constraints incrementally and then uses combination of traditional and enhanced operators to optimize the solution. Generally CPs solved by EAs are problem dependent penalty based fitness functions. We also proposed a generic preference based solution model that does not require a problem dependent fitness function, however currently it only works for mutually exclusive constraints.
Differential evolution (DE) is a well-known type of evolutionary algorithms (EA). Similarly to other EA variants it can suffer from small populations and loose diversity too quickly. This paper presents a new approach to mitigate this issue: We propose to generate new candidate solutions by utilizing reversible linear transformation applied to a triplet of solutions from the population. In other words, the population is enlarged by using newly generated individuals without evaluating their fitness. We assess our methods on three problems: (i) benchmark function optimization, (ii) discovering parameter values of the gene repressilator system, (iii) learning neural networks. The empirical results indicate that the proposed approach outperforms vanilla DE and a version of DE with applying differential mutation three times on all testbeds.