Siamese networks are one of the most trending methods to achieve self-supervised visual representation learning (SSL). Since hand labeling is costly, SSL can play a crucial part by allowing deep learning to train on large unlabeled datasets. Meanwhile, Neural Architecture Search (NAS) is becoming increasingly important as a technique to discover novel deep learning architectures. However, early NAS methods based on reinforcement learning or evolutionary algorithms suffered from ludicrous computational and memory costs. In contrast, differentiable NAS, a gradient-based approach, has the advantage of being much more efficient and has thus retained most of the attention in the past few years. In this article, we present NASiam, a novel approach that uses for the first time differentiable NAS to improve the multilayer perceptron projector and predictor (encoder/predictor pair) architectures inside siamese-networks-based contrastive learning frameworks (e.g., SimCLR, SimSiam, and MoCo) while preserving the simplicity of previous baselines. We crafted a search space designed explicitly for multilayer perceptrons, inside which we explored several alternatives to the standard ReLU activation function. We show that these new architectures allow ResNet backbone convolutional models to learn strong representations efficiently. NASiam reaches competitive performance in both small-scale (i.e., CIFAR-10/CIFAR-100) and large-scale (i.e., ImageNet) image classification datasets while costing only a few GPU hours. We discuss the composition of the NAS-discovered architectures and emit hypotheses on why they manage to prevent collapsing behavior. Our code is available at https://github.com/aheuillet/NASiam.
Evolutionary algorithms are popular algorithms for multiobjective optimisation (also called Pareto optimisation) as they use a population to store trade-offs between different objectives. Despite their popularity, the theoretical foundation of multiobjective evolutionary optimisation (EMO) is still in its early development. Fundamental questions such as the benefits of the crossover operator are still not fully understood. We provide a theoretical analysis of the well-known EMO algorithms GSEMO and NSGA-II to showcase the possible advantages of crossover: we propose classes of "royal road" functions on which these algorithms cover the whole Pareto front in expected polynomial time if crossover is being used. But when disabling crossover, they require exponential time in expectation to cover the Pareto front. The latter even holds for a large class of black-box algorithms using any elitist selection and any unbiased mutation operator. Moreover, even the expected time to create a single Pareto-optimal search point is exponential. We provide two different function classes, one tailored for one-point crossover and another one tailored for uniform crossover, and we show that immune-inspired hypermutations cannot avoid exponential optimisation times. Our work shows the first example of an exponential performance gap through the use of crossover for the widely used NSGA-II algorithm and contributes to a deeper understanding of its limitations and capabilities.
Evolutionary Reinforcement Learning (ERL) that applying Evolutionary Algorithms (EAs) to optimize the weight parameters of Deep Neural Network (DNN) based policies has been widely regarded as an alternative to traditional reinforcement learning methods. However, the evaluation of the iteratively generated population usually requires a large amount of computational time and can be prohibitively expensive, which may potentially restrict the applicability of ERL. Surrogate is often used to reduce the computational burden of evaluation in EAs. Unfortunately, in ERL, each individual of policy usually represents millions of weights parameters of DNN. This high-dimensional representation of policy has introduced a great challenge to the application of surrogates into ERL to speed up training. This paper proposes a PE-SAERL Framework to at the first time enable surrogate-assisted evolutionary reinforcement learning via policy embedding (PE). Empirical results on 5 Atari games show that the proposed method can perform more efficiently than the four state-of-the-art algorithms. The training process is accelerated up to 7x on tested games, comparing to its counterpart without the surrogate and PE.
The goal of constrained multiobjective evolutionary optimization is to obtain a set of well-converged and welldistributed feasible solutions. To complete this goal, there should be a tradeoff among feasibility, diversity, and convergence. However, it is nontrivial to balance these three elements simultaneously by using a single tradeoff model since the importance of each element varies in different evolutionary phases. As an alternative, we adapt different tradeoff models in different phases and propose a novel algorithm called ATM-R. In the infeasible phase, ATM-R takes the tradeoff between diversity and feasibility into account, aiming to move the population toward feasible regions from diverse search directions. In the semi-feasible phase, ATM-R promotes the transition from "the tradeoff between feasibility and diversity" to "the tradeoff between diversity and convergence", which can facilitate the discovering of enough feasible regions and speed up the search for the feasible Pareto optima in succession. In the feasible phase, the tradeoff between diversity and convergence is considered to attain a set of well-converged and well-distributed feasible solutions. It is worth noting that the merits of reference points are leveraged in ATM-R to accomplish these tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is developed to generate promising solutions beneficial to different evolutionary phases. Systemic experiments on a wide range of benchmark test functions demonstrate that ATM-R is effective and competitive, compared against five state-of-the-art constrained multiobjective optimization evolutionary algorithms.
The Makespan Scheduling problem is an extensively studied NP-hard problem, and its simplest version looks for an allocation approach for a set of jobs with deterministic processing times to two identical machines such that the makespan is minimized. However, in real life scenarios, the actual processing time of each job may be stochastic around the expected value with a variance, under the influence of external factors, and the actual processing times of these jobs may be correlated with covariances. Thus within this paper, we propose a chance-constrained version of the Makespan Scheduling problem and investigate the theoretical performance of the classical Randomized Local Search and (1+1) EA for it. More specifically, we first study two variants of the Chance-constrained Makespan Scheduling problem and their computational complexities, then separately analyze the expected runtime of the two algorithms to obtain an optimal solution or almost optimal solution to the instances of the two variants. In addition, we investigate the experimental performance of the two algorithms for the two variants.
Candidate axiom scoring is the task of assessing the acceptability of a candidate axiom against the evidence provided by known facts or data. The ability to score candidate axioms reliably is required for automated schema or ontology induction, but it can also be valuable for ontology and/or knowledge graph validation. Accurate axiom scoring heuristics are often computationally expensive, which is an issue if you wish to use them in iterative search techniques like level-wise generate-and-test or evolutionary algorithms, which require scoring a large number of candidate axioms. We address the problem of developing a predictive model as a substitute for reasoning that predicts the possibility score of candidate class axioms and is quick enough to be employed in such situations. We use a semantic similarity measure taken from an ontology's subsumption structure for this purpose. We show that the approach provided in this work can accurately learn the possibility scores of candidate OWL class axioms and that it can do so for a variety of OWL class axioms.
The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific phenomena, is one of the key techniques at the forefront of recent advances. PINNs are typically trained using stochastic gradient descent methods, akin to their deep learning counterparts. However, analysis in this paper shows that PINNs' unique loss formulations lead to a high degree of complexity and ruggedness that may not be conducive for gradient descent. Unlike in standard deep learning, PINN training requires globally optimum parameter values that satisfy physical laws as closely as possible. Spurious local optimum, indicative of erroneous physics, must be avoided. Hence, neuroevolution algorithms, with their superior global search capacity, may be a better choice for PINNs relative to gradient descent methods. Here, we propose a set of five benchmark problems, with open-source codes, spanning diverse physical phenomena for novel neuroevolution algorithm development. Using this, we compare two neuroevolution algorithms against the commonly used stochastic gradient descent, and our baseline results support the claim that neuroevolution can surpass gradient descent, ensuring better physics compliance in the predicted outputs. %Furthermore, implementing neuroevolution with JAX leads to orders of magnitude speedup relative to standard implementations.
In this paper, we present an open-source pure-Python library called PyPop7 for black-box optimization (BBO). As population-based methods (e.g., evolutionary algorithms, swarm intelligence, and pattern search) become increasingly popular for BBO, the design goal of PyPop7 is to provide a unified API and elegant implementations for them, particularly in challenging high-dimensional scenarios. Since these population-based methods easily suffer from the notorious curse of dimensionality owing to random sampling as one of core operations for most of them, recently various improvements and enhancements have been proposed to alleviate this issue more or less mainly via exploiting possible problem structures: such as, decomposition of search distribution or space, low-memory approximation, low-rank metric learning, variance reduction, ensemble of random subspaces, model self-adaptation, and fitness smoothing. These novel sampling strategies could better exploit different problem structures in high-dimensional search space and therefore they often result in faster rates of convergence and/or better qualities of solution for large-scale BBO. Now PyPop7 has covered many of these important advances on a set of well-established BBO algorithm families and also provided an open-access interface to adding the latest or missed black-box optimizers for further functionality extensions. Its well-designed source code (under GPL-3.0 license) and full-fledged online documents (under CC-BY 4.0 license) have been freely available at \url{https://github.com/Evolutionary-Intelligence/pypop} and \url{https://pypop.readthedocs.io}, respectively.
A hybrid framework combining the branch and bound method with multiobjective evolutionary algorithms is proposed for nonconvex multiobjective optimization. The hybridization exploits the complementary character of the two optimization strategies. A multiobjective evolutionary algorithm is intended for inducing tight lower and upper bounds during the branch and bound procedure. Tight bounds such as the ones derived in this way can reduce the number of subproblems that have to be solved. The branch and bound method guarantees the global convergence of the framework and improves the search capability of the multiobjective evolutionary algorithm. An implementation of the hybrid framework considering NSGA-II and MOEA/D-DE as multiobjective evolutionary algorithms is presented. Numerical experiments verify the hybrid algorithms benefit from synergy of the branch and bound method and multiobjective evolutionary algorithms.
Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar. Due to its importance and NP-hardness, a lot of methods have been proposed, among which evolutionary algorithms are a class of popular ones. Evolutionary clustering has found many successful applications, but all the results are empirical, lacking theoretical support. This paper fills this gap by proving that the approximation performance of the GSEMO (a simple multi-objective evolutionary algorithm) for solving four formulations of clustering, i.e., $k$-tMM, $k$-center, discrete $k$-median and $k$-means, can be theoretically guaranteed. Furthermore, we consider clustering under fairness, which tries to avoid algorithmic bias, and has recently been an important research topic in machine learning. We prove that for discrete $k$-median clustering under individual fairness, the approximation performance of the GSEMO can be theoretically guaranteed with respect to both the objective function and the fairness constraint.
Most multimodal multi-objective evolutionary algorithms (MMEAs) aim to find all global Pareto optimal sets (PSs) for a multimodal multi-objective optimization problem (MMOP). However, in real-world problems, decision makers (DMs) may be also interested in local PSs. Also, searching for both global and local PSs is more general in view of dealing with MMOPs, which can be seen as a generalized MMOP. In addition, the state-of-the-art MMEAs exhibit poor convergence on high-dimension MMOPs. To address the above two issues, in this study, a novel coevolutionary framework termed CoMMEA for multimodal multi-objective optimization is proposed to better obtain both global and local PSs, and simultaneously, to improve the convergence performance in dealing with high-dimension MMOPs. Specifically, the CoMMEA introduces two archives to the search process, and coevolves them simultaneously through effective knowledge transfer. The convergence archive assists the CoMMEA to quickly approaching the Pareto optimal front (PF). The knowledge of the converged solutions is then transferred to the diversity archive which utilizes the local convergence indicator and the $\epsilon$-dominance-based method to obtain global and local PSs effectively. Experimental results show that CoMMEA is competitive compared to seven state-of-the-art MMEAs on fifty-four complex MMOPs.
Hundreds of Evolutionary Computation approaches have been reported. From an evolutionary perspective they focus on two fundamental mechanisms: cultural inheritance in Swarm Intelligence and genetic inheritance in Evolutionary Algorithms. Contemporary evolutionary biology looks beyond genetic inheritance, proposing a so-called ``Extended Evolutionary Synthesis''. Many concepts from the Extended Evolutionary Synthesis have been left out of Evolutionary Computation as interest has moved toward specific implementations of the same general mechanisms. One such concept is epigenetic inheritance, which is increasingly considered central to evolutionary thinking. Epigenetic mechanisms allow quick non- or partially-genetic adaptations to environmental changes. Dynamic multi-objective optimisation problems represent similar circumstances to the natural world where fitness can be determined by multiple objectives (traits), and the environment is constantly changing. This paper asks if the advantages that epigenetic inheritance provide in the natural world are replicated in dynamic multi-objective optimisation problems. Specifically, an epigenetic blocking mechanism is applied to a state-of-the-art multi-objective genetic algorithm, MOEA/D-DE, and its performance is compared on three sets of dynamic test functions, FDA, JY, and UDF. The mechanism shows improved performance on 12 of the 16 test problems, providing initial evidence that more algorithms should explore the wealth of epigenetic mechanisms seen in the natural world.
A fascinating aspect of nature lies in its ability to produce a collection of organisms that are all high-performing in their niche. Quality-Diversity (QD) methods are evolutionary algorithms inspired by this observation, that obtained great results in many applications, from wing design to robot adaptation. Recently, several works demonstrated that these methods could be applied to perform neuro-evolution to solve control problems in large search spaces. In such problems, diversity can be a target in itself. Diversity can also be a way to enhance exploration in tasks exhibiting deceptive reward signals. While the first aspect has been studied in depth in the QD community, the latter remains scarcer in the literature. Exploration is at the heart of several domains trying to solve control problems such as Reinforcement Learning and QD methods are promising candidates to overcome the challenges associated. Therefore, we believe that standardized benchmarks exhibiting control problems in high dimension with exploration difficulties are of interest to the QD community. In this paper, we highlight three candidate benchmarks and explain why they appear relevant for systematic evaluation of QD algorithms. We also provide open-source implementations in Jax allowing practitioners to run fast and numerous experiments on few compute resources.
The act of telling stories is a fundamental part of what it means to be human. This work introduces the concept of narrative information, which we define to be the overlap in information space between a story and the items that compose the story. Using contrastive learning methods, we show how modern artificial neural networks can be leveraged to distill stories and extract a representation of the narrative information. We then demonstrate how evolutionary algorithms can leverage this to extract a set of narrative templates and how these templates -- in tandem with a novel curve-fitting algorithm we introduce -- can reorder music albums to automatically induce stories in them. In the process of doing so, we give strong statistical evidence that these narrative information templates are present in existing albums. While we experiment only with music albums here, the premises of our work extend to any form of (largely) independent media.
The design of binary error-correcting codes is a challenging optimization problem with several applications in telecommunications and storage, which has also been addressed with metaheuristic techniques and evolutionary algorithms. Still, all these efforts focused on optimizing the minimum distance of unrestricted binary codes, i.e., with no constraints on their linearity, which is a desirable property for efficient implementations. In this paper, we present an Evolutionary Strategy (ES) algorithm that explores only the subset of linear codes of a fixed length and dimension. To that end, we represent the candidate solutions as binary matrices and devise variation operators that preserve their ranks. Our experiments show that up to length $n=14$, our ES always converges to an optimal solution with a full success rate, and the evolved codes are all inequivalent to the Best-Known Linear Code (BKLC) given by MAGMA. On the other hand, for larger lengths, both the success rate of the ES as well as the diversity of the evolved codes start to drop, with the extreme case of $(16,8,5)$ codes which all turn out to be equivalent to MAGMA's BKLC.
Multi-objective evolutionary algorithms (MOEAs) are widely used to solve multi-objective optimization problems. The algorithms rely on setting appropriate parameters to find good solutions. However, this parameter tuning could be very computationally expensive in solving non-trial (combinatorial) optimization problems. This paper proposes a framework that integrates MOEAs with adaptive parameter control using Deep Reinforcement Learning (DRL). The DRL policy is trained to adaptively set the values that dictate the intensity and probability of mutation for solutions during optimization. We test the proposed approach with a simple benchmark problem and a real-world, complex warehouse design and control problem. The experimental results demonstrate the advantages of our method in terms of solution quality and computation time to reach good solutions. In addition, we show the learned policy is transferable, i.e., the policy trained on a simple benchmark problem can be directly applied to solve the complex warehouse optimization problem, effectively, without the need for retraining.
For many years, Evolutionary Algorithms (EAs) have been applied to improve Neural Networks (NNs) architectures. They have been used for solving different problems, such as training the networks (adjusting the weights), designing network topology, optimizing global parameters, and selecting features. Here, we provide a systematic brief survey about applications of the EAs on the specific domain of the recurrent NNs named Reservoir Computing (RC). At the beginning of the 2000s, the RC paradigm appeared as a good option for employing recurrent NNs without dealing with the inconveniences of the training algorithms. RC models use a nonlinear dynamic system, with fixed recurrent neural network named the \textit{reservoir}, and learning process is restricted to adjusting a linear parametric function. %so the performance of learning is fast and precise. However, an RC model has several hyper-parameters, therefore EAs are helpful tools to figure out optimal RC architectures. We provide an overview of the results on the area, discuss novel advances, and we present our vision regarding the new trends and still open questions.
Designing a transcranial electrical stimulation (TES) strategy requires considering multiple objectives, such as intensity in the target area, focality, stimulation depth, and avoidance zone, which are often mutually exclusive. A computational framework for optimizing different strategies and comparing trade-offs between these objectives is currently lacking. In this paper, we propose a general framework called multi-objective optimization via evolutionary algorithms (MOVEA) to address the non-convex optimization problem in designing TES strategies without predefined direction. MOVEA enables simultaneous optimization of multiple targets through Pareto optimization, generating a Pareto front after a single run without manual weight adjustment and allowing easy expansion to more targets. This Pareto front consists of optimal solutions that meet various requirements while respecting trade-off relationships between conflicting objectives such as intensity and focality. MOVEA is versatile and suitable for both transcranial alternating current stimulation (tACS) and transcranial temporal interference stimulation (tTIS) based on high definition (HD) and two-pair systems. We performed a comprehensive comparison between tACS and tTIS in terms of intensity, focality, and steerability for targets at different depths.MOVEA facilitates the optimization of TES based on specific objectives and constraints, advancing tTIS and tACS-based neuromodulation in understanding the causal relationship between brain regions and cognitive functions and in treating diseases. The code for MOVEA is available at https://github.com/ncclabsustech/MOVEA.
Technical indicators use graphic representations of data sets by applying various mathematical formulas to financial time series of prices. These formulas comprise a set of rules and parameters whose values are not necessarily known and depend on many factors: the market in which it operates, the size of the time window, and others. This paper focuses on the real-time optimization of the parameters applied for analyzing time series of data. In particular, we optimize the parameters of technical and financial indicators and propose other applications, such as glucose time series. We propose the combination of several Multi-objective Evolutionary Algorithms (MOEAs). Unlike other approaches, this paper applies a set of different MOEAs, collaborating to construct a global Pareto Set of solutions. Solutions for financial problems seek high returns with minimal risk. The optimization process is continuous and occurs at the same frequency as the investment time interval. This technique permits the application of non-dominated solutions obtained with different MOEAs simultaneously. Experimental results show that this technique increases the returns of the commonly used Buy \& Hold strategy and other multi-objective strategies, even for daily operations.
Filter pruning is a common method to achieve model compression and acceleration in deep neural networks (DNNs).Some research regarded filter pruning as a combinatorial optimization problem and thus used evolutionary algorithms (EA) to prune filters of DNNs. However, it is difficult to find a satisfactory compromise solution in a reasonable time due to the complexity of solution space searching. To solve this problem, we first formulate a multi-objective optimization problem based on a sub-network of the full model and propose a Sub-network Multiobjective Evolutionary Algorithm (SMOEA) for filter pruning. By progressively pruning the convolutional layers in groups, SMOEA can obtain a lightweight pruned result with better performance.Experiments on VGG-14 model for CIFAR-10 verify the effectiveness of the proposed SMOEA. Specifically, the accuracy of the pruned model with 16.56% parameters decreases by 0.28% only, which is better than the widely used popular filter pruning criteria.