This article presents a "Hybrid Self-Attention NEAT" method to improve the original NeuroEvolution of Augmenting Topologies (NEAT) algorithm in high-dimensional inputs. Although the NEAT algorithm has shown a significant result in different challenging tasks, as input representations are high dimensional, it cannot create a well-tuned network. Our study addresses this limitation by using self-attention as an indirect encoding method to select the most important parts of the input. In addition, we improve its overall performance with the help of a hybrid method to evolve the final network weights. The main conclusion is that Hybrid Self- Attention NEAT can eliminate the restriction of the original NEAT. The results indicate that in comparison with evolutionary algorithms, our model can get comparable scores in Atari games with raw pixels input with a much lower number of parameters.
Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper addresses the design of permutation codes by evolutionary algorithms (EA) by developing an iterative approach. Starting from a single random permutation, new permutations satisfying the minimum distance constraint are incrementally added to the code by using a permutation-based EA. We investigate our approach against four different fitness functions targeting the minimum distance requirement at different levels of detail and with two different policies concerning code expansion and pruning. We compare the results achieved by our EA approach to those of a simple random search, remarking that neither method scales well with the problem size.
Optimization problems are crucial in artificial intelligence. Optimization algorithms are generally used to adjust the performance of artificial intelligence models to minimize the error of mapping inputs to outputs. Current evaluation methods on optimization algorithms generally consider the performance in terms of quality. However, not all optimization algorithms for all test cases are evaluated equal from quality, the computation time should be also considered for optimization tasks. In this paper, we investigate the quality and computation time of optimization algorithms in optimization problems, instead of the one-for-all evaluation of quality. We select the well-known optimization algorithms (Bayesian optimization and evolutionary algorithms) and evaluate them on the benchmark test functions in terms of quality and computation time. The results show that BO is suitable to be applied in the optimization tasks that are needed to obtain desired quality in the limited function evaluations, and the EAs are suitable to search the optimal of the tasks that are allowed to find the optimal solution with enough function evaluations. This paper provides the recommendation to select suitable optimization algorithms for optimization problems with different numbers of function evaluations, which contributes to the efficiency that obtains the desired quality with less computation time for optimization problems.
Classifying nodes in knowledge graphs is an important task, e.g., for predicting missing types of entities, predicting which molecules cause cancer, or predicting which drugs are promising treatment candidates. While black-box models often achieve high predictive performance, they are only post-hoc and locally explainable and do not allow the learned model to be easily enriched with domain knowledge. Towards this end, learning description logic concepts from positive and negative examples has been proposed. However, learning such concepts often takes a long time and state-of-the-art approaches provide limited support for literal data values, although they are crucial for many applications. In this paper, we propose EvoLearner - an evolutionary approach to learn concepts in ALCQ(D), which is the attributive language with complement (ALC) paired with qualified cardinality restrictions (Q) and data properties (D). We contribute a novel initialization method for the initial population: starting from positive examples, we perform biased random walks and translate them to description logic concepts. Moreover, we improve support for data properties by maximizing information gain when deciding where to split the data. We show that our approach significantly outperforms the state of the art on the benchmarking framework SML-Bench for structured machine learning. Our ablation study confirms that this is due to our novel initialization method and support for data properties.
Many real-world optimization problems such as engineering design can be eventually modeled as the corresponding multiobjective optimization problems (MOPs) which must be solved to obtain approximate Pareto optimal fronts. Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been regarded as a significantly promising approach for solving MOPs. Recent studies have shown that MOEA/D with uniform weight vectors is well-suited to MOPs with regular Pareto optimal fronts, but its performance in terms of diversity usually deteriorates when solving MOPs with irregular Pareto optimal fronts. In this way, the solution set obtained by the algorithm can not provide more reasonable choices for decision makers. In order to efficiently overcome this drawback, we propose an improved MOEA/D algorithm by virtue of the well-known Pascoletti-Serafini scalarization method and a new strategy of multi-reference points. Specifically, this strategy consists of the setting and adaptation of reference points generated by the techniques of equidistant partition and projection. For performance assessment, the proposed algorithm is compared with existing four state-of-the-art multiobjective evolutionary algorithms on benchmark test problems with various types of Pareto optimal fronts. According to the experimental results, the proposed algorithm exhibits better diversity performance than that of the other compared algorithms. Finally, our algorithm is applied to two real-world MOPs in engineering optimization successfully.
This paper investigates the application of machine learning when training a credit decision model over real, publicly available data whilst accounting for "bias objectives". We use the term "bias objective" to describe the requirement that a trained model displays discriminatory bias against a given groups of individuals that doesn't exceed a prescribed level, where such level can be zero. This research presents an empirical study examining the tension between competing model training objectives which in all cases include one or more bias objectives. This work is motivated by the observation that the parties associated with creditworthiness models have requirements that can not certainly be fully met simultaneously. The research herein seeks to highlight the impracticality of satisfying all parties' objectives, demonstrating the need for "trade-offs" to be made. The results and conclusions presented by this paper are of particular importance for all stakeholders within the credit scoring industry that rely upon artificial intelligence (AI) models as part of the decision-making process when determining the creditworthiness of individuals. This paper provides an exposition of the difficulty of training AI models that are able to simultaneously satisfy multiple bias objectives whilst maintaining acceptable levels of accuracy. Stakeholders should be aware of this difficulty and should acknowledge that some degree of discriminatory bias, across a number of protected characteristics and formulations of bias, cannot be avoided.
We present a literature survey on non-interactive computational story generation. The article starts with the presentation of requirements for creative systems, three types of models of creativity (computational, socio-cultural, and individual), and models of human creative writing. Then it reviews each class of story generation approach depending on the used technology: story-schemas, analogy, rules, planning, evolutionary algorithms, implicit knowledge learning, and explicit knowledge learning. Before the concluding section, the article analyses the contributions of the reviewed work to improve the quality of the generated stories. This analysis addresses the description of the story characters, the use of narrative knowledge including about character believability, and the possible lack of more comprehensive or more detailed knowledge or creativity models. Finally, the article presents concluding remarks in the form of suggestions of research topics that might have a significant impact on the advancement of the state of the art on autonomous non-interactive story generation systems. The article concludes that the autonomous generation and adoption of the main idea to be conveyed and the autonomous design of the creativity ensuring criteria are possibly two of most important topics for future research.
Given a ground set of items, the result diversification problem aims to select a subset with high "quality" and "diversity" while satisfying some constraints. It arises in various real-world artificial intelligence applications, such as web-based search, document summarization and feature selection, and also has applications in other areas, e.g., computational geometry, databases, finance and operations research. Previous algorithms are mainly based on greedy or local search. In this paper, we propose to reformulate the result diversification problem as a bi-objective maximization problem, and solve it by a multi-objective evolutionary algorithm (EA), i.e., the GSEMO. We theoretically prove that the GSEMO can achieve the (asymptotically) optimal theoretical guarantees under both static and dynamic environments. For cardinality constraints, the GSEMO can achieve the optimal polynomial-time approximation ratio, $1/2$. For more general matroid constraints, the GSEMO can achieve an asymptotically optimal polynomial-time approximation ratio, $1/2-\epsilon/(4n)$, where $\epsilon>0$ and $n$ is the size of the ground set of items. Furthermore, when the objective function (i.e., a linear combination of quality and diversity) changes dynamically, the GSEMO can maintain this approximation ratio in polynomial running time, addressing the open question proposed by Borodin. This also theoretically shows the superiority of EAs over local search for solving dynamic optimization problems for the first time, and discloses the robustness of the mutation operator of EAs against dynamic changes. Experiments on the applications of web-based search, multi-label feature selection and document summarization show the superior performance of the GSEMO over the state-of-the-art algorithms (i.e., the greedy algorithm and local search) under both static and dynamic environments.
Designing complex architectures has been an essential cogwheel in the revolution deep learning has brought about in the past decade. When solving difficult problems in a datadriven manner, a well-tried approach is to take an architecture discovered by renowned deep learning scientists as a basis (e.g. Inception) and try to apply it to a specific problem. This might be sufficient, but as of now, achieving very high accuracy on a complex or yet unsolved task requires the knowledge of highly-trained deep learning experts. In this work, we would like to contribute to the area of Automated Machine Learning (AutoML), specifically Neural Architecture Search (NAS), which intends to make deep learning methods available for a wider range of society by designing neural topologies automatically. Although several different approaches exist (e.g. gradient-based or evolutionary algorithms), our focus is on one of the most promising research directions, reinforcement learning. In this scenario, a recurrent neural network (controller) is trained to create problem-specific neural network architectures (child). The validation accuracies of the child networks serve as a reward signal for training the controller with reinforcement learning. The basis of our proposed work is Efficient Neural Architecture Search (ENAS), where parameter sharing is applied among the child networks. ENAS, like many other RL-based algorithms, emphasize the learning of child networks as increasing their convergence result in a denser reward signal for the controller, therefore significantly reducing training times. The controller was originally trained with REINFORCE. In our research, we propose to modify this to a more modern and complex algorithm, PPO, which has demonstrated to be faster and more stable in other environments. Then, we briefly discuss and evaluate our results.
Adequate labeled data and expensive compute resources are the prerequisites for the success of neural architecture search(NAS). It is challenging to apply NAS in meta-learning scenarios with limited compute resources and data. In this paper, an across-task neural architecture search (AT-NAS) is proposed to address the problem through combining gradient-based meta-learning with EA-based NAS to learn over the distribution of tasks. The supernet is learned over an entire set of tasks by meta-learning its weights. Architecture encodes of subnets sampled from the supernet are iteratively adapted by evolutionary algorithms while simultaneously searching for a task-sensitive meta-network. Searched meta-network can be adapted to a novel task via a few learning steps and only costs a little search time. Empirical results show that AT-NAS surpasses the related approaches on few-shot classification accuracy. The performance of AT-NAS on classification benchmarks is comparable to that of models searched from scratch, by adapting the architecture in less than an hour from a 5-GPU-day pretrained meta-network.
A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for generating the individuals of a new generation. The evolved pattern is embedded into a standard evolutionary scheme that is used for solving a particular problem. Several evolutionary algorithms for function optimization are evolved by using the considered model. The evolved evolutionary algorithms are compared with a human-designed Genetic Algorithm. Numerical experiments show that the evolved evolutionary algorithms can compete with standard approaches for several well-known benchmarking problems.
Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability. One explainable approach is case-based reasoning (CBR), where each decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making. In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability. These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance.
The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization performance of evolutionary algorithms. Within the paper, we consider a constrained version of the problem named 2-Hop (1,2)-Minimum Spanning Tree problem (abbr. 2H-(1,2)-MSTP) in the context of evolutionary algorithms, which has been shown to be NP-hard. Following how evolutionary algorithms are applied to solve the MSTP, we first consider the evolutionary algorithms with search points in edge-based representation adapted to the 2H-(1,2)-MSTP (including the (1+1) EA, Global Simple Evolutionary Multi-Objective Optimizer and its two variants). More specifically, we separately investigate the upper bounds on their expected time (i.e., the expected number of fitness evaluations) to obtain a $\frac{3}{2}$-approximate solution with respect to different fitness functions. Inspired by the special structure of 2-hop spanning trees, we also consider the (1+1) EA with search points in vertex-based representation that seems not so natural for the problem and give an upper bound on its expected time to obtain a $\frac{3}{2}$-approximate solution, which is better than the above mentioned ones.
Multi-task optimization (MTO) studies how to simultaneously solve multiple optimization problems for the purpose of obtaining better performance on each problem. Over the past few years, evolutionary MTO (EMTO) was proposed to handle MTO problems via evolutionary algorithms. So far, many EMTO algorithms have been developed and demonstrated well performance on solving real-world problems. However, there remain many works to do in adapting knowledge transfer to task relatedness in EMTO. Different from the existing works, we develop a self-adaptive multi-task particle swarm optimization (SaMTPSO) through the developed knowledge transfer adaptation strategy, the focus search strategy and the knowledge incorporation strategy. In the knowledge transfer adaptation strategy, each task has a knowledge source pool that consists of all knowledge sources. Each source (task) outputs knowledge to the task. And knowledge transfer adapts to task relatedness via individuals' choice on different sources of a pool, where the chosen probabilities for different sources are computed respectively according to task's success rate in generating improved solutions via these sources. In the focus search strategy, if there is no knowledge source benefit the optimization of a task, then all knowledge sources in the task's pool are forbidden to be utilized except the task, which helps to improve the performance of the proposed algorithm. Note that the task itself is as a knowledge source of its own. In the knowledge incorporation strategy, two different forms are developed to help the SaMTPSO explore and exploit the transferred knowledge from a chosen source, each leading to a version of the SaMTPSO. Several experiments are conducted on two test suites. The results of the SaMTPSO are comparing to that of 3 popular EMTO algorithms and a particle swarm algorithm, which demonstrates the superiority of the SaMTPSO.
We present an empirical study of a range of evolutionary algorithms applied to various noisy combinatorial optimisation problems. There are three sets of experiments. The first looks at several toy problems, such as OneMax and other linear problems. We find that UMDA and the Paired-Crossover Evolutionary Algorithm (PCEA) are the only ones able to cope robustly with noise, within a reasonable fixed time budget. In the second stage, UMDA and PCEA are then tested on more complex noisy problems: SubsetSum, Knapsack and SetCover. Both perform well under increasing levels of noise, with UMDA being the better of the two. In the third stage, we consider two noisy multi-objective problems (CountingOnesCountingZeros and a multi-objective formulation of SetCover). We compare several adaptations of UMDA for multi-objective problems with the Simple Evolutionary Multi-objective Optimiser (SEMO) and NSGA-II. We conclude that UMDA, and its variants, can be highly effective on a variety of noisy combinatorial optimisation, outperforming many other evolutionary algorithms.
Dynamic community detection is the hotspot and basic problem of complex network and artificial intelligence research in recent years. It is necessary to maximize the accuracy of clustering as the network structure changes, but also to minimize the two consecutive clustering differences between the two results. There is a trade-off relationship between these two objectives. In this paper, we propose a Feature Transfer Based Multi-Objective Optimization Genetic Algorithm (TMOGA) based on transfer learning and traditional multi-objective evolutionary algorithm framework. The main idea is to extract stable features from past community structures, retain valuable feature information, and integrate this feature information into current optimization processes to improve the evolutionary algorithms. Additionally, a new theoretical framework is proposed in this paper to analyze community detection problem based on information theory. Then, we exploit this framework to prove the rationality of TMOGA. Finally, the experimental results show that our algorithm can achieve better clustering effects compared with the state-of-the-art dynamic network community detection algorithms in diverse test problems.
Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark problems: OneMax and Deceptive. It is proven that using binomial crossover leads to the dominance of transition matrices. As a result, the algorithm with binomial crossover asymptotically outperforms that without crossover on both OneMax and Deceptive, and outperforms on OneMax, however, not on Deceptive. Furthermore, an adaptive parameter strategy is proposed which can strengthen the superiority of binomial crossover on Deceptive.
Death has long been overlooked in evolutionary algorithms. Recent research has shown that death (when applied properly) can benefit the overall fitness of a population and can outperform sub-sections of a population that are "immortal" when allowed to evolve together in an environment [1]. In this paper, we strive to experimentally determine whether death is an adapted trait and whether this adaptation can be used to enhance our implementations of conventional genetic algorithms. Using some of the most widely accepted evolutionary death and aging theories, we observed that senescent death (in various forms) can lower the total run-time of genetic algorithms, increase the optimality of a solution, and decrease the variance in an algorithm's performance. We believe that death-enhanced genetic algorithms can accomplish this through their unique ability to backtrack out of and/or avoid getting trapped in local optima altogether.
According to the No Free Lunch (NFL) theorems all black-box algorithms perform equally well when compared over the entire set of optimization problems. An important problem related to NFL is finding a test problem for which a given algorithm is better than another given algorithm. Of high interest is finding a function for which Random Search is better than another standard evolutionary algorithm. In this paper, we propose an evolutionary approach for solving this problem: we will evolve test functions for which a given algorithm A is better than another given algorithm B. Two ways for representing the evolved functions are employed: as GP trees and as binary strings. Several numerical experiments involving NFL-style Evolutionary Algorithms for function optimization are performed. The results show the effectiveness of the proposed approach. Several test functions for which Random Search performs better than all other considered algorithms have been evolved.
Finding the optimal parameter setting (i.e. the optimal population size, the optimal mutation probability, the optimal evolutionary model etc) for an Evolutionary Algorithm (EA) is a difficult task. Instead of evolving only the parameters of the algorithm we will evolve an entire EA capable of solving a particular problem. For this purpose the Multi Expression Programming (MEP) technique is used. Each MEP chromosome will encode multiple EAs. An nongenerational EA for function optimization is evolved in this paper. Numerical experiments show the effectiveness of this approach.