Evolutionary algorithms are sensitive to the mutation rate (MR); no single value of this parameter works well across domains. Self-adaptive MR approaches have been proposed but they tend to be brittle: Sometimes they decay the MR to zero, thus halting evolution. To make self-adaptive MR robust, this paper introduces the Group Elite Selection of Mutation Rates (GESMR) algorithm. GESMR co-evolves a population of solutions and a population of MRs, such that each MR is assigned to a group of solutions. The resulting best mutational change in the group, instead of average mutational change, is used for MR selection during evolution, thus avoiding the vanishing MR problem. With the same number of function evaluations and with almost no overhead, GESMR converges faster and to better solutions than previous approaches on a wide range of continuous test optimization problems. GESMR also scales well to high-dimensional neuroevolution for supervised image-classification tasks and for reinforcement learning control tasks. Remarkably, GESMR produces MRs that are optimal in the long-term, as demonstrated through a comprehensive look-ahead grid search. Thus, GESMR and its theoretical and empirical analysis demonstrate how self-adaptation can be harnessed to improve performance in several applications of evolutionary computation.
Dynamic multi-objective optimization problems (DMOPs) are widely accepted to be more challenging than stationary problems due to the time-dependent nature of the objective functions and/or constraints. Evaluation of purpose-built algorithms for DMOPs is often performed on narrow selections of dynamic instances with differing change magnitude and frequency or a limited selection of problems. In this paper, we focus on the reproducibility of simulation experiments for parameters of DMOPs. Our framework is based on an extension of PlatEMO, allowing for the reproduction of results and performance measurements across a range of dynamic settings and problems. A baseline schema for dynamic algorithm evaluation is introduced, which provides a mechanism to interrogate performance and optimization behaviours of well-known evolutionary algorithms that were not designed specifically for DMOPs. Importantly, by determining the maximum capability of non-dynamic multi-objective evolutionary algorithms, we can establish the minimum capability required of purpose-built dynamic algorithms to be useful. The simplest modifications to manage dynamic changes introduce diversity. Allowing non-dynamic algorithms to incorporate mutated/random solutions after change events determines the improvement possible with minor algorithm modifications. Future expansion to include current dynamic algorithms will enable reproduction of their results and verification of their abilities and performance across DMOP benchmark space.
Evolutionary algorithms have proven to be highly effective in continuous optimization, especially when numerous fitness function evaluations (FFEs) are possible. In certain cases, however, an expensive optimization approach (i.e. with relatively low number of FFEs) must be taken, and such a setting is considered in this work. The paper introduces an extension to the well-known LSHADE algorithm in the form of a pre-screening mechanism (psLSHADE). The proposed pre-screening relies on the three following components: a specific initial sampling procedure, an archive of samples, and a global linear meta-model of a fitness function that consists of 6 independent transformations of variables. The pre-screening mechanism preliminary assesses the trial vectors and designates the best one of them for further evaluation with the fitness function. The performance of psLSHADE is evaluated using the CEC2021 benchmark in an expensive scenario with an optimization budget of 10^2-10^4 FFEs per dimension. We compare psLSHADE with the baseline LSHADE method and the MadDE algorithm. The results indicate that with restricted optimization budgets psLSHADE visibly outperforms both competitive algorithms. In addition, the use of the pre-screening mechanism results in faster population convergence of psLSHADE compared to LSHADE.
Fault tree analysis is a well-known technique in reliability engineering and risk assessment, which supports decision-making processes and the management of complex systems. Traditionally, fault tree (FT) models are built manually together with domain experts, considered a time-consuming process prone to human errors. With Industry 4.0, there is an increasing availability of inspection and monitoring data, making techniques that enable knowledge extraction from large data sets relevant. Thus, our goal with this work is to propose a data-driven approach to infer efficient FT structures that achieve a complete representation of the failure mechanisms contained in the failure data set without human intervention. Our algorithm, the FT-MOEA, based on multi-objective evolutionary algorithms, enables the simultaneous optimization of different relevant metrics such as the FT size, the error computed based on the failure data set and the Minimal Cut Sets. Our results show that, for six case studies from the literature, our approach successfully achieved automatic, efficient, and consistent inference of the associated FT models. We also present the results of a parametric analysis that tests our algorithm for different relevant conditions that influence its performance, as well as an overview of the data-driven methods used to automatically infer FT models.
Evolutionary algorithms are wildly used in unmanned aerial vehicle path planning for their flexibility and effectiveness. Nevertheless, they are so sensitive to the change of environment that can't adapt to all scenarios. Due to this drawback, the previously successful planner frequently fail in a new scene. In this paper, a first-of-its-kind machine learning method named Evolutionary Programmer is proposed to solve this problem. Concretely, the most commonly used Evolutionary Algorithms are decomposed into a series of operators, which constitute the operator library of the system. The new method recompose the operators to a integrated planner, thus, the most suitable operators can be selected for adapting to the changing circumstances. Different from normal machine programmers, this method focuses on a specific task with high-level integrated instructions and thus alleviate the problem of huge search space caused by the briefness of instructions. On this basis, a 64-bit sequence is presented to represent path planner and then evolved with the modified Genetic Algorithm. Finally, the most suitable planner is created by utilizing the information of the previous planner and various randomly generated ones.
Evolutionary algorithms (EA) based neural architecture search (NAS) involves evaluating each architecture by training it from scratch, which is extremely time-consuming. This can be reduced by using a supernet for estimating the fitness of an architecture due to weight sharing among all architectures in the search space. However, the estimated fitness is very noisy due to the co-adaptation of the operations in the supernet which results in NAS methods getting trapped in local optimum. In this paper, we propose a method called NEvoNAS wherein the NAS problem is posed as a multi-objective problem with 2 objectives: (i) maximize architecture novelty, (ii) maximize architecture fitness/accuracy. The novelty search is used for maintaining a diverse set of solutions at each generation which helps avoiding local optimum traps while the architecture fitness is calculated using supernet. NSGA-II is used for finding the \textit{pareto optimal front} for the NAS problem and the best architecture in the pareto front is returned as the searched architecture. Exerimentally, NEvoNAS gives better results on 2 different search spaces while using significantly less computational resources as compared to previous EA-based methods. The code for our paper can be found in https://github.com/nightstorm0909/NEvoNAS.
Evolving swarm behaviors with artificial agents is computationally expensive and challenging. Because reward structures are often sparse in swarm problems, only a few simulations among hundreds evolve successful swarm behaviors. Additionally, swarm evolutionary algorithms typically rely on ad hoc fitness structures, and novel fitness functions need to be designed for each swarm task. This paper evolves swarm behaviors by systematically combining Postcondition-Precondition-Action (PPA) canonical Behavior Trees (BT) with a Grammatical Evolution. The PPA structure replaces ad hoc reward structures with systematic postcondition checks, which allows a common grammar to learn solutions to different tasks using only environmental cues and BT feedback. The static performance of learned behaviors is poor because no agent learns all necessary subtasks, but performance while evolving is excellent because agents can quickly change behaviors in new contexts. The evolving algorithm succeeded in 75\% of learning trials for both foraging and nest maintenance tasks, an eight-fold improvement over prior work.
Repair operators are often used for constraint handling in constrained combinatorial optimization. We investigate the (1+1)~EA equipped with a tailored jump-and-repair operation that can be used to probabilistically repair infeasible offspring in graph problems. Instead of evolving candidate solutions to the entire graph, we expand the genotype to allow the (1+1)~EA to develop in parallel a feasible solution together with a growing subset of the instance (an induced subgraph). With this approach, we prove that the EA is able to probabilistically simulate an iterative compression process used in classical fixed-parameter algorithmics to obtain a randomized FPT performance guarantee on three NP-hard graph problems. For $k$-VertexCover, we prove that the (1+1) EA using focused jump-and-repair can find a $k$-vertex cover (if one exists) in $O(2^k n^2\log n)$ iterations in expectation. This leads to an exponential (in $k$) improvement over the best-known parameterized bound for evolutionary algorithms on VertexCover. For the $k$-FeedbackVertexSet problem in tournaments, we prove that the EA finds a feasible feedback set in $O(2^kk!n^2\log n)$ iterations in expectation, and for OddCycleTransversal, we prove the optimization time for the EA is $O(3^k k m n^2\log n)$. For the latter two problems, this constitutes the first parameterized result for any evolutionary algorithm. We discuss how to generalize the framework to other parameterized graph problems closed under induced subgraphs and report experimental results that illustrate the behavior of the algorithm on a concrete instance class.
Non-dominated sorting is a computational bottleneck in Pareto-based multi-objective evolutionary algorithms (MOEAs) due to the runtime-intensive comparison operations involved in establishing dominance relationships between solution candidates. In this paper we introduce Rank Sort, a non-dominated sorting approach exploiting sorting stability and ordinal information to avoid expensive dominance comparisons in the rank assignment phase. Two algorithmic variants are proposed: the first one, RankOrdinal (RO), uses ordinal rank comparisons in order to determine dominance and requires O(N) space; the second one, RankIntersect (RS), uses set intersections and bit-level parallelism and requires O(N^2) space. We demonstrate the efficiency of the proposed methods in comparison with other state of the art algorithms in empirical simulations using the NSGA2 algorithm as well as synthetic benchmarks. The RankIntersect algorithm is able to significantly outperform the current state of the art offering up to 30% speed-up for many objectives. C++ implementations are provided for all algorithms.
Estimation of distribution algorithms are evolutionary algorithms that use extracted information from the population instead of traditional genetic operators to generate new solutions. This information is represented as a probabilistic model and the effectiveness of these algorithms is dependent on the quality of these models. However, some studies have shown that even multivariate EDAs fail to build a proper model in some problems. Usually, in these problems, there is intrinsic pairwise independence between variables. In the literature, there are few studies that investigate the difficulty and the nature of problems that can not be solved by EDAs easily. This paper proposes a new metric for measuring problem difficulty by examining the properties of model-building mechanisms in EDAs. For this purpose, we use the estimated Walsh coefficients of dependent and independent variables. The proposed metric is used to evaluate the difficulty of some well-known benchmark problems in EDAs. Different metrics like Fitness Distance Correlation (FDC) are used to compare how well the proposed metric measures problem difficulty for EDAs. Results indicate that the proposed metric can accurately predict the EDA's performance in different problems.
We consider a type of constrained optimization problem, where the violation of a constraint leads to an irrevocable loss, such as breakage of a valuable experimental resource/platform or loss of human life. Such problems are referred to as safe optimization problems (SafeOPs). While SafeOPs have received attention in the machine learning community in recent years, there was little interest in the evolutionary computation (EC) community despite some early attempts between 2009 and 2011. Moreover, there is a lack of acceptable guidelines on how to benchmark different algorithms for SafeOPs, an area where the EC community has significant experience in. Driven by the need for more efficient algorithms and benchmark guidelines for SafeOPs, the objective of this paper is to reignite the interest of this problem class in the EC community. To achieve this we (i) provide a formal definition of SafeOPs and contrast it to other types of optimization problems that the EC community is familiar with, (ii) investigate the impact of key SafeOP parameters on the performance of selected safe optimization algorithms, (iii) benchmark EC against state-of-the-art safe optimization algorithms from the machine learning community, and (iv) provide an open-source Python framework to replicate and extend our work.
Machine learning driven trading strategies have garnered a lot of interest over the past few years. There is, however, limited consensus on the ideal approach for the development of such trading strategies. Further, most literature has focused on trading strategies for short-term trading, with little or no focus on strategies that attempt to build long-term wealth. Our paper proposes a new approach for developing long-term investment strategies using an ensemble of evolutionary algorithms and a deep learning model by taking a series of short-term purchase decisions. Our methodology focuses on building long-term wealth by improving systematic investment planning (SIP) decisions on Exchange Traded Funds (ETF) over a period of time. We provide empirical evidence of superior performance (around 1% higher returns) using our ensemble approach as compared to the traditional daily systematic investment practice on a given ETF. Our results are based on live trading decisions made by our algorithm and executed on the Robinhood trading platform.
Evolutionary algorithms (EAs) have been widely used to solve multi-objective optimization problems, and have become the most popular tool. However, the theoretical foundation of multi-objective EAs (MOEAs), especially the essential theoretical aspect, i.e., running time analysis, has been still largely underdeveloped. The few existing theoretical works mainly considered simple MOEAs, while the non-dominated sorting genetic algorithm II (NSGA-II), probably the most influential MOEA, has not been analyzed except for a very recent work considering a simplified variant without crossover. In this paper, we present a running time analysis of the standard NSGA-II for solving LOTZ, OneMinMax and COCZ, the three commonly used bi-objective optimization problems. Specifically, we prove that the expected running time (i.e., number of fitness evaluations) is $O(n^3)$ for LOTZ, and $O(n^2\log n)$ for OneMinMax and COCZ, which is surprisingly as same as that of the previously analyzed simple MOEAs, GSEMO and SEMO. Next, we introduce a new parent selection strategy, stochastic tournament selection (i.e., $k$ tournament selection where $k$ is uniformly sampled at random), to replace the binary tournament selection strategy of NSGA-II, decreasing the required expected running time to $O(n^2)$ for all the three problems. Experiments are also conducted, suggesting that the derived running time upper bounds are tight for LOTZ, and almost tight for OneMinMax and COCZ.
Modern optimization strategies such as evolutionary algorithms, ant colony algorithms, Bayesian optimization techniques, etc. come with several parameters that steer their behavior during the optimization process. To obtain high-performing algorithm instances, automated algorithm configuration techniques have been developed. One of the most popular tools is irace, which evaluates configurations in sequential races, making use of iterated statistical tests to discard poorly performing configurations. At the end of the race, a set of elite configurations are selected from those survivor configurations that were not discarded, using greedy truncation selection. We study two alternative selection methods: one keeps the best survivor and selects the remaining configurations uniformly at random from the set of survivors, while the other applies entropy to maximize the diversity of the elites. These methods are tested for tuning ant colony optimization algorithms for traveling salesperson problems and the quadratic assignment problem and tuning an exact tree search solver for satisfiability problems. The experimental results show improvement on the tested benchmarks compared to the default selection of irace. In addition, the obtained results indicate that non-elitist can obtain diverse algorithm configurations, which encourages us to explore a wider range of solutions to understand the behavior of algorithms.
Model-Based Evolutionary Algorithms (MBEAs) can be highly scalable by virtue of linkage (or variable interaction) learning. This requires, however, that the linkage model can capture the exploitable structure of a problem. Usually, a single type of linkage structure is attempted to be captured using models such as a linkage tree. However, in practice, problems may exhibit multiple linkage structures. This is for instance the case in multi-objective optimization when the objectives have different linkage structures. This cannot be modelled sufficiently well when using linkage models that aim at capturing a single type of linkage structure, deteriorating the advantages brought by MBEAs. Therefore, here, we introduce linkage kernels, whereby a linkage structure is learned for each solution over its local neighborhood. We implement linkage kernels into the MBEA known as GOMEA that was previously found to be highly scalable when solving various problems. We further introduce a novel benchmark function called Best-of-Traps (BoT) that has an adjustable degree of different linkage structures. On both BoT and a worst-case scenario-based variant of the well-known MaxCut problem, we experimentally find a vast performance improvement of linkage-kernel GOMEA over GOMEA with a single linkage tree as well as the MBEA known as DSMGA-II.
According to the published papers and books since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems treated by population-based optimizers like Evolutionary Algorithms. However, is it always the method of choice for real-world applications, where either more than four objectives have to be considered, or the same type of task is repeated again and again with only minor modifications, in an automated optimization or planning process? This paper presents a classification of application scenarios and compares the Pareto approach with an extended version of the weighted sum, called cascaded weighted sum, for the different scenarios. Its range of application within the field of multi-objective optimization is discussed as well as its strengths and weaknesses.
Vanilla neural architecture search using evolutionary algorithms (EA) involves evaluating each architecture by training it from scratch, which is extremely time-consuming. This can be reduced by using a supernet to estimate the fitness of every architecture in the search space due to its weight sharing nature. However, the estimated fitness is very noisy due to the co-adaptation of the operations in the supernet. In this work, we propose a method called pEvoNAS wherein the whole neural architecture search space is progressively reduced to smaller search space regions with good architectures. This is achieved by using a trained supernet for architecture evaluation during the architecture search using genetic algorithm to find search space regions with good architectures. Upon reaching the final reduced search space, the supernet is then used to search for the best architecture in that search space using evolution. The search is also enhanced by using weight inheritance wherein the supernet for the smaller search space inherits its weights from previous trained supernet for the bigger search space. Exerimentally, pEvoNAS gives better results on CIFAR-10 and CIFAR-100 while using significantly less computational resources as compared to previous EA-based methods. The code for our paper can be found in https://github.com/nightstorm0909/pEvoNAS
Multi-objective optimization problems with constraints (CMOPs) are generally considered more challenging than those without constraints. This in part can be attributed to the creation of infeasible regions generated by the constraint functions, and/or the interaction between constraints and objectives. In this paper, we explore the relationship between constrained multi-objective evolutionary algorithms (CMOEAs) performance and CMOP instances characteristics using Instance Space Analysis (ISA). To do this, we extend recent work focused on the use of Landscape Analysis features to characterise CMOP. Specifically, we scrutinise the multi-objective landscape and introduce new features to describe the multi-objective-violation landscape, formed by the interaction between constraint violation and multi-objective fitness. Detailed evaluation of problem-algorithm footprints spanning six CMOP benchmark suites and fifteen CMOEAs, illustrates that ISA can effectively capture the strength and weakness of the CMOEAs. We conclude that two key characteristics, the isolation of non-dominate set and the correlation between constraints and objectives evolvability, have the greatest impact on algorithm performance. However, the current benchmarks problems do not provide enough diversity to fully reveal the efficacy of CMOEAs evaluated.
Neural architecture search (NAS), the study of automating the discovery of optimal deep neural network architectures for tasks in domains such as computer vision and natural language processing, has seen rapid growth in the machine learning research community. While there have been many recent advancements in NAS, there is still a significant focus on reducing the computational cost incurred when validating discovered architectures by making search more efficient. Evolutionary algorithms, specifically genetic algorithms, have a history of usage in NAS and continue to gain popularity versus other optimization approaches as a highly efficient way to explore the architecture objective space. Most NAS research efforts have centered around computer vision tasks and only recently have other modalities, such as the rapidly growing field of natural language processing, been investigated in depth. In this work, we show how genetic algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate multi-objective architectural exploration in a way that works in the modalities of both machine translation and image classification.
Recent advances in Neural Architecture Search (NAS) which extract specialized hardware-aware configurations (a.k.a. "sub-networks") from a hardware-agnostic "super-network" have become increasingly popular. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still largely under-explored. For example, some recent network morphism techniques allow a super-network to be trained once and then have hardware-specific networks extracted from it as needed. These methods decouple the super-network training from the sub-network search and thus decrease the computational burden of specializing to different hardware platforms. We propose a comprehensive system that automatically and efficiently finds sub-networks from a pre-trained super-network that are optimized to different performance metrics and hardware configurations. By combining novel search tactics and algorithms with intelligent use of predictors, we significantly decrease the time needed to find optimal sub-networks from a given super-network. Further, our approach does not require the super-network to be refined for the target task a priori, thus allowing it to interface with any super-network. We demonstrate through extensive experiments that our system works seamlessly with existing state-of-the-art super-network training methods in multiple domains. Moreover, we show how novel search tactics paired with evolutionary algorithms can accelerate the search process for ResNet50, MobileNetV3 and Transformer while maintaining objective space Pareto front diversity and demonstrate an 8x faster search result than the state-of-the-art Bayesian optimization WeakNAS approach.