Evolutionary Optimization Algorithm Research Articles

Surrogate-assisted evolutionary algorithms for expensive combinatorial optimization: a survey

AbstractAs potent approaches for addressing computationally expensive optimization problems, surrogate-assisted evolutionary algorithms (SAEAs) have garnered increasing attention. Prevailing endeavors in evolutionary computation predominantly concentrate on expensive continuous optimization problems, with a notable scarcity of investigations directed toward expensive combinatorial optimization problems (ECOPs). Nevertheless, numerous ECOPs persist in practical applications. The widespread prevalence of such problems starkly contrasts the limited development of relevant research. Motivated by this disparity, this paper conducts a comprehensive survey on SAEAs tailored to address ECOPs. This survey comprises two primary segments. The first segment synthesizes prevalent global, local, hybrid, and learning search strategies, elucidating their respective strengths and weaknesses. Subsequently, the second segment furnishes an overview of surrogate-based evaluation technologies, delving into three pivotal facets: model selection, construction, and management. The paper also discusses several potential future directions for SAEAs with a focus towards expensive combinatorial optimization.

Automatic evolutionary design of quantum rule-based systems and applications to quantum reinforcement learning

Explainable artificial intelligence is a research topic whose relevance has increased in recent years, especially with the advent of large machine learning models. However, very few attempts have been proposed to improve interpretability in the case of quantum artificial intelligence, and many existing quantum machine learning models in the literature can be considered almost as black boxes. In this article, we argue that an appropriate semantic interpretation of a given quantum circuit that solves a problem can be of interest to the user not only to certify the correct behavior of the learned model, but also to obtain a deeper insight into the problem at hand and its solution. We focus on decision-making problems that can be formulated as classification tasks and propose a method for learning quantum rule-based systems to solve them using evolutionary optimization algorithms. The approach is tested to learn rules that solve control and decision-making tasks in reinforcement learning environments, to provide interpretable agent policies that help to understand the internal dynamics of an unknown environment. Our results conclude that the learned policies are not only highly explainable, but can also help detect non-relevant features of problems and produce a minimal set of rules.

A two-stage direction-guided evolutionary algorithm for large-scale multiobjective optimization

Large-scale multiobjective optimization problems (LSMOPs) have exponential growth in the search space as the decision variables increase, and the vast search space poses a challenge to the performance of multiobjective evolutionary algorithms (MOEAs). Many current large-scale MOEAs need to consume a large amount of computational resources to get good performance. This paper proposes a two-stage direction-guided evolutionary algorithm for large-scale multiobjective optimization (LMOEA-S2D) to balance the performance and computational resource overhead. The algorithm exploits the Pareto-optimality property of domination and the diversity-preserving property of decomposition to optimize the performance in the two stages, respectively, and designs a corresponding direction-guided mechanism to improve search efficiency. LMOEA-S2D designs global direction search and local direction search in the domination-based stage for efficient exploitation to accelerate population convergence. To promote greater population diversity, a hybrid direction search was devised to aid diversity exploration in the decomposition-based stage, and this facilitates even distribution of candidate solutions across the Pareto optimal frontier. LMOEA-S2D is compared with five state-of-the-art large-scale MOEAs on some large-scale multiobjective test suites with 100 to 5,000 decision variables. The experimental results show that LMOEA-S2D significantly outperformed all compared algorithms under limited computational resources.

AxOMaP : Designing FPGA-based A ppro x imate Arithmetic O perators using Ma thematical P rogramming

With the increasing application of machine learning (ML) algorithms in embedded systems, there is a rising necessity to design low-cost computer arithmetic for these resource-constrained systems. As a result, emerging models of computation, such as approximate and stochastic computing, that leverage the inherent error-resilience of such algorithms are being actively explored for implementing ML inference on resource-constrained systems. Approximate computing (AxC) aims to provide disproportionate gains in the power, performance, and area (PPA) of an application by allowing some level of reduction in its behavioral accuracy (BEHAV). Using approximate operators (AxOs) for computer arithmetic forms one of the more prevalent methods of implementing AxC. AxOs provide the additional scope for finer granularity of optimization, compared to only precision scaling of computer arithmetic. To this end, the design of platform-specific and cost-efficient approximate operators forms an important research goal. Recently, multiple works have reported the use of AI/ML-based approaches for synthesizing novel FPGA-based AxOs. However, most of such works limit the use of AI/ML to designing ML-based surrogate functions that are used during iterative optimization processes. To this end, we propose a novel data analysis-driven mathematical programming-based approach to synthesizing approximate operators for FPGAs. Specifically, we formulate mixed integer quadratically constrained programs based on the results of correlation analysis of the characterization data and use the solutions to enable a more directed search approach for evolutionary optimization algorithms. Compared to traditional evolutionary algorithms-based optimization, we report up to 21% improvement in the hypervolume, for joint optimization of PPA and BEHAV, in the design of signed 8-bit multipliers. Further, we report up to 27% better hypervolume than other state-of-the-art approaches to DSE for FPGA-based application-specific AxOs.

A Systematic Review of Multi-Objective Evolutionary Algorithms Optimization Frameworks

The study of evolutionary algorithms (EAs) has witnessed an impressive increase during the last decades. The need to explore this area is determined by the growing request for design and the optimization of more and more engineering problems in society, such as highway construction processes, food and agri-technologies processes, resource allocation problems, logistics and transportation systems, microarchitectures, suspension systems optimal design, etc. All of these matters refer to specific highly computational problems with a huge design space, hence the obvious need for evolutionary algorithms and frameworks, or platforms that allow for the implementing and testing of such algorithms and methods. This paper aims to comparatively analyze the existing software platforms and state-of-the-art multi-objective optimization algorithms and make a review of what features exist and what features might be included next as further developments in such tools, from a researcher’s perspective. Additionally, it is essential for a framework to be easily extendable with new types of problems and optimization algorithms, metrics and quality indicators, genetic operators or specific solution representations and results analysis and comparison features. After presenting the most relevant existing features in these types of platforms, we suggest some future steps and the developments we have been working on.

A novel differential evolution algorithm with multi-population and elites regeneration.

Differential Evolution (DE) is widely recognized as a highly effective evolutionary algorithm for global optimization. It has proven its efficacy in tackling diverse problems across various fields and real-world applications. DE boasts several advantages, such as ease of implementation, reliability, speed, and adaptability. However, DE does have certain limitations, such as suboptimal solution exploitation and challenging parameter tuning. To address these challenges, this research paper introduces a novel algorithm called Enhanced Binary JADE (EBJADE), which combines differential evolution with multi-population and elites regeneration. The primary innovation of this paper lies in the introduction of strategy with enhanced exploitation capabilities. This strategy is based on utilizing the sorting of three vectors from the current generation to perturb the target vector. By introducing directional differences, guiding the search towards improved solutions. Additionally, this study adopts a multi-population method with a rewarding subpopulation to dynamically adjust the allocation of two different mutation strategies. Finally, the paper incorporates the sampling concept of elite individuals from the Estimation of Distribution Algorithm (EDA) to regenerate new solutions through the selection process in DE. Experimental results, using the CEC2014 benchmark tests, demonstrate the strong competitiveness and superior performance of the proposed algorithm.

Mixed-model sequencing with reinsertion of failed vehicles: a case study for automobile industry

In the automotive industry, some vehicles, failed vehicles, cannot be produced according to the planned schedule due to some reasons such as material shortage, paint failure, etc. These vehicles are pulled out of the sequence, potentially resulting in an increased work overload. On the other hand, the reinsertion of failed vehicles is executed dynamically as suitable positions occur. In case such positions do not occur enough, either the vehicles waiting for reinsertion accumulate or reinsertions are made to worse positions by sacrificing production efficiency. This study proposes a bi-objective two-stage stochastic program and formulation improvements for a mixed-model sequencing problem with stochastic product failures and integrated reinsertion process. Moreover, an evolutionary optimisation algorithm, a two-stage local search algorithm, and a hybrid approach are developed. Numerical experiments over a case study show that while the hybrid algorithm better explores the Pareto front representation, the local search algorithm provides more reliable solutions regarding work overload objective. Finally, the results of the dynamic reinsertion simulations show that we can decrease the work overload by 20% while significantly decreasing the waiting time of the failed vehicles by considering vehicle failures and integrating the reinsertion process into the mixed-model sequencing problem.

A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control

A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control

An Efficient Binary Hybrid Equilibrium Algorithm for Binary Optimization Problems: Analysis, Validation, and Case Studies

Binary optimization problems belong to the NP-hard class because their solutions are hard to find in a known time. The traditional techniques could not be applied to tackle those problems because the computational cost required by them increases exponentially with increasing the dimensions of the optimization problems. Therefore, over the last few years, researchers have paid attention to the metaheuristic algorithms for tackling those problems in an acceptable time. But unfortunately, those algorithms still suffer from not being able to avert local minima, a lack of population diversity, and low convergence speed. As a result, this paper presents a new binary optimization technique based on integrating the equilibrium optimizer (EO) with a new local search operator, which effectively integrates the single crossover, uniform crossover, mutation operator, flipping operator, and swapping operator to improve its exploration and exploitation operators. In a more general sense, this local search operator is based on two folds: the first fold borrows the single-point crossover and uniform crossover to accelerate the convergence speed, in addition to avoiding falling into local minima using the mutation strategy; the second fold is based on applying two different mutation operators on the best-so-far solution in the hope of finding a better solution: the first operator is the flip mutation operator to flip a bit selected randomly from the given solution, and the second operator is the swap mutation operator to swap two unique positions selected randomly from the given solution. This variant is called a binary hybrid equilibrium optimizer (BHEO) and is applied to three common binary optimization problems: 0–1 knapsack, feature selection, and the Merkle–Hellman knapsack cryptosystem (MHKC) to investigate its effectiveness. The experimental findings of BHEO are compared with those of the classical algorithm and six other well-established evolutionary and swarm-based optimization algorithms. From those findings, it is concluded that BHEO is a strong alternative to tackle binary optimization problems. Quantatively, BHEO could reach an average fitness of 0.090737884 for the feature section problem and an average difference from the optimal profits for some used Knapsack problems of 2.482.

A Novel Mayfly Algorithm with Response Surface for Static Damage Identification Based on Multiple Indicators

This paper proposes a novel structural damage identification approach coupling the Mayfly algorithm (MA) with static displacement-based response surface (RS). Firstly, a hybrid optimal objective function is established that simultaneously considers the sensitivity-based residual errors of static damage identification equation and the static displacement residual. In the objective function, the static damage identification equation is addressed by the Tikhonov regularization technique. The MA is subsequently employed to conduct an optimal search and pinpoint the location and intensity of damages at the structural element level. To handle the inconformity of the static loading points and the measurement points of displacements, the model reduction and displacement extension techniques are implemented to reconstruct the static damage identification equation. Meanwhile, the static displacement-based RS is constructed to calculate the displacement residual in the hybrid objective function, thereby circumventing the time-consuming finite element calculations and improving computational efficiency. The identification results of the numerical box girder bridge demonstrate that the proposed method outperforms the particle swarm optimization, differential evolution, Jaya and whale optimization algorithms about both convergence rate in optimal searching and identification accuracy. The proposed method enables more accurate damage identification compared to methods solely based on the indicator of the residual of static damage identification equations or displacement residual. The results of identifying damage in the 21 element-truss structure and the static experiments on identifying damage in an aluminum alloy cantilever beam confirm the high efficiency of the proposed approach.

A neighborhood-assisted evolutionary algorithm for multimodal multi-objective optimization

A neighborhood-assisted evolutionary algorithm for multimodal multi-objective optimization

Enhancing forest optimization algorithm with gravitational search for nonlinear continuous optimization

Meta-heuristic algorithms have great role in solving problems related to optimization. Meta-heuristic method cannot solve problems related to optimization due to No Free Lunch theory. Hence different optimization methods are proposed by various researchers each year in order to solve optimization problems. Forest Optimization Algorithm (FOA) is an evolutionary optimization algorithm that is appropriate for continuous nonlinear optimization problems. The algorithm drawbacks include entrapment in local optimum and failure in achieving global optimum. The paper proposes hybrid algorithm called FOAGSA, in which the Gravitational Search Algorithm (GSA) is employed to improve the FOA performance in order to solve nonlinear continuous problems. The FOAGSA was evaluated through 39 benchmark optimization functions and two engineering problems. The experimental results proved that the FOAGSA exhibited acceptable results compared to state-of-art and well-known Meta-heuristic algorithms. Friedman ranking algorithm was utilized to compare FOAGSA with existing methods. The FOAGSA was ranked first on that basis.

A similarity-detection-based evolutionary algorithm for large-scale multimodal multi-objective optimization

In recent years, there has been a surge in the development of evolutionary algorithms tailored for multimodal multi-objective optimization problems (MMOPs). These algorithms aim to find multiple equivalent Pareto optimal solution sets (PSs). However, little work has been done on MMOPs with large-scale decision variables, especially when the Pareto optimal solutions are sparse. These problems pose significant challenges due to the dimension curse, the unknown sparsity, and the unknown number of equivalent PSs. In this paper, we propose an evolutionary algorithm based on similarity detection called SD-MMEA to solve large-scale MMOPs with sparse Pareto-optimal solutions. Specifically, it employs a multi-population independent evolution to explore multiple PSs and distinguishes different PSs by double detection of the similarity between subpopulations. Simultaneously, develop online scoring mechanisms for decision variables to guide the subpopulations to explore in different directions. In addition, during the latter stage of evolution, the decision variables of individuals are further optimized by a double-layer grouping process. The proposed algorithm is compared with six state-of-the-art algorithms. Experimental results show that SD-MMEA has significant advantages in solving large-scale MMOPs with sparse solutions.

Multiobjective optimization of laser welding parameters for P92 steel based on MFO/MOEAD-Kriging

P92 steel is used in steam equipment of thermal power plants and nuclear power plants. It needs to withstand high temperature and high pressure during service, so high-quality welds are required. Laser welding can easily obtain good weld quality and reduce the probability of coarse grains and welding defects in the heat-affected zone. Post-weld deformation, residual stress, and weld hardness are important indexes for evaluating weld quality, which largely depends on the combination of laser welding process parameters. The multiobjective optimization methods of moth-flame optimization (MFO) and multiobjective evolutionary algorithm based on decomposition under the Kriging model were compared in this research. It was found that the MFO algorithm has a faster optimization speed and better overall effect. The Optimal Latin hypercube sampling method was used to design the simulation test. The welding seam-forming process was simulated by the SYSWELD software. The Kriging model was used to make the nonlinear relationship between the process parameters and the weld quality indexes significant. A new data set was designed to evaluate the accuracy of the model. On this basis, the efficiency of the combination of process parameters optimized by the two algorithms was compared. The simulation and experimental results were in good agreement with the multiobjective optimization results of the MFO. In the experimental verification, the optimized weld quality was analyzed from the aspects of microstructure and mechanical properties. The results showed that the multiobjective optimization method quickly and effectively reduces the probability of weld quality defects in actual welding, thereby improving weld quality. This multiobjective optimization method provides valuable research ideas for engineering research and development to effectively shorten its development cycle.

Evolutionary Multi-Objective Optimization Algorithm for Resource Allocation Using Deep Neural Network in Ultra-Dense Networks

Evolutionary Multi-Objective Optimization Algorithm for Resource Allocation Using Deep Neural Network in Ultra-Dense Networks

Detecting Hidden and Irrelevant Objectives in Interactive Multiobjective Optimization

Evolutionary multi-objective optimization algorithms (EMOAs) typically assume that all objectives that are relevant to the decision-maker (DM) are optimized by the EMOA. In some scenarios, however, there are irrelevant objectives that are optimized by the EMOA but ignored by the DM, as well as, hidden objectives that the DM considers when judging the utility of solutions but are not optimized. This discrepancy between the EMOA and the DM’s preferences may impede the search for the most-preferred solution and waste resources evaluating irrelevant objectives. Research on objective reduction has focused so far on the structure of the problem and correlations between objectives and neglected the role of the DM. We formally define here the concepts of irrelevant and hidden objectives and propose methods for detecting them, based on uni-variate feature selection and recursive feature elimination, that use the preferences already elicited when a DM interacts with a ranking-based interactive EMOA (iEMOA). We incorporate the detection methods into an iEMOA capable of dynamically switching the objectives being optimized. Our experiments show that this approach can efficiently identify which objectives are relevant to the DM and reduce the number of objectives being optimized, while keeping and often improving the utility, according to the DM, of the best solution found.

Neural Architecture Search as Multiobjective Optimization Benchmarks: Problem Formulation and Performance Assessment

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning (e.g., autonomous driving) have raised higher demands for network architectures considering multiple design criteria: number of parameters/weights, number of floating-point operations, inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: (i) we formulate NAS tasks into general multi-objective optimization problems and analyze the complex characteristics from an optimization point of view; (ii) we present an end-to-end pipeline, dubbed EvoXBench, to generate benchmark test problems for EMO algorithms to run efficiently -without the requirement of GPUs or Pytorch/Tensorflow; (iii) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code of EvoXBench is available at https://github.com/EMI-Group/EvoXBench.

Improved Evolutionary Operators for Sparse Large-Scale Multiobjective Optimization Problems

Many critical science, societal, and engineering fields contain large-scale multiobjective optimization problems (LSMOPs), comprised of many decision variables. However, as the number of decision variables increases, optimization algorithms face exponentially large search spaces, thereby exhibiting a degraded performance. Nonetheless, LSMOPs whose optimal solutions correspond to sparse variable vectors can be solved more efficiently by evolutionary multiobjective optimization (EMO) algorithms. Despite the great recent strides in developing generic EMO algorithms for sparse LSMOPs, there is still room for improvement. Specifically, algorithms still struggle to find convergent and diverse Pareto fronts in an acceptable amount of time when solving sparse LSMOPs with thousands of decision variables. To better solve sparse LSMOPs, we propose a novel set of evolutionary operators to adapt small-scale EMO algorithms for sparse LSMOPs. These simple, novel, and effective operators include varied striped sparse population sampling (VSSPS), sparse simulated binary crossover (S-SBX), and sparse polynomial mutation (S-PM). These operators, combined with NSGA-II, make the proposed S-NSGA-II algorithm. S-NSGA-II runs near-universally faster than existing methods for problems containing up to 6,400 decision variables, while performing as well as or better than contemporary sparse LSMOP algorithms with respect to hypervolume, especially with problems with larger than 5,000 decision variables.

Offline Data-Driven Multiobjective Optimization Evolutionary Algorithm Based on Generative Adversarial Network

Usually, data-driven multi-objective optimiza -tion problems (DD-MOPs) are indirectly solved by evolutionary algorithms through the built surrogate model which is well-trained from sample data. However, in most DD-MOPs, only a few available data can be practicably collected from real engineering experiments due to the unaffordable cost and time. The key challenge in such a DD-MOP is to prevent the serious deterioration on the accuracy of the obtained approximate Pareto front. In this paper, two novel strategies, critical fitness for evolutionary algorithms and data augmentation for a surrogate model, are complementarily imposed by a generative adversarial network (GAN) to tackle with the challenges in DD-MOPs. In the critical fitness strategy, a new critical fitness, composed of the critical score from the discriminator of GAN and the prediction value of surrogate model, is proposed to improve the accuracy of approximate Pareto front of a DD-MOP. In the data augmentation strategy, some new samples are synthetized by the generator of GAN to build a better-trained surrogate model. As a result, the GAN concurrently serves the critical fitness strategy and the data augmentation strategy as the roles of “killing two birds with one stone”. The performance of the proposed algorithm for DD-MOPs was well-verified over 26 benchmark problems and successfully applied to discover new NdFeB materials.

Agent-based modeling and optimization of the characteristics for research-and-production clusters

This paper presents a developed agent-based simulation model for the development of research-and-production clusters in Russia implemented with the use of high-tech enterprises located in four science cities (Troitsk, Obninsk, Pushchino and Protvino) as the case study. A new approach to modeling and optimization of gross metropolitan product (GMP) is proposed, taking into account the influence of the “gravity effect” on the redistribution of labor resources between developing science cities and appropriate enterprises united in single research and research-and-production clusters An important element of this approach is the formation of various scenarios for the strategic development of the research-and-production clusters being assessed and support for the possibility of choosing the most preferable scenario using an evolutionary optimization algorithm. An enlarged simulation model has been developed and implemented in AnyLogic describing the possible development trajectories of science cities with a corresponding change in the values of the most important characteristics: the number of economically active population, the number of research-and-production enterprises, the volume of products produced in high-tech sectors of the economy, GMP, etc. The designed framework is intended primarily for the management of research-and-production clusters implementing the strategy of innovative development. Such a framework uses methods of system dynamics and agent-based simulation modeling supported in the AnyLogic system, genetic optimization algorithms and GIS mapping for science cities, etc. to implement the required functionality. The approbation of the framework was completed with the use of real data published in the approved strategies of the relevant science cities development. As a result of the numerical experiments carried out, some recommendations were proposed for the development of the research-and-production clusters under study considering their mutual influence and the existing base of resources.