A comprehensive survey of fitness approximation in evolutionary computation

Artificial intelligence-empowered functional design of semi-transparent optoelectronic and photonic devices via deep Q-learning

Photonic-based design of semi-transparent organic solar cells (ST-OSCs) demands a careful balance between optical transparency and photovoltaic efficiency, often requiring trade-offs that complicate optimization. This study, for the first time, employs deep Q-learning, a reinforcement learning algorithm, to address this challenge, integrating transfer matrix method for precise optical calculations. The proposed framework optimizes asymmetric dielectric/metal/dielectric photonic-based transparent contact systems combined with novel PBDB-T:ITIC-based active layers, achieving superior optical and photovoltaic performance. The deep Q-learning algorithm successfully identified configurations yielding a maximum photo-current density (Jph) while effectively maintaining average visible transmittance (AVT), balancing transparency, and photon harvesting by learning Maxwell's equations. Precise tuning of material thicknesses and optical properties further enhanced performance, ensuring color neutrality and high rendering index. These ST-OSC designs are particularly suited for building-integrated photovoltaics and photovoltaic windows, where both functionality and aesthetics are critical. This study also highlights the transformative potential of artificial intelligence in optoelectronic device design. The deep Q-learning framework accelerates optimization processes, reduces computational demands, and enables scalable solutions, surpassing traditional methods in efficiency and precision. By addressing the complex interplay of optical and photovoltaic parameters, this research advances the state-of-the-art ST-OSCs and establishes a foundation for future machine learning-driven innovations in sustainable energy technologies.

Optimal design of groundwater pollution monitoring network based on a back-propagation neural network surrogate model and grey wolf optimizer algorithm under uncertainty

In the optimal design of groundwater pollution monitoring network (GPMN), the uncertainty of the simulation model always affects the reliability of the monitoring network design when applying simulation-optimization methods. To address this issue, in the present study, we focused on the uncertainty of the pollution source intensity and hydraulic conductivity. In particular, we utilized simulation-optimization and Monte Carlo methods to determine the optimal layout scheme for monitoring wells under these uncertainty conditions. However, there is often a substantial computational load incurred due to multiple calls to the simulation model. Hence, we employed a back-propagation neural network (BPNN) to develop a surrogate model, which could substantially reduce the computational load. We considered the dynamic pollution plume migration process in the optimal design of the GPMN. Consequently, we formulated a long-term GPMN optimization model under uncertainty conditions with the aim of maximizing the pollution monitoring accuracy for each yearly period. The spatial moment method was used to measure the approximation degree between the pollution plume interpolated for the monitoring network and the actual plume, which could effectively evaluate the superior monitoring accuracy. Traditional methods are easily trapped in local optima when solving the optimization model. To overcome this limitation, we used the grey wolf optimizer (GWO) algorithm. The GWO algorithm has been found to be effective in avoiding local optima and in exploring the search space more effectively, especially when dealing with complex optimization problems. A hypothetical example was designed for evaluating the effectiveness of our method. The results indicated that the BPNN surrogate model could effectively fit the input-output relationship from the simulation model, as well as significantly reduce the computational load. The GWO algorithm effectively solved the optimization model and improved the solution accuracy. The pollution plume distribution in each monitoring yearly period could be accurately characterized by the optimized monitoring network. Thus, combining the simulation-optimization method with the Monte Carlo method effectively addressed the optimal monitoring network design problem under uncertainty.

A construction strategy of Kriging surrogate model based on Rosenblatt transformation of associated random variables and its application in groundwater remediation

When using simulation-optimization models for optimizing the design of groundwater pumping-treatment plans for pollution, building a surrogate model for the numerical simulation model has become an effective means of overcoming the computational load of such models. However, previous studies often treated pumping time as a single optimization variable, leading to unnecessary excessive pumping. This paper considers the location, pumping rate, start time, and end time of each candidate pumping well as optimization variables, and proposes a Rosenblatt-transform-based optimal Latin hypercube sampling method for the associated random variables to ensure that the start time is less than or equal to the end time. This method is coupled with an adaptive sampling method based on batch local optimal solutions to construct a dynamic adaptive Kriging surrogate model for the numerical model, ensuring that the true value of the optimal remediation scheme is not lost. The results show that, at the final stage of remediation, the pollutant concentration in the 4 scenarios achieves comprehensive compliance. However, when considering the minimization of remediation costs as the evaluation criterion, the remediation scheme in scenario 1 (the pumping start and end times are independent optimization variables for all candidate pumping wells) is optimal. In the optimization design of groundwater pumping-treatment plans, the pumping wells should be arranged in the midstream and downstream regions of the contaminant plume and parallel to the regional flow direction. This paper provides a method reference for the construction and adaptive updating of surrogate models involving associated random variables, as well as guidance for the dynamic optimization of groundwater pumping and treatment at contaminated sites.

Optimal layout design of groundwater pollution monitoring network using parameter iterative updating strategy-based ant colony optimization algorithm

The scientific layout design of the groundwater pollution monitoring network (GPMN) can provide high quality groundwater monitoring data, which is essential for the timely detection and remediation of groundwater pollution. The simulation optimization approach was effective in obtaining the optimal design of the GPMN. The ant colony optimization (ACO) algorithm is an effective method for solving optimization models. However, the parameters used in the conventional ACO algorithm are empirically adopted with fixed values, which may affect the global searchability and convergence speed. Therefore, a parameter-iterative updating strategy-based ant colony optimization (PIUSACO) algorithm was proposed to solve this problem. For the GPMN optimal design problem, a simulation-optimization framework using PIUSACO algorithm was applied in a municipal waste landfill in BaiCheng city in China. Moreover, to reduce the computational load of the design process while considering the uncertainty of aquifer parameters and pollution sources, a genetic algorithm-support vector regression (GA-SVR) method was proposed to develop the surrogate model for the numerical model. The results showed that the layout scheme obtained using the PIUSACO algorithm had a significantly higher detection rate than ACO algorithm and random layout schemes, indicating that the designed layout scheme based on the PIUSACO algorithm can detect the groundwater pollution occurrence timely. The comparison of the iteration processes of the PIUSACO and conventional ACO algorithms shows that the global searching ability is improved and the convergence speed is accelerated significantly using the iteration updating strategy of crucial parameters. This study demonstrates the feasibility of the PIUSACO algorithm for the optimal layout design of the GPMN for the timely detection of groundwater pollution.

Simultaneous identification of groundwater contaminant source and hydraulic parameters based on multilayer perceptron and flying foxes optimization

Groundwater contaminant source identification (GCSI) has practical significance for groundwater remediation and liability. However, when applying the simulation-optimization method to precisely solve GCSI, the optimization model inevitably encounters the problems of high-dimensional unknown variables to identify, which might increase the nonlinearity. In particular, to solve such optimization models, the well-known heuristic optimization algorithms might fall into a local optimum, resulting in low accuracy of inverse results. For this reason, this paper proposes a novel optimization algorithm, namely, the flying foxes optimization (FFO) to solve the optimization model. We perform simultaneous identification of the release history of groundwater pollution sources and hydraulic conductivity and compare the results with those of the traditional genetic algorithm. In addition, to alleviate the massive computational load caused by the frequent invocation of the simulation model when solving the optimization model, we utilized the multilayer perception (MLP) to establish a surrogate model of the simulation model and compared it with the method of backpropagation algorithm (BP). The results show that the average relative error of the results of FFO is 2.12%, significantly outperforming the genetic algorithm (GA); the surrogate model of MLP can replace the simulation model for calculation with fitting accuracy of more than 0.999, which is better than the commonly used surrogate model of BP.

Evolutionary Algorithms for Parameter Optimization-Thirty Years Later

Thirty years, 1993-2023, is a huge time frame in science. We address some major developments in the field of evolutionary algorithms, with applications in parameter optimization, over these 30 years. These include the covariance matrix adaptation evolution strategy and some fast-growing fields such as multimodal optimization, surrogate-assisted optimization, multiobjective optimization, and automated algorithm design. Moreover, we also discuss particle swarm optimization and differential evolution, which did not exist 30 years ago, either. One of the key arguments made in the paper is that we need fewer algorithms, not more, which, however, is the current trend through continuously claiming paradigms from nature that are suggested to be useful as new optimization algorithms. Moreover, we argue that we need proper benchmarking procedures to sort out whether a newly proposed algorithm is useful or not. We also briefly discuss automated algorithm design approaches, including configurable algorithm design frameworks, as the proposed next step toward designing optimization algorithms automatically, rather than by hand.

AI-driven and automated MRI sequence optimization in scanner-independent MRI sequences formulated by a domain-specific language

Introduction

The complexity of Magnetic Resonance Imaging (MRI) sequences requires expert knowledge about the underlying contrast mechanisms to select from the wide range of available applications and protocols. Automation of this process using machine learning (ML) can support the radiologists and MR technicians by complementing their experience and finding the optimal MRI sequence and protocol for certain applications.

Methods

We define domain-specific languages (DSL) both for describing MRI sequences and for formulating clinical demands for sequence optimization. By using various abstraction levels, we allow different key users exact definitions of MRI sequences and make them more accessible to ML. We use a vendor-independent MRI framework (gammaSTAR) to build sequences that are formulated by the DSL and export them using the generic file format introduced by the Pulseq framework, making it possible to simulate phantom data using the open-source MR simulation framework JEMRIS to build a training database that relates input MRI sequences to output sets of metrics. Utilizing ML techniques, we learn this correspondence to allow efficient optimization of MRI sequences meeting the clinical demands formulated as a starting point.

Results

ML methods are capable of capturing the relation of input and simulated output parameters. Evolutionary algorithms show promising results in finding optimal MRI sequences with regards to the training data. Simulated and acquired MRI data show high correspondence to the initial set of requirements.

Discussion

This work has the potential to offer optimal solutions for different clinical scenarios, potentially reducing exam times by preventing suboptimal MRI protocol settings. Future work needs to cover additional DSL layers of higher flexibility as well as an optimization of the underlying MRI simulation process together with an extension of the optimization method.

Structural optimisation for controlled deflections of additively manufactured single material beams

Closely controlling the mechanical behaviour and characterization of the deflection of a beam structure is a well-known and widely studied engineering problem. The progress in additive manufacturing methods and the possibilities to closely control the material property variations with the controlled placement of materials further widen the opportunities to achieve given beam deflection criteria. The multi-material additive manufacturing solutions suffer from the lack of real engineering material options, and the quality and performance of the printed parts are usually unsuitable for producing functional parts. A novel cellular structured solution is proposed here, which utilises optimisation of geometries of individual cells of a single material structured beam to obtain deflection profiles closely matched with preset conditions under different loading conditions. The cellular geometry of the structured beam is continually altered for searching and converging on the optimal structure of the cells by the covariance matrix adaptation evolution strategy algorithm in an iterative manner. The optimised beam structures could also be physically produced with single material additive manufacturing methods and the experimental and numerical beam deflection responses correlated closely.

Multisurrogate-Assisted Multitasking Particle Swarm Optimization for Expensive Multimodal Problems

Many real-world applications can be formulated as expensive multimodal optimization problems (EMMOPs). When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face the problem of selecting surrogate models but also need to tackle the problem of discovering and updating multiple modalities. Different optimization problems and different stages of evolutionary algorithms (EAs) generally require different types of surrogate models. To address this issue, in this article, we present a multisurrogate-assisted multitasking particle swarm optimization algorithm to seek multiple optimal solutions of EMMOPs at a low computational cost. The proposed algorithm first transforms an EMMOP into a multitasking optimization problem by integrating various surrogate models, and designs a multitasking niche particle swarm algorithm to solve it. Following that, a surrogate model management strategy based on the skill factor and clustering is developed to effectively balance the number of real function evaluations and the prediction accuracy of candidate optimal solutions. In addition, an adaptive local search strategy based on the trust region is proposed to enhance the capability of swarm in exploiting potential optimal modalities. We compare the proposed algorithm with five state-of-the-art SAEAs and seven multimodal EAs on 19 benchmark functions and the building energy conservation problem and experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.

Bi-indicator driven surrogate-assisted multi-objective evolutionary algorithms for computationally expensive problems

This paper presents a bi-indicator-based surrogate-assisted evolutionary algorithm (BISAEA) for multi-objective optimization problems (MOPs) with computationally expensive objectives. In BISAEA, a Pareto-based bi-indictor strategy is proposed based on convergence and diversity indicators, where a nondominated sorting approach is adopted to carry out two-objective optimization (convergence and diversity indicators) problems. The radius-based function (RBF) models are used to approximate the objective values. In addition, the proposed algorithm adopts a one-by-one selection strategy to obtain promising samples from new samples for evaluating the true objectives by their angles and Pareto dominance relationship with real non-dominated solutions to improve the diversity. After the comparison with four state-of-the-art surrogate-assisted evolutionary algorithms and three evolutionary algorithms on 76 widely used benchmark problems, BISAEA shows high efficiency and a good balance between convergence and diversity. Finally, BISAEA is applied to the multidisciplinary optimization of blend-wing-body underwater gliders with 30 decision variables and three objectives, and the results demonstrate that BISAEA has superior performance on computationally expensive engineering problems.

Precision agriculture management based on a surrogate model assisted multiobjective algorithmic framework

Sustainable intensification needs to optimize irrigation and fertilization strategies while increasing crop yield. To enable more precision and effective agricultural management, a bi-level screening and bi-level optimization framework is proposed. Irrigation and fertilization dates are obtained by upper-level screening and upper-level optimization. Subsequently, due to the complexity of the problem, the lower-level optimization uses a data-driven evolutionary algorithm, which combines the fast non-dominated sorting genetic algorithm (NSGA-II), surrogate-assisted model of radial basis function and Decision Support System for Agrotechnology Transfer to handle the expensive objective problem and produce a set of optimal solutions representing a trade-off between conflicting objectives. Then, the lower-level screening quickly finds better irrigation and fertilization strategies among thousands of solutions. Finally, the experiment produces a better irrigation and fertilization strategy, with water consumption reduced by 44%, nitrogen application reduced by 37%, and economic benefits increased by 7 to 8%.

Choose Appropriate Subproblems for Collaborative Modeling in Expensive Multiobjective Optimization

In dealing with the expensive multiobjective optimization problem, some algorithms convert it into a number of single-objective subproblems for optimization. At each iteration, these algorithms conduct surrogate-assisted optimization on one or multiple subproblems. However, these subproblems may be unnecessary or resolved. Operating on such subproblems can cause server inefficiencies, especially in the case of expensive optimization. To overcome this shortcoming, we propose an adaptive subproblem selection (ASS) strategy to identify the most promising subproblems for further modeling. To better leverage the cross information between the subproblems, we use the collaborative multioutput Gaussian process surrogate to model them jointly. Moreover, the commonly used acquisition functions (also known as infill criteria) are investigated in this article. Our analysis reveals that these acquisition functions may cause severe imbalances between exploitation and exploration in multiobjective optimization scenarios. Consequently, we develop a new acquisition function, namely, adaptive lower confidence bound (ALCB), to cope with it. The experimental results on three different sets of benchmark problems indicate that our proposed algorithm is competitive. Beyond that, we also quantitatively validate the effectiveness of the ASS strategy, the CoMOGP model, and the ALCB acquisition function.

Machine learning-based optimal design of groundwater pollution monitoring network

It is an important task of environmental management to design groundwater pollution monitoring network (GPMN) to find out the occurrence of pollution events and carry out remediation in time. However, there are many uncertain factors in the process of designing GPMN, which affect the GPMN design result. In the process of applying the Monte Carlo method for uncertainty analysis, groundwater numerical simulation model may be utilized thousands of times, which results in a huge computational load. In order to overcome this disadvantage, a machine learning (ML)-based surrogate model is constructed with Kriging method, to replace the computational simulation model under uncertainty of pollution sources and parameters. The 0-1 integer programming optimization model is constructed to maximally cover serious polluted area to detect the occurrence of groundwater pollution in time. The optimal design framework of GPMN based on proposed ML algorithm was applied in a domestic landfill in Baicheng City, China. The results showed that the ML-based surrogate model has a great fitness with the groundwater solute transport simulation model. The optimal results of GPMN indicated that monitoring wells should be mainly placed at the downstream of the leachate equalization basin. If more wells are allowed to be placed, part of wells could be placed at the downstream of the landfill. Moreover, the area where the pollution plumes of landfill site meet that of leachate equalization basin should be set as the key monitoring objective. Verification and comparison showed that the pollutant detection rate of the optimal layout scheme is far higher than random layout schemes, which proves the reliability of the ML-based optimal design scheme of GPMN.

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.

Vegetation Evolution: An Optimization Algorithm Inspired by the Life Cycle of Plants

In this paper, we have observed that different types of plants in nature can use their own survival mechanisms to adapt to various living environments. A new population-based vegetation evolution (VEGE) algorithm is proposed to solve optimization problems by interactively simulating the growth and maturity periods of plants. In the growth period, individuals explore their local areas and grow in potential directions, while individuals generate many seed individuals and spread them as widely as possible in the maturity period. The main contribution of our proposed VEGE is to balance exploitation and exploration from a novel perspective, which is to perform these two periods in alternation to switch between two different search capabilities. To evaluate the performance of the proposed VEGE, we compare it with three well-known algorithms in the evolutionary computation community: differential evolution, particle swarm optimization, and enhanced fireworks algorithm — and run them on 28 benchmark functions with 2-dimensions (2D), 10D, and 30D with 30 trial runs. The experimental results show that VEGE is efficient and promising in terms of faster convergence speed and higher accuracy. In addition, we further analyze the effects of the composition of VEGE on performance, and some open topics are also given.

An in silico Model of T Cell Infiltration Dynamics Based on an Advanced in vitro System to Enhance Preclinical Decision Making in Cancer Immunotherapy

Cancer immunotherapy often involves the use of engineered molecules to selectively bind and activate T cells located within tumour tissue. Fundamental to the success of such treatments is the presence or recruitment of T cells localised within the tumour microenvironment. Advanced organ-on-a-chip systems provide an in vitro setting in which to investigate how novel molecules influence the spatiotemporal dynamics of T cell infiltration into tissue, both in the context of anti-tumour efficacy and off-tumour toxicity. While highly promising, the complexity of these systems is such that mathematical modelling plays a crucial role in the quantitative evaluation of experimental results and maximising the mechanistic insight derived. We develop a mechanistic, mathematical model of a novel microphysiological in vitro platform that recapitulates T cell infiltration into epithelial tissue, which may be normal or transformed. The mathematical model describes the spatiotemporal dynamics of infiltrating T cells in response to chemotactic cytokine signalling. We integrate the model with dynamic imaging data to optimise key model parameters. The mathematical model demonstrates a good fit to the observed experimental data and accurately describes the distribution of infiltrating T cells. This model is designed to complement the in vitro system; with the potential to elucidate complex biological mechanisms, including the mode of action of novel therapies and the drivers of safety events, and, ultimately, improve the efficacy-safety profile of T cell-targeted cancer immunotherapies.

A Neighborhood Regression Optimization Algorithm for Computationally Expensive Optimization Problems

Expensive optimization problems arise in diverse fields, and the expensive computation in terms of function evaluation poses a serious challenge to global optimization algorithms. In this article, a simple yet effective optimization algorithm for computationally expensive optimization problems is proposed, which is called the neighborhood regression optimization algorithm. For a minimization problem, the proposed algorithm incorporates the regression technique based on a neighborhood structure to predict a descent direction. The descent direction is then adopted to generate new potential offspring around the best solution obtained so far. The proposed algorithm is compared with 12 popular algorithms on two benchmark suites with up to 30 decision variables. Empirical results demonstrate that the proposed algorithm shows clear advantages when dealing with unimodal and smooth problems, and is better than or competitive with other peer algorithms in terms of the overall performance. In addition, the proposed algorithm is efficient and keeps a good tradeoff between solution quality and running time.

Multi-Objective RANS Aerodynamic Optimization of a Hypersonic Intake Ramp at Mach 5

The work describes a systematic optimization strategy for designing hypersonic inlet intakes. A Reynolds-averaged Navier-Stokes database is mined using genetic algorithms to develop ideal designs for a priori defined targets. An intake geometry from the literature is adopted as a baseline. Thus, a steady-state numerical assessment is validated and the computational grid is tuned under nominal operating conditions. Following validation tasks, the model is used for multi-objective optimization. The latter aims at minimizing the drag coefficient while boosting the static and total pressure ratios, respectively. The Pareto optimal solutions are analyzed, emphasizing the flow patterns that result in the improvements. Although the approach is applied to a specific setup, the method is entirely general, offering a valuable flowchart for designing super/hypersonic inlets. Notably, because high-quality computational fluid dynamics strategies drive the innovation process, the latter accounts for the complex dynamics of such devices from the early design stages, including shock-wave/boundary-layer interactions and recirculating flow portions in the geometrical shaping.

Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

Surrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

WiSM: Windowing Surrogate Model for Evaluation of Curvature-Constrained Tours With Dubins Vehicle

Dubins tours represent a solution of the Dubins traveling salesman problem (DTSP) that is a variant of the optimization routing problem to determine a curvature-constrained shortest path to visit a set of locations such that the path is feasible for Dubins vehicle, which moves only forward and has a limited turning radius. The DTSP combines the NP-hard combinatorial optimization to determine the optimal sequence of visits to the locations, as in the regular TSP, with the continuous optimization of the heading angles at the locations, where the optimal heading values depend on the sequence of visits and vice versa. We address the computationally challenging DTSP by fast evaluation of the sequence of visits by the proposed windowing surrogate model (WiSM), which estimates the length of the optimal Dubins path connecting a sequence of locations in a Dubins tour. The estimation is sped up by a regression model trained using close to optimum solutions of small Dubins tours that are generalized for large-scale instances of the addressed DTSP utilizing the sliding-window technique and a cache for already computed results. The reported results support that the proposed WiSM enables fast convergence of a relatively simple evolutionary algorithm to high-quality solutions of the DTSP. We show that with an increasing number of locations, our algorithm scales significantly better than other state-of-the-art DTSP solvers.

Evolutionary Computation for Expensive Optimization: A Survey

Expensive optimization problem (EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation (EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.

A multi-model assisted differential evolution algorithm for computationally expensive optimization problems

Surrogate models are commonly used to reduce the number of required expensive fitness evaluations in optimizing computationally expensive problems. Although many competitive surrogate-assisted evolutionary algorithms have been proposed, it remains a challenging issue to develop an effective model management strategy to address problems with different landscape features under a limited computational budget. This paper adopts a coarse-to-fine evaluation scheme basing on two surrogate models, i.e., a coarse Gaussian process and a fine radial basis function, for assisting a differential evolution algorithm to solve computationally expensive optimization problems. The coarse Gaussian process model is meant to capture the general contour of the fitness landscape to estimate the fitness and its degree of uncertainty. A surrogate-assisted environmental selection strategy is then developed according to the non-dominance relationship between approximated fitness and estimated uncertainty. Meanwhile, the fine radial basis function model aims to learn the details of the local fitness landscape to refine the approximation quality of the new parent population and find the local optima for real-evaluations. The performance and scalability of the proposed method are extensively evaluated on two sets of widely used benchmark problems. Experimental results show that the proposed method can outperform several state-of-the-art algorithms within a limited computational budget.

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy).

A federated data-driven evolutionary algorithm for expensive multi-/many-objective optimization

Data-driven optimization has found many successful applications in the real world and received increased attention in the field of evolutionary optimization. Most existing algorithms assume that the data used for optimization are always available on a central server for construction of surrogates. This assumption, however, may fail to hold when the data must be collected in a distributed way and are subject to privacy restrictions. This paper aims to propose a federated data-driven evolutionary multi-/many-objective optimization algorithm. To this end, we leverage federated learning for surrogate construction so that multiple clients collaboratively train a radial-basis-function-network as the global surrogate. Then a new federated acquisition function is proposed for the central server to approximate the objective values using the global surrogate and estimate the uncertainty level of the approximated objective values based on the local models. The performance of the proposed algorithm is verified on a series of multi-/many-objective benchmark problems by comparing it with two state-of-the-art surrogate-assisted multi-objective evolutionary algorithms.

Data-Driven Evolutionary Algorithm With Perturbation-Based Ensemble Surrogates

Data-driven evolutionary algorithms (DDEAs) aim to utilize data and surrogates to drive optimization, which is useful and efficient when the objective function of the optimization problem is expensive or difficult to access. However, the performance of DDEAs relies on their surrogate quality and often deteriorates if the amount of available data decreases. To solve these problems, this article proposes a new DDEA framework with perturbation-based ensemble surrogates (DDEA-PES), which contain two efficient mechanisms. The first is a diverse surrogate generation method that can generate diverse surrogates through performing data perturbations on the available data. The second is a selective ensemble method that selects some of the prebuilt surrogates to form a final ensemble surrogate model. By combining these two mechanisms, the proposed DDEA-PES framework has three advantages, including larger data quantity, better data utilization, and higher surrogate accuracy. To validate the effectiveness of the proposed framework, this article provides both theoretical and experimental analyses. For the experimental comparisons, a specific DDEA-PES algorithm is developed as an instance by adopting a genetic algorithm as the optimizer and radial basis function neural networks as the base models. The experimental results on widely used benchmarks and an aerodynamic airfoil design real-world optimization problem show that the proposed DDEA-PES algorithm outperforms some state-of-the-art DDEAs. Moreover, when compared with traditional nondata-driven methods, the proposed DDEA-PES algorithm only requires about 2% computational budgets to produce competitive results.

A survey on evolutionary computation for complex continuous optimization

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

Computational Screening of Trillions of Metal-Organic Frameworks for High-Performance Methane Storage

In the past decade, there has been an increasing number of computational screening works to facilitate finding optimal materials for a variety of different applications. Unfortunately, most of these screening studies are limited to their initial set of materials and result in a brute-force type of screening approach. In this work, we present a systematic strategy that can find metal-organic frameworks (MOFs) with the desired properties from an extremely diverse and large set of over 100 trillion possible MOFs using machine learning and evolutionary algorithm. It is demonstrated that our algorithm can discover 964 MOFs with methane working capacity over 200 cm³ cm^-3 and 96 MOFs with methane working capacity over the current world record of 208 cm³ cm^-3. We believe that this methodology can take advantage of the modular nature of MOFs and can readily be extended to other important applications as well.

Surrogate-assisted firefly algorithm for breast cancer detection

Breast cancer is a severe disease for women health, however, with expensive diagnostic cost or obsolete medical technique, many patients are hard to obtain prompt medical treatment. Thus, efficient detection result of breast cancer while lower medical cost may be a promising way to protect women health. Breast cancer detection using all features will take a lot of time and computational resources. Thus, in this paper, we proposed a novel framework with surrogate-assisted firefly algorithm (FA) for breast cancer detection (SFA-BCD). As an advanced evolutionary algorithm (EA), FA is adopted to make feature selection, and the machine learning as classifier identify the breast cancer. Moreover, the surrogate model is utilized to decrease computation cost and expensive computation, which is the approximation function built by offline data to the real object function. The comprehensive experiments have been conducted under several breast cancer dataset derived from UCI. Experimental results verified that the proposed framework with surrogate-assisted FA significantly reduced the computation cost.

Joint Structure and Parameter Optimization of Multiobjective Sparse Neural Network

This work addresses the problem of network pruning and proposes a novel joint training method based on a multiobjective optimization model. Most of the state-of-the-art pruning methods rely on user experience for selecting the sparsity ratio of the weight matrices or tensors, and thus suffer from severe performance reduction with inappropriate user-defined parameters. Moreover, networks might be inferior due to the inefficient connecting architecture search, especially when it is highly sparse. It is revealed in this work that the network model might maintain sparse characteristic in the early stage of the backpropagation (BP) training process, and evolutionary computation-based algorithms can accurately discover the connecting architecture with satisfying network performance. In particular, we establish a multiobjective sparse model for network pruning and propose an efficient approach that combines BP training and two modified multiobjective evolutionary algorithms (MOEAs). The BP algorithm converges quickly, and the two MOEAs can search for the optimal sparse structure and refine the weights, respectively. Experiments are also included to prove the benefits of the proposed algorithm. We show that the proposed method can obtain a desired Pareto front (PF), leading to a better pruning result comparing to the state-of-the-art methods, especially when the network structure is highly sparse.