Evolutionary Optimization Process Research Articles

A fixed point evolution algorithm based on expanded Aitken rapid iteration method for global numeric optimization

Evolution algorithms based on mathematical models whose reproduction operators are derived from mathematical models are a promising branch of metaheuristic algorithms. Aitken rapid iteration method, as a fixed point iteration technique for solving nonlinear equations, performs a procedure of progressive display of a root and generates an iterative sequence that exhibits a convergent trend. Inspired by the idea that an iterative sequence gradually converges to the optimal point during the progressive display procedure of a fixed point of an equation, a fixed point evolution algorithm based on the expanded Aitken rapid iteration method (FPEea) is proposed. To develop FPEea, an expanded Aitken rapid model is first constructed. Then, three polynomials which are derived from the expanded Aitken rapid model are used as the reproduction operator of FPEea to produce offspring. The performance of FPEea is investigated on CEC2019 and CEC2020 benchmark function sets, as well as four engineering design problems. Experimental results show that FPEea is an effective and competitive algorithm compared with several classical evolution algorithms and state-of-the-art algorithms.

Multi-UAV Path Planning Based on Cooperative Co-Evolutionary Algorithms with Adaptive Decision Variable Selection

When dealing with UAV path planning problems, evolutionary algorithms demonstrate strong flexibility and global search capabilities. However, as the number of UAVs increases, the scale of the path planning problem grows exponentially, leading to a significant rise in computational complexity. The Cooperative Co-Evolutionary Algorithm (CCEA) effectively addresses this issue through its divide-and-conquer strategy. Nonetheless, the CCEA needs to find a balance between computational efficiency and algorithmic performance while also resolving convergence difficulties arising from the increased number of decision variables. Moreover, the complex interrelationships between the decision variables of each UAV add to the challenge of selecting appropriate decision variables. To tackle this problem, we propose a novel collaborative algorithm called CCEA-ADVS. This algorithm reduces the difficulty of the problem by decomposing high-dimensional variables into sub-variables for collaborative optimization. To improve the efficiency of decision variable selection in the collaborative algorithm and to accelerate the convergence speed, an adaptive decision variable selection strategy is introduced. This strategy selects decision variables according to the order of solving single-UAV constraints and multi-UAV constraints, reducing the cost of the optimization objective. Furthermore, to improve computational efficiency, a two-stage evolutionary optimization process from coarse to fine is adopted.Specifically, the Adaptive Differential Evolution with Optional External Archive algorithm (JADE) is first used to optimize the waypoints of the UAVs to generate a basic path, and then, the Dubins algorithm is combined to optimize the trajectory, yielding the final flight path. The experimental results show that in four different scenarios involving 40 UAVs, the CCEA-ADVS algorithm significantly outperforms the Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and JADE algorithms in terms of path performance, running time, computational efficiency, and convergence speed. In addition, in large-scale experiments involving 500 UAVs, the algorithm also demonstrates good adaptability, stability, and scalability.

Proximal evolutionary strategy: improving deep reinforcement learning through evolutionary policy optimization

Evolutionary Algorithms (EAs), including Evolutionary Strategies (ES) and Genetic Algorithms (GAs), have been widely accepted as competitive alternatives to Policy Gradient techniques for Deep Reinforcement Learning (DRL). However, they remain eclipsed by cutting-edge DRL algorithms in terms of time efficiency, sample complexity, and learning effectiveness. In this paper, aiming at advancing evolutionary DRL research, we develop an evolutionary policy optimization algorithm with three key technical improvements. First, we design an efficient layer-wise strategy for training DNNs through Covariance Matrix Adaptation Evolutionary Strategies (CMA-ES) in a highly scalable manner. Second, we establish a surrogate model based on proximal performance lower bound for fitness evaluations with low sample complexity. Third, we embed a gradient-based local search technique within the evolutionary policy optimization process to further improve the learning effectiveness. The three technical innovations jointly forge a new EA for DRL method named Proximal Evolutionary Strategies (PES). Our experiments on ten continuous control problems show that PES with layer-wise training can be more computationally efficient than CMA-ES; our surrogate model can remarkably reduce the sample complexity of PES in comparison to latest EAs for DRL including CMA-ES, OpenAI-ES, and Uber-GA; PES with gradient-based local search can significantly outperform several promising DRL algorithms including TRPO, AKCTR, PPO, OpenAI-ES, and Uber-GA.

Semi-supervised soft sensor development based on dynamic dimensionality reduction-assisted large-scale pseudo label optimization and sample-weighted quality-relevant deep learning

Data-driven soft sensors have become popular tools for estimating critical quality variables in the process industry. However, in practical applications, it is very common that the unlabeled data are abundant but the labeled data are scarce, which poses a great challenge for developing high-performance data-based soft sensors. Thus, a dynamic dimensionality reduction-assisted large-scale pseudo label optimization method (DDR-LSPLO) is proposed for achieving sample expansion. This method repeatedly converts the LSPLO issue into a reduced-dimension pseudo label optimization problem with the low-confidence pseudo labels as new decision variables during the evolutionary optimization process. Meanwhile, to tackle the sample imbalance problem resulting from the inclusion of large-scale pseudo-labeled samples, a sample expansion and weighting-based quality-relevant autoencoder (SEWQAE) is developed for semi-supervised soft sensor modeling. The effectiveness and superiority of the proposed DDR-LSPLO and SEWQAE methods are verified through an industrial chlortetracycline (CTC) fermentation process and a simulated Tennessee Eastman (TE) chemical process.

Optimization of Uplift Piles for a Base Plate Considering Local Anti-Floating Stability

This paper focuses on the optimization of uplift piles for a base plate considering local anti-floating stability. According to the force characteristics of the base plate subjected to buoyancy, a bi-directional evolutionary structural optimization (BESO) process is proposed. The optimization process takes the pile length as the design variable and the pile end displacement as the sensitive coefficient. The proposed process is conducted with FLAC3D to optimize the length of each uplift pile, including two cases with different pile diameters and spacing. The optimization process shows that the deformation degree of the base plate is significantly reduced when the piles are adopted with large diameters and sparse spacing, and oscillates at a low level when the piles are adopted with small diameters and dense spacing. Consequently, the design method of uplift piles considering the local anti-floating stability is proposed by referring to the optimization results of two cases. Finally, the proposed design method is applied to a practical project, and the original design of the uplift piles is optimized. The comparison results show that the deformation degree of the base plate of optimization designs is significantly lower than the original design.

Ensemble of Domain Adaptation-Based Knowledge Transfer for Evolutionary Multitasking

Recently, a number of domain adaptation methods have been proposed for knowledge transfer in evolutionary multitasking (EMT). However, the learnt mappings in these methods often have unique biases in representing the connection between source and target tasks. Few studies have paid attention to the complementarity of different mappings in knowledge transfer. To fill this research gap, this paper proposes an ensemble method to combine multiple domain adaptation methods for knowledge transfer in EMT by considering the efficacy and diversity of these methods. First, a hierarchical clustering method is used to divide the population of each task into multiple clusters. Then, when two parental solutions are selected for knowledge transfer across tasks, the solutions within the same cluster are checked. In particular, if none of these solutions has been transferred before, the efficacy of domain adaptation methods is considered first by using roulette wheel selection based on the corresponding performance improvements in the evolutionary optimization process. Otherwise, the diversity of domain adaptation methods is emphasized by randomly selecting one of the domain adaptation methods for knowledge transfer. The effectiveness of our proposed ensemble method is validated by embedding it into existing state-of-the-art EMT algorithms, and the experimental results show that our algorithm outperforms several recently proposed EMT algorithms on most cases of two multitasking benchmark suites and one practical case.

(Photoredox) Organocatalysis in the Emergence of Life: Discovery, Applications, and Molecular Evolution.

ConspectusLife as we know it is built on complex and perfectly interlocking processes that have evolved over millions of years through evolutionary optimization processes. The emergence of life from nonliving matter and the evolution of such highly efficient systems therefore constitute an enormous synthetic and systems chemistry challenge. Advances in supramolecular and systems chemistry are opening new perspectives that provide insights into living and self-sustaining reaction networks as precursors for life. However, the ab initio synthesis of such a system requires the possibility of autonomous optimization of catalytic properties and, consequently, of an evolutionary system at the molecular level. In this Account, we present our discovery of the formation of substituted imidazolidine-4-thiones (photoredox) organocatalysts from simple prebiotic building blocks such as aldehydes and ketones under Strecker reaction conditions with ammonia and cyanides in the presence of hydrogen sulfide. The necessary aldehydes are formed from CO2 and hydrogen under prebiotically plausible meteoritic or volcanic iron-particle catalysis in the atmosphere of the early Earth. Remarkably, the investigated imidazolidine-4-thiones undergo spontaneous resolution by conglomerate crystallization, opening a pathway for symmetry breaking, chiral amplification, and enantioselective organocatalysis. These imidazolidine-4-thiones enable α-alkylations of aldehydes and ketones by photoredox organocatalysis. Therefore, these photoredox organocatalysts are able to modify their aldehyde building blocks, which leads in an evolutionary process to mutated second-generation and third-generation catalysts. In our experimental studies, we found that this mutation can occur not only by new formation of the imidazolidine core structure of the catalyst from modified aldehyde building blocks or by continuous supply from a pool of available building blocks but also by a dynamic exchange of the carbonyl moiety in ring position 2 of the imidazolidine moiety. Remarkably, it can be shown that by incorporating aldehyde building blocks from their environment, the imidazolidine-4-thiones are able to change and adapt to altering environmental conditions without undergoing the entire formation process. The selection of the mutated catalysts is then based on the different catalytic activities in the modification of the aldehyde building blocks and on the catalysis of subsequent processes that can lead to the formation of molecular reaction networks as progenitors for cellular processes. We were able to show that these imidazolidine-4-thiones not only enable α-alkylations but also facilitate other important transformations, such as the selective phosphorylation of nucleosides to nucleotides as a key step leading to the oligomerization to RNA and DNA. It can therefore be expected that evolutionary processes have already taken place on a small molecular level and have thus developed chemical tools that change over time, representing a hidden layer on the path to enzymatically catalyzed biochemical processes.

Evolutionary optimization processes for acoustic applications where size matters

In acoustics, the relevance of size, scale and shape of the structures involved in a problem often brings complications when it comes to find the best possible solution. Scenarios such as the design of a room or a sound diffuser are some of the problems that we can find in which shape and size are factors to consider. In recent years, computational optimization methods have been developed to bring a different approach to the solving of these problems. These methods, based on genetic algorithms, provides us with continuous modifications and combinations between the elements involved in a problem that can help us obtain solutions that would be almost impossible to find with regular analytic solving. Our goal is to develop a multi-objective genetic algorithm to optimize various parameters of a design problem, being one of them related to the physical size of the element under study. For this purpose, we will not treat the objects being optimized as individuals, but as groups of individuals with the same proportions but variable scale, called "concepts". With this method, we should obtain the optimum proportions for the problem faced, not only optimized individuals.

Batched Data-Driven Evolutionary Multiobjective Optimization Based on Manifold Interpolation

Multiobjective optimization problems are ubiquitous in real-world science, engineering, and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of nondominated tradeoff solutions, where the expensive objective functions are approximated as a surrogate model. In this article, we propose a framework for implementing batched data-driven evolutionary multiobjective optimization (EMO). It is so general that any off-the-shelf EMO algorithms can be applied in a plug-in manner. There are two unique components: 1) based on the Karush–Kuhn–Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set and 2) a batch recommendation approach that reduces the computational time of the data-driven evolutionary optimization process by evaluating multiple samples at a time in parallel. Comparing against seven state-of-the-art surrogate-assisted evolutionary algorithms, experiments on 168 benchmark test problem instances with various properties and a real-world application on hyper-parameter optimization fully demonstrate the effectiveness and superiority of our proposed framework, which is featured with a faster convergence and a stronger resilience to various Pareto-optimal front shapes.

Evolutionary neural network for learning of scalable heuristics for pickup and delivery problems with time windows

In this paper, we address the pickup and delivery problem with time windows (PDP-TW) and heterogenous vehicles for minimisation of total tardiness by learning heuristics from a given set of solutions. In order to extract scalable heuristics from optimal or best feasible solutions, we propose a machine-learning (ML)-based approach called ENSIGHT (Evolutionary Neural network with Scalable Information for Generation of Heuristics for Transportation). ENSIGHT consists of three phases: solution generation, interpretation of solutions, and improvement of heuristics by an evolutionary neural network (ENN). First, a set of optimal or best feasible solutions for the training set of problem instances is acquired by using the proposed mathematical model. Second, as for the process interpreting those solutions, an approach for transforming them into training data by way of scalable input attributes as well as output discretisation is followed. Third, the ENN improves the learned heuristics by an evolutionary parameter optimisation process for minimization of total tardiness. To verify the performance of the proposed ENSIGHT, we conducted experiments and the results of which showed that it outperforms other ML techniques and the current dispatching rules (DRs). Moreover, the approach was demonstrated to be effective in learning scalable heuristics based on combined scalable inputs and discretisation as well as an evolutionary improvement process.

Time-domain model and optimization for single-axis kinetic energy harvesters driven by arbitrary non-harmonic excitation

Energy harvesting is employed to extend the life of battery-powered devices, however, demanding applications such as wildlife tracking collars, the operating conditions impose size and weight constraints. They also only provide non-harmonic mechanical motion, which renders much of the existing literature inapplicable, which focuses on harvesting energy from harmonic mechanical sources. As a solution, we propose an energy harvesting architecture that consists of variable number of evenly-spaced magnets, forming a fixed assembly that is free to move through a series of evenly-spaced coils, and is supported by a magnetic spring. We present an electromechanical model for this architecture, and evolutionary optimization process that finds the model parameters which describe the time-domain behaviour observed in ground truth measurements. The resulting model can predict the time-domain behaviour of the energy harvester for any configuration of the proposed architecture and for any mechanical excitation. We also propose an optimization process that, using the electromechanical model, optimizes the energy harvester configuration to maximize the power delivered to a resistive load. The resulting optimized harvester design is specific to the particular kind of non-harmonic mechanical excitation to which it will be exposed. To demonstrate the effectiveness of our proposed model and optimization procedure, we constructed four energy harvesters, each with different configurations, and compared their measured behaviour with that predicted by the model, given an excitation that approximates footstep-like motion. We show that the model predictions were consistently within 25% of the RMS load voltage. We then synthesize an optimal energy harvester using the proposed optimization process. The resulting optimal design was constructed and tested using the same footstep-like excitation, and delivered an average power of 1.526 mW to a 30Ωload. This is a 2.8-fold improvement over an unoptimized reference design. We conclude that our proposed behavioural model and optimization process allows the determination of energy harvester designs that are optimized for a non-harmonic and specific input excitation.

RAILS: A Robust Adversarial Immune-Inspired Learning System

Adversarial attacks against deep neural networks (DNNs) are continuously evolving, requiring increasingly powerful defense strategies. We develop a novel adversarial defense framework inspired by the adaptive immune system: the Robust Adversarial Immune-inspired Learning System (RAILS). Initializing a population of exemplars that is balanced across classes, RAILS starts from a uniform label distribution that encourages diversity and uses an evolutionary optimization process to adaptively adjust the predictive label distribution in a manner that emulates the way the natural immune system recognizes novel pathogens. RAILS’ evolutionary optimization process explicitly captures the tradeoff between robustness (diversity) and accuracy (specificity) of the network, and represents a new immune-inspired perspective on adversarial learning. The benefits of RAILS are empirically demonstrated under eight types of adversarial attacks on a DNN adversarial image classifier for several benchmark datasets, including: MNIST; SVHN; CIFAR-10; and CIFAR-10. We find that PGD is the most damaging attack strategy and that for this attack RAILS is significantly more robust than other methods, achieving improvements in adversarial robustness by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\geq 5.62\%, 12.5\%$ </tex-math></inline-formula> , 10.32%, and 8.39%, on these respective datasets, without appreciable loss of classification accuracy. Codes for the results in this paper are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/wangren09/RAILS</uri> .

Integrated multi-objective evolutionary optimization of production layout scenarios for parametric structural design of flexible industrial buildings

Due to product individualization, customization and rapid technological advances in manufacturing, production systems are faced with frequent reconfiguration and expansion. Industrial buildings that allow changing production scenarios require flexible load-bearing structures and a coherent planning of the production layout and building systems. Yet, current production planning and structural building design are mostly sequential and the data and models lack interoperability. In this paper, a novel parametric evolutionary design method for automated production layout generation and optimization (PLGO) is presented, producing layout scenarios to be respected in structural building design. Results of a state-of-the-art analysis and a case study are combined to develop a novel concept of integrated production cubes and the design space for PLGO as basis for a parametric production layout design method. The integrated production cubes concept is then translated into a parametric PLGO framework, which is tested on a pilot-project of a hygiene production facility to evaluate the framework and validate the defined constraints and objectives. Results suggest that our framework can produce feasible production layout scenarios, which respect flexibility and building requirements. In future research the design process will be extended by the development of a multi-objective evolutionary optimization process for industrial buildings to provide flexible building solutions that can accommodate a selection of several prioritized production layouts.

Artificial Evolutionary Optimization Process to Improve the Functionality of Cell Penetrating Peptides.

Crossing cellular membranes is a versatile molecular property that allows for a wide variety of peptides with cell penetrating capabilities. This broadness complicates identification of candidates suited best for a specific application. To facilitate the screening of this enormous molecular space in a supervised manner we here present a method to "breed" the desired molecules by applying the rules of Darwinian evolution. With this mate-and-check protocol, which combines an in silico evolution step with an in vitro performance test, cell penetrating peptides that are optimized for a specific task can be achieved in a few rounds of breeding. The procedure is simple and straightforward on the synthetic site but requires robust, highly reproducible and close-to-reality biological assays to yield realistic functional output. With this technology even top-performing peptides can be further improved and functionally adjusted.

Coarse–fine surrogate model driven multiobjective evolutionary fuzzy clustering algorithm with dual memberships for noisy image segmentation

To improve the segmentation performance and boost evolutionary efficiency of multiobjective evolutionary clustering algorithms on noisy images, this paper proposes a coarse–fine surrogate model driven multiobjective evolutionary fuzzy clustering algorithm with dual membership functions (CFS-MOEFC). The existing fuzzy clustering validity-based fitness functions generally consider one single fuzzy membership function, which cannot fully process the uncertainty in an image. Moreover, most existing fitness functions used in image segmentation only utilize one type of spatial information derived from the image, which cannot behave robust on images with uncertain types of noise. To deal with the above problems, dual fuzzy membership functions are first designed by utilizing the local and non-local image spatial information. Then, the designed dual membership functions and the two kinds of spatial information are both used to construct spatial information-motivated fitness functions for image segmentation. To promote the time efficiency, the coarse–fine surrogate model is employed to assist the evolutionary optimization process, such as approximating the fitness functions instead of real function evaluations and evolving satisfactory cluster centers for CFS-MOEFC. Besides, a dual memberships-driven cluster validity index combining the local and non-local spatial information is designed for selecting an optimal solution from the final non-dominated solution set of CFS-MOEFC. Experiments on Berkeley and Magnetic Resonance (MR) images indicate that CFS-MOEFC greatly improves the segmentation accuracy on images with multiple types of noise, preserves more significant detailed image information, and behaves well on time cost comparing with state-of-the-art methods.

Productive fitness in diversity-aware evolutionary algorithms

In evolutionary algorithms, the notion of diversity has been adopted from biology and is used to describe the distribution of a population of solution candidates. While it has been known that maintaining a reasonable amount of diversity often benefits the overall result of the evolutionary optimization process by adjusting the exploration/exploitation trade-off, little has been known about what diversity is optimal. We introduce the notion of productive fitness based on the effect that a specific solution candidate has some generations down the evolutionary path. We derive the notion of final productive fitness, which is the ideal target fitness for any evolutionary process. Although it is inefficient to compute, we show empirically that it allows for an a posteriori analysis of how well a given evolutionary optimization process hit the ideal exploration/exploitation trade-off, providing insight into why diversity-aware evolutionary optimization often performs better.

Development of ensemble learning classification with density peak decomposition-based evolutionary multi-objective optimization

The ensemble learning methods have always been paid attention to their successful performance in handling supervised classification problems. Nevertheless, some deficiencies, such as inadequate diversity between classifiers and existing redundant classifiers, are among the main challenges in this kind of learning. In recent years, a method called density peak has been used in clustering methods to improve this process, which selects cluster centers from the local density peak. In this paper, inspiring this matter, and using the density peak criterion, a new method is proposed to create parallel ensembles. This criterion creates diverse training sets resulting in the generation of diverse classifiers. In the proposed method, during a multi-objective evolutionary decomposition-based optimization process, some (near) optimum diverse training datasets are created to improve the performance of the non-sequential ensemble learning methods. To do so, in addition to density peak as the first objective, the accuracy criterion is used as the second objective function. To show the superiority of the proposed method, it has been compared with the state-of-the-art methods over 19 datasets. To conduct a better comparison, non-parametric statistical tests are used, where the obtained results demonstrate that the proposed method can significantly dominate the other employed methods.

Automatic mesh-free boundary analysis: Multi-objective optimization

The paper is concerned with the numerical solution of two-dimensional potential problems, through a mesh-free boundary model in a multi-objective optimization framework that automatically generates Pareto-optimal mesh-free discretization arrangements. This robust new strategy of analysis allows for simultaneously improving the solution accuracy, the conditioning of the numerical solver, the stability and efficiency of the mesh-free analysis.The boundary mesh-free model (BMFM) is built on the boundary integral equation of the Laplace potential, with a moving least squares (MLS) approximation of variables. The model considers independent MLS approximations in each boundary segment and performs integration with standard numerical quadrature.The main novelty of the paper is the automatic generation of Pareto-optimal nodal arrangements and corresponding compact supports of the mesh-free boundary model, by means of an evolutionary multi-objective optimization process, based on genetic algorithms, which uses reliable very efficient objective functions.A benchmark problem is presented to assess the accuracy and efficiency of the modeling strategy. The remarkably accurate results obtained, in perfect agreement with those of analytical solutions, make very reliable this robust new strategy of automatic mesh-free boundary analysis in a multi-objective optimization framework.

Adaptive Range Composite Differential Evolution for Fast Optimal Reactive Power Dispatch

This paper proposes a novel adaptive range composite differential evolution (ARCoDE) algorithm to efficiently and accurately solve optimal reactive power dispatch (ORPD) problem. Because of a novel adaptive range strategy for control parameters, the proposed ARCoDE possesses superior exploration and exploitation capabilities that can efficiently handle the ORPD problem involving complicated constraints and discrete and continuous variables. This has been demonstrated in case studies using the IEEE optimal power flow testbeds considering complex wind and demand scenarios. The superior performance of ARCoDE has been further validated through comparisons with several award-winning algorithms in 2014 IEEE Competition on “Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems”, given limited iterations of in evolutionary optimization process.

Multi-objective Optimization of Combined Economic Emission Dispatch Problem in Solar PV Energy Using Hybrid Bat-Crow Search Algorithm

The current paper deals with multi-objective fuel cost optimization of a conventional power plant (CPP) and emission minimization in CPPs and Solar PV Power Plants (SPVPPs) using hybrid Bat-Crow search algorithm. To resolve this complicated, non-convex, and excessively nonlinear problem, a variety of meta-heuristic optimization algorithms are developed and effectively employed. To handle the evolutionary multi-objective algorithms’ inadequacies like early convergences, slowly meeting Pareto-optimal front, and narrow trapping, generally applying a combination of different algorithms is unusual. This paper presents the hybrid evolutionary multi-objective optimization process, which is based on combining the Crow search optimization with the Bat algorithm for dealing with the combined economic emission dispatch (CEED) through SPVPP. A hybrid technique combined with the proposed constriction handling method can balance out exploitation and exploration tasks. Different IEEE standard bus systems were tested with the proposed hybrid method using the quadratic cost function and monitoring the transmission losses. The result of proposed algorithm is compared with Bat, PSO and Crow Search Algorithm. The proposed method can be effective with the simulation results.