Evolutionary Global Optimization Research Articles

Soft-Finite-Element-Method-Driven Multiphysics Airfoil Optimization

The soft finite element method (SoftFEM) was recently developed as an efficient black-box engineering optimization framework combining population-based evolutionary global optimization and a local search technique using a hybrid self-adaptive strategy. This framework simultaneously leverages exploration and exploitation without the need to know a priori which strategy is best fitted to the problem at hand. In this work, we first improve SoftFEM by replacing the original differential evolution by the so-called success-history-based adaptive differential evolution. The developed framework is then applied to optimize the aerodynamic performance of 1) an airfoil, 2) a wing, and 3) the fluid–structure interaction problem of an airfoil with a flexible trailing edge. In the first two cases, the open-source computational fluid dynamics code OpenFOAM is considered to evaluate the aerodynamic characteristics of the airfoil, while in the latter case, we combine OpenFOAM and MuPhiSim—our recently released open-source code for computational solids mechanics—to conduct fluid–structure interaction simulations. The results demonstrate that this approach can effectively find optimal solutions with improved aerodynamic performance in all three cases. The proposed framework has the potential to significantly impact the design and optimization of aerodynamic systems in complex design spaces. In particular, new systems involving soft components and soft–hard junctions would benefit from a seamless application of the developed framework to their optimization.

Homotopic quantum fuzzy adaptive simulated annealing [HQF ASA

The work proposes a new approach for evolutionary global optimization which, in simple terms, may be described as a fusion of quantum and simulated annealing. This becomes possible by using basic concepts from Homotopy Theory, conjugated to the already existing Fuzzy Adaptive Simulated Annealing paradigm and other components. In this fashion, it occurs a temporal and nonlinear superposition of the two types of annealing, provoking interesting effects in runtime, including the so-called quantum tunneling, when there is a sudden transition between attraction basins of different minima without “climbing” potential barriers. In addition, the proposal includes a generalization of the “deformation” of Hamiltonians used in quantum annealing by suggesting the use of general homotopies between the surface corresponding to the cost function under processing and another specific landscape, being this possible because of the ability of Fuzzy ASA of handling time-varying objective functions. The proposed paradigm shows that it is possible and beneficial to superpose the two types of annealing, displaying amazing numerical results and suggesting a kind of interlacing or synergic behavior - perhaps we could call it an “annealing entanglement”. Finally, given the fast advances in commercial quantum annealing processors, it seems sensible to expect that an implementation of the proposed approach using such devices may occur very soon. In order to demonstrate the efficacy of the proposed algorithm, some significant and detailed examples are included in the text, so as to illustrate and clarify the presented ideas.

An Individual Evolutionary Game Model Guided by Global Evolutionary Optimization for Vehicle Energy Station Distribution

Collective decision-making problems consisting of individual decisions are commonly seen in social applications. In this article, the vehicle energy station distribution problem (VESDP) is considered, which is modeled as a network-based collective decision-making problem fulfilling consumers’ requirements by arranging the distribution of energy stations rationally. This problem involves the game among the government and energy station investors. The government intends to maximize the satisfaction of both gas and electric vehicle (EV) customers through policy guidance, while investors aim to maximize their own profits. To solve this problem, we propose an individual evolutionary game model guided by global evolutionary optimization with the following three features. From the individual perspective, we use a network-based evolutionary game with a confidence mechanism to describe the behavior of investors. From the global perspective, we design a genetic algorithm to find out the global-optimized program, which considers the satisfaction of all customers. To heal the divergence between these two perspectives, we design a policy formulation method for the government to motivate selfish investors to adopt strategies in accordance with the overall interests of all customers by using subsidies and taxation. Experiments are performed on both square grid and real-world networks. Experimental results demonstrate the effectiveness of the proposed model.

Lithiation of phosphorus at the nanoscale: a computational study of LinPm clusters.

Systematic structure prediction of LinPm nanoclusters was performed for a wide range of compositions (0 ≤ n ≤ 10, 0 ≤ m ≤ 20) using the evolutionary global optimization algorithm USPEX coupled with density functional calculations. With increasing Li concentration, the number of P-P bonds in the cluster reduces and the phosphorus backbone undergoes the following transformations: elongated tubular → multi-fragment (with mainly P5 rings and P7 cages) → cyclic topology → branched topology → P-P dumbbells → isolated P ions. By applying several stability criteria, we determined the most favorable LinPm clusters and found that they are located in the compositional area between m ≈ n/3 and m ≈ n/3 + 6. For instance, the Li3P7 cluster has the highest stability and is known to be the structural basis of the corresponding bulk crystal. The obtained results provide valuable insights into the lithiation mechanism of nanoscale phosphorus which is of interest for development of novel phosphorus-based anode materials.

Topologically assisted optimization for rotor design

We develop and apply a novel shape optimization exemplified for a two-blade rotor with respect to the figure of merit. This topologically assisted optimization contains two steps. First, a global evolutionary optimization is performed for the shape parameters, and then a topological analysis reveals the local and global extrema of the objective function directly from the data. This non-dimensional objective function compares the achieved thrust with the required torque. Rotor blades have a decisive contribution to the performance of quadcopters. A two-blade rotor with pre-defined chord length distribution is chosen as the baseline model. The simulation is performed in a moving reference frame with a k−ω turbulence model for the hovering condition. The rotor shape is parameterized by the twist angle distribution. The optimization of this distribution employs a genetic algorithm. The local maxima are distilled from the data using a novel topological analysis inspired by discrete scalar-field topology. We identify one global maximum to be located in the interior of the data and five further local maxima related to errors from non-converged simulations. The interior location of the global optimum suggests that small improvements can be gained from further optimization. The local maxima have a small persistence, i.e., disappear under a small ε perturbation of the figure of merit values. In other words, the data may be approximated by a smooth mono-modal surrogate model. Thus, the topological data analysis provides valuable insight for optimization and surrogate modeling.

Determining Lennard-Jones Parameters Using Multiscale Target Data through Presampling-Enhanced, Surrogate-Assisted Global Optimization.

Force field-based models are a Newtonian mechanics approximation of reality and are inherently noisy. Coupling models from different molecular scale domains (including single, gas-phase molecules up to multimolecule, condensed phase ensembles) is difficult, which is also the case for finding solutions that transfer well between the scales. In this contribution, we introduce a surrogate-assisted algorithm to optimize Lennard-Jones parameters for target data from different scale domains to overcome the difficulties named above. Specifically, our approach combines a surrogate-assisted global evolutionary optimization method with a presampling phase that takes advantage of one scale domain being less computationally expensive to evaluate. The algorithm's components were evaluated individually, elucidating their individual merits. Our findings show that the process of parametrizing force fields can significantly benefit from both the presampling method, which alleviates the need to have a good initial guess for the parameters, and the surrogate model, which improves efficiency.

Robust Tuning of Multiresonant Current Controllers for Grid-Tied Converters and Erroneous Use of the Naslin Polynomial Method

The majority of the paper is devoted to debunking flawed methods proposed in the literature within the context of multiresonant control systems for grid-connected converters and then a novel approach is proposed. Several flawed approaches to grid tied power electronic converters (rectifiers and shunt active power filters) are discussed to initiate a critical discussion regarding some tuning methods reported in the topical literature. In this paper we analytically show that some of them are even erroneous from the control theory point of view or are based on mathematically erroneous derivations. That is especially prevalent for papers in which the Naslin polynomial method is employed to tune proportional-multiresonant controllers. Some authors recognize that the resulting control systems are not robust, i.e. not practical, and use obtained gains only as a starting point for further tuning using the trial and error method or evolutionary global optimization. Robustness of such systems is often not guaranteed and if it occurs at all, it is by chance or thanks to a combination of luck and expert knowledge of the engineer (not by deliberate design). Therefore, the absence of such a guarantee motivates the search for better ways to tune such controllers. As a result, a practical robust controller tuning method for multiresonant grid current controllers is proposed and verified experimentally. We are convinced that one of the solutions can be based on the disk margin stability analysis and a global search algorithm. The required robustness is expressed as stability margins. The design procedure is very user-friendly and the disk size is the key design parameter to be selected by an engineer. The practicality of the tuning method is demonstrated empirically in a 10 kVA physical grid-tied converter.

Balancing Exploration and Exploitation with Decomposition-Based Dynamic Multi-objective Evolutionary Algorithm

Balancing exploration and exploitation is a crucial issue in evolutionary global optimization. This paper proposes a decomposition-based dynamic multi-objective evolutionary algorithm for addressing global optimization problems. In the proposed method, the niche count function is regarded as a helper objective to maintain the population diversity, which converts a global optimization problem to a multi-objective optimization problem (MOP). The niche-count value is controlled by the niche radius. In the early stage of evolution, a large niche radius promotes the population diversity for better exploration; in the later stage of evolution, a niche radius close to 0 focuses on convergence for better exploitation. Through the whole evolution process, the niche radius is dynamically decreased from a large value to zero, which can provide a sound balance between the exploration and exploitation. Experimental results on CEC 2014 benchmark problems reveal that the proposed algorithm is capable of offering high-quality solutions, in comparison with four state-of-the-art algorithms.

Balancing Exploration and Exploitation With Decomposition-Based Dynamic Multi-Objective Evolutionary Algorithm

Balancing exploration and exploitation is a crucial issue in evolutionary global optimization. This paper proposes a decomposition-based dynamic multi-objective evolutionary algorithm for addressing global optimization problems. In the proposed method, the niche count function is regarded as a helper objective to maintain the population diversity, which converts a global optimization problem to a multi-objective optimization problem (MOP). The niche-count value is controlled by the niche radius. In the early stage of evolution, a large niche radius promotes the population diversity for better exploration; in the later stage of evolution, a niche radius close to 0 focuses on convergence for better exploitation. Through the whole evolution process, the niche radius is dynamically decreased from a large value to zero, which can provide a sound balance between the exploration and exploitation. Experimental results on CEC 2014 benchmark problems reveal that the proposed algorithm is capable of offering high-quality solutions, in comparison with four state-of-the-art algorithms.

Inverse design of metasurfaces with non-local interactions

Conventional metasurfaces have demonstrated efficient wavefront manipulation by using thick and high-aspect-ratio nanostructures in order to eliminate interactions between adjacent phase-shifter elements. Thinner-than-wavelength dielectric metasurfaces are highly desirable because they can facilitate fabrication and integration with both electronics and mechanically tunable platforms. Unfortunately, because their constitutive phase-shifter elements exhibit strong electromagnetic coupling between neighbors, the design requires a global optimization methodology that considers the non-local interactions. Here, we propose a global evolutionary optimization approach to inverse design non-local metasurfaces. The optimal designs are experimentally validated, demonstrating the highest efficiencies for the thinnest transmissive metalenses reported to-date for visible light. In a departure from conventional design methods based on the search of a library of pre-determined and independent meta-atoms, we take full advantage of the strong interactions among nanoresonators to improve the focusing efficiency of metalenses and demonstrate that efficiency improvements can be obtained by lowering the metasurface filling factors.

CFM-BD: A Distributed Rule Induction Algorithm for Building Compact Fuzzy Models in Big Data Classification Problems

Interpretability has always been a major concern for fuzzy rule-based classifiers. The usage of human-readable models allows them to explain the reasoning behind their predictions and decisions. However, when it comes to Big Data classification problems, fuzzy rule-based classifiers have not been able to maintain the good trade-off between accuracy and interpretability that has characterized these techniques in non-Big Data environments. The most accurate methods build too complex models composed of a large number of rules and fuzzy sets, while those approaches focusing on interpretability do not provide state-of-the-art discrimination capabilities. In this paper, we propose a new distributed learning algorithm named CFM-BD to construct accurate and compact fuzzy rule-based classification systems for Big Data. This method has been specifically designed from scratch for Big Data problems and does not adapt or extend any existing algorithm. The proposed learning process consists of three stages: 1) pre-processing based on the probability integral transform theorem; 2) rule induction inspired by CHI-BD and Apriori algorithms; 3) rule selection by means of a global evolutionary optimization. We conducted a complete empirical study to test the performance of our approach in terms of accuracy, complexity, and runtime. The results obtained were compared and contrasted with four state-of-the-art fuzzy classifiers for Big Data (FBDT, FMDT, Chi-Spark-RS, and CHI-BD). According to this study, CFM-BD is able to provide competitive discrimination capabilities using significantly simpler models composed of a few rules of less than 3 antecedents, employing 5 linguistic labels for all variables.

Atomic Energies from a Convolutional Neural Network

Understanding interactions and structural properties at the atomic level is often a prerequisite to the design of novel materials. Theoretical studies based on quantum-mechanical first-principles calculations can provide this knowledge but at an immense computational cost. In recent years, machine learning has been successful in predicting structural properties at a much lower cost. Here we propose a simplified structure descriptor with no empirical parameters, "k-Bags", together with a scalable and comprehensive machine learning framework that can deepen our understanding of atomic properties of structures. This model can readily predict structure-energy relations that can provide results close to the accuracy of ab initio methods. The model provides chemically meaningful atomic energies enabling theoretical analysis of organic and inorganic molecular structures. Utilization of the local information provided by the atomic energies significantly improves upon the stochastic steps in our evolutionary global structure optimization, resulting in a much faster global minimum search of molecules, clusters, and surfaced supported species.

A Bi-Level Evolutionary Optimization for Coordinated Transmission Expansion Planning

In this paper, a real-life application of bi-level evolutionary optimization is proposed to optimize the electricity industry infrastructure. It offers a coordinated generation and transmission expansion planning (CGTEP) from the perspective of an independent system operator (ISO). The main objective of the proposed study is to show the effect of optimizing the generators concerning capacity and location both to reduce the transmission investment and increasing the reliability of the network. The proposed framework of bi-level optimization contributes to utilize global evolutionary optimization method GA in its hybrid form in level-I to select the location of lines and energy generators. The respective capacities of the corresponding selected lines and generators are optimized in the level-II by RW. In conflicting objectives of minimizing the investment for capacity addition in the network and maximizing the reliability, a Pareto-optimal solution is achieved by using the theory of marginal value (TMV). To satisfy TMV, the total cost is minimized, which comprises the cost of investment in building new transmission and generation capacities, cost of not-served expected energy, cost of unutilized expected generation, and cost of unserved energy due to the constrained network. Proposed methodology on IEEE 24-bus power system is presented encountering the combination of N-1 and probable N-2 contingency security criteria. The comparison results show that bi-level GA-RW optimization minimizes the investment with increasing power system reliability.

Structure and Stability of Hydrolysis Reaction Products of MgO Nanoparticles Leading to the Formation of Brucite

The bottom-up formation of MgxOy(OH)z nanoparticles leading to Mg(OH)2 nanoparticles was modeled in two steps by using an evolutionary global optimization approach: (1) the formation of small MgnOm+nH2m clusters via the hydrolysis of (MgO)n and (2) the formation of multilayered (Mg(OH)2)n clusters via monolayer stacking. The sheet-like (Mg(OH)2)n structures were predicted as the energetically favorable reaction products for the (MgO)n + nH2O reaction, whereas more compact structures were found to dominate for the products of (MgO)n + mH2O, m < n. The stepwise hydrolysis reactions most likely follow the compact reaction path until the crossover point is reached. Multistep structural rearrangements are required for the conversion between the compact products and the sheet-like products even after the crossover point. The protective shell formed by the hydroxyl groups may inhibit the further hydrolysis reaction of the compact products, even though the hydrolysis reactions are both exothermic and exergonic; s...

An enhanced artificial neural network with a shuffled complex evolutionary global optimization with principal component analysis

The classical Back-Propagation (BP) scheme with gradient-based optimization in training Artificial Neural Networks (ANNs) suffers from many drawbacks, such as the premature convergence, and the tendency of being trapped in local optimums. Therefore, as an alternative for the BP and gradient-based optimization schemes, various Evolutionary Algorithms (EAs), i.e., Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Simulated Annealing (SA), and Differential Evolution (DE), have gained popularity in the field of ANN weight training. This study applied a new efficient and effective Shuffled Complex Evolutionary Global Optimization Algorithm with Principal Component Analysis – University of California Irvine (SP-UCI) to the weight training process of a three-layer feed-forward ANN. A large-scale numerical comparison is conducted among the SP-UCI-, PSO-, GA-, SA-, and DE-based ANNs on 17 benchmark, complex, and real-world datasets. Results show that SP-UCI-based ANN outperforms other EA-based ANNs in the context of convergence and generalization. Results suggest that the SP-UCI algorithm possesses good potential in support of the weight training of ANN in real-word problems. In addition, the suitability of different kinds of EAs on training ANN is discussed. The large-scale comparison experiments conducted in this paper are fundamental references for selecting proper ANN weight training algorithms in practice.

Problem features vs. algorithm performance on rugged multi-objective combinatorial fitness landscapes

In this paper, we attempt to understand and to contrast the impact of performance of randomized search heuristics for black-box multiobjective combinatorial optimization problems. At first, we measure the performance of two conventional dominance-based approaches with unbounded archive on a benchmark of enumerable binary optimization problems with tunable ruggedness, objective space dimension, and objective correlation (ρMNK-landscapes). Precisely, we investigate the expected runtime required by a global evolutionary optimization algorithm with an ergodic variation operator (GSEMO) and by a neighborhood-based local search heuristic (PLS), to identify a -approximation of the Pareto set. Then, we define a number of problem features characterizing the fitness landscape, and we study their intercorrelation and their association with algorithm runtime on the benchmark instances. At last, with a mixed-effects multi-linear regression we assess the individual and joint effect of problem features on the performance of both algorithms, within and across the instance classes defined by benchmark parameters. Our analysis reveals further insights into the importance of ruggedness and multi-modality to characterize instance hardness for this family of multi-objective optimization problems and algorithms.

Slobodno evoluciono i gradijentno opadajuće usklađivanje fazi particija kod dinamičkog modeliranja bespilotnih letelica

In this paper, a novel fuzzy identification method for dynamic modelling of quadrotors UAV is presented. The method is based on a special parameterization of the antecedent part of fuzzy systems that results in fuzzy-partitions for antecedents. This antecedent parameter representation method of fuzzy rules ensures upholding of predefined linguistic value ordering and ensures that fuzzy-partitions remain intact throughout an unconstrained hybrid evolutionary and gradient descent based optimization process. In the equations of motion the first order derivative component is calculated based on Christoffel symbols, the derivatives of fuzzy systems are used for modelling the Coriolis effects, gyroscopic and centrifugal terms. The non-linear parameters are subjected to an initial global evolutionary optimization scheme and fine tuning with gradient descent based local search. Simulation results of the proposed new quadrotor dynamic model identification method are promising.

Problem Features versus Algorithm Performance on Rugged Multiobjective Combinatorial Fitness Landscapes.

In this article, we attempt to understand and to contrast the impact of problem features on the performance of randomized search heuristics for black-box multiobjective combinatorial optimization problems. At first, we measure the performance of two conventional dominance-based approaches with unbounded archive on a benchmark of enumerable binary optimization problems with tunable ruggedness, objective space dimension, and objective correlation ([Formula: see text]MNK-landscapes). Precisely, we investigate the expected runtime required by a global evolutionary optimization algorithm with an ergodic variation operator (GSEMO) and by a neighborhood-based local search heuristic (PLS), to identify a ([Formula: see text]approximation of the Pareto set. Then, we define a number of problem features characterizing the fitness landscape, and we study their intercorrelation and their association with algorithm runtime on the benchmark instances. At last, with a mixed-effects multilinear regression we assess the individual and joint effect of problem features on the performance of both algorithms, within and across the instance classes defined by benchmark parameters. Our analysis reveals further insights into the importance of ruggedness and multimodality to characterize instance hardness for this family of multiobjective optimization problems and algorithms.

Brillouin distributed temperature sensor employing phase modulation and optimization techniques

The process of signal-to-noise ratio (SNR) improvement and the suppression of stimulated Brillouin scattering (SBS) effects on a long-range distributed sensor are presented in this paper. We have proposed an improved performance Brillouin distributed temperature sensor using phase modulation and optimization techniques. Global evolutionary computing-based optimization techniques (genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution algorithm (DE)) are applied for both fiber and receiver optimization. The combination of phase modulation and the global evolutionary computing technique improved the SBS threshold power of the proposed system to an extent of 5.95dBm. However, with receiver and fiber optimization, for an input power of 0dBm, the proposed system provides SNR improvement up to 3.5dB, for temperature sensing over a distance of 50km with temperature resolution of 1.44K and spatial resolution of 32m without using filter. However, for the equivalent sensing range, we have achieved a temperature resolution as 0.51K using the above optimized system with filter.

An efficient approach for solving the HP protein folding problem based on UEGO

This work applies the methodology of the Universal Evolutionary Global Optimization, UEGO, to solve the protein structure optimization problem based on the HP model. The UEGO algorithm was initially designed to solve problems whose solutions were codified as real vectors. However, in this work the HP protein folding solutions have been defined as means of conformations encoded by relative coordinates. Consequently several main concepts in UEGO have been re-defined, i.e. the representation of a solution, the distance concept, the computation of a middle point, etc. In addition, a new efficient local optimizer has been designed based on the characteristics of the protein model. This work develops the adaptation and implementation of UEGO to the HP model and analyzes the UEGO solutions of HP protein folding for different 3D problems. Finally, obtained HP solutions are converted into all-atom models so that comparison with real proteins can be carried out, and a good agreement is obtained for small size proteins.