Evolutionary Optimization Procedure Research Articles

The Basics of Evolution Strategies: The Implementation of the Biomimetic Optimization Method in Educational Modules.

With a focus on education and teaching, we provide general background information on bioinspired optimization methods by comparing the concept of optimization and the search for an optimum in engineering and biology. We introduce both the principles of Darwinian evolution and the basic evolutionary optimization procedure of evolution strategies. We provide three educational modules in work sheets that can be used by teachers and students to improve their understanding of evolution strategies. The educational module "Optimization of a Milk Carton" shows that the material consumption in producing a milk carton can be minimized using an evolution strategy with a mutative step size control. The use of a standard dice and a pocket calculator enables new milk cartons to be generated, with the offspring having the lowest material consumption becoming the parent of the next generation. The other educational modules deal with the so-called brachistochrone problem. The module "Fastest and Shortest Marble Track" provides a construction plan for a marble track whereby students can experimentally compare the "path of shortest length" with the "path of shortest time". The EvoBrach software, is used in the module "Various Marble Track Shapes" to compare the running times of a marble on a straight line, a parabola, and a brachistochrone. In conclusion, the introduction to the biomimetic method of evolution strategies and the educational modules should deepen the understanding of both optimization problems and biological evolution.

An enhanced surrogate-assisted differential evolution for constrained optimization problems

The application of evolutionary algorithms (EAs) to complex engineering optimization problems may present difficulties as they require many evaluations of the objective functions by computationally expensive simulation procedures. To deal with this issue, surrogate models have been employed to replace those expensive simulations. In this work, a surrogate-assisted evolutionary optimization procedure is proposed. The procedure combines the differential evolution method with a $$k$$ -nearest neighbors (k-NN) similarity-based surrogate model. In this approach, the database that stores the solutions evaluated by the exact model, which are used to approximate new solutions, is managed according to a merit scheme. Constraints are handled by a rank-based technique that builds multiple separate queues based on the values of the objective function and the violation of each constraint. Also, to avoid premature convergence of the method, a strategy that triggers a random reinitialization of the population is considered. The performance of the proposed method is assessed by numerical experiments using 24 constrained benchmark functions and 5 mechanical engineering problems. The results show that the method achieves optimal solutions with a remarkably reduction in the number of function evaluations compared to the literature.

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive, aviation and construction industries. This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization (BESO). The conventional BESO is provided with constant evolutionary volume ratio (EVR), whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements. To address the issue, the modified BESO with variable EVR is introduced. To compromise the natural frequency and the dynamic stiffness, a weighting scheme of sensitivity numbers is employed to form the Pareto solution space. Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method. Most importantly, the dynamic removal strategy with the variable EVR sharply springs up the optimization process. Therefore, it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

Reliability-Based Topology Optimization: An Extension of the SESO and SERA Methods for Three-Dimensional Structures

This study takes an approach to reliability-based topology optimization (RBTO) for 3D structures by applying an expansion of smoothing evolutionary structural optimization (SESO) and sequential element rejection and admission (SERA) for three-dimensional optimization. In the search for the stable optimal solution, and a more reliable structure, we present a performance index with the ability to monitor the evolutionary optimization procedure and adopt the filtering scheme usually applied in solid isotropic material with penalization (SIMP). The limit state functions are the maximum displacement constraints imposed in the topology optimization procedure and a structure’s performance control; a comparative analysis of the deterministic topology optimization (DTO) with the RBTO models is also explored. The obtained results suggest the importance of using the RBTO concept in 3D structures as part of the design analysis process.

Development of method of decoding block codes based on differential evolution procedure

The approach of soft decoding of block codes based on determining the most reliable basis of the generator matrix and applying the differential evolution procedure is proposed. The choice of this search optimization procedure was made as a result of the analysis of the features and limitations of evolutionary optimization procedures. The scheme and the essence of the main stages of the developed method of soft decoding of block codes are presented. At the first stage, a hard decision is formed and the received word syndrome is calculated. After that, the received symbols are ranked by reliability and the generator matrix of the block code is transformed into the corresponding most reliable basis. Next, a differential evolution procedure is applied to search for the most probable transmitted information message and a binary codeword. Decoding is completed by inverse transformation of the found most probable binary codeword by rearranging the corresponding elements. It is shown that the key stage of decoding is the search for the transmitted codeword using the differential evolution procedure, and the formation of the most reliable basis of the generator matrix of block code makes it possible to increase the decoding efficiency. In order to be able to technically implement this decoding method, an appropriate algorithm has been developed and its main steps are given. The results of the work can be used for the implementation of new generation radio communication technologies to improve the reliability of the transmission of service messages. It is also recommended to use the obtained results when solving the problem of decoding other error-correcting code structures that are used in modern telecommunication technologies.

Design of Metasurface-Based Multi-layer THz Filters Utilizing Optimization Algorithm with Distinct Fitness Function Definitions

In this paper, an evolutionary optimization procedure is presented to generate band-pass metasurface-based filters in terahertz regime. As a measure of novelty, pass-band, transition, and out-band characteristics are investigated separately, all of which result in different metasurfaces for filtering applications. The presented approach is defined based on random hill climbing algorithm, regarding the established link between Matlab and HFSS software. A metasurface-based filter with specific properties is considered as the main problem to be solved by the optimization method. Moreover, the fuzzy theory, mean square method, and weighting coefficient procedure are considered to define an efficient fitness function evaluation approach. Also, a step-by-step procedure is used to generate desired structures with a great note of efficiency. The final generated structure has magnificent characteristics including sharp transitions together with transmittance around 0.68 and less than 0.04 at pass-band and out-band regions, respectively. Also, the generated metasurface benefits from wide bandwidth (65%) and great compactness compared to other previous works.

An Evolutionary-Optimized Surgical Path Planner for a Programmable Bevel-Tip Needle

Path planning algorithms for steerable needles in medical applications must guarantee the anatomical obstacle avoidance, reduce the insertion length, and ensure the compliance with the needle kinematics. The majority of the solutions from the literature focus either on fast computation or on path optimality, the former at the expense of suboptimal paths, the latter by making unbearable the computation in case of a high-dimensional workspace. In this article, we implement a three-dimensional path planner for neurosurgical applications, which keeps the computational cost consistent with standard preoperative planning algorithms and fine-tunes the estimated pathways in accordance to multiple optimization objectives. From a user-defined entry point, our method confines a sample-based path search within a subsection of the original workspace considering the degree of curvature admitted by the needle. An evolutionary optimization procedure is used to maximize the obstacle avoidance and reduce the insertion length. The pool of optimized solutions is examined through a cost function to determine the best path. Simulations on one dataset showed the ability of the planner to save time and overcome the state of the art in terms of obstacle avoidance, insertion length, and probability of failure, proving this algorithm as a valid planning method for complex environments.

Robust evolutionary shape optimization for ergonomic excellence based on contact pressure distribution

The aim of this paper is the development of a robust evolutionary shape optimization procedure for ergonomic excellence based on contact pressure distribution. FEM - based numerical analysis is implemented to obtain the resulting contact pressure distribution. An example of person-seat interaction is analysed in this paper since plenty of experimental data set exists on this topic. A simplified geometrical model of the human body and seat is used and partly parameterized using a generic B-spline surface. The impact of the changes in geometry on the pressure distribution is analysed by the optimizer, and the seat geometry is steered into a shape with minimal high contact pressure areas. The procedure is general and can be adapted (with changes in geometry and boundary conditions) to distinct ergonomic problems such as footwear, therapeutic beds, automotive or aeronautical seating. The developed procedure can aid in virtual testing during the seat development phase in cases when the seat is designed for a selected population or for a single person and expected postural variations.

A Three-Dimensional Statistical Volume Element for Histology Informed Micromechanical Modeling of Brain White Matter.

This study presents a novel statistical volume element (SVE) for micromechanical modeling of the white matter structures, with histology-informed randomized distribution of axonal tracts within the extracellular matrix. The model was constructed based on the probability distribution functions obtained from the results of diffusion tensor imaging as well as the histological observations of scanning electron micrograph, at two structures of white matter susceptible to traumatic brain injury, i.e. corpus callosum and corona radiata. A simplistic representative volume element (RVE) with symmetrical arrangement of fully alligned axonal fibers was also created as a reference for comparison. A parametric study was conducted to find the optimum grid and edge size which ensured the periodicity and ergodicity of the SVE and RVE models. A multi-objective evolutionary optimization procedure was used to find the hyperelastic and viscoelastic material constants of the constituents, based on the experimentally reported responses of corpus callosum to axonal and transverse loadings. The optimal material properties were then used to predict the homogenized and localized responses of corpus callosum and corona radiata. The results indicated similar homogenized responses of the SVE and RVE under quasi-static extension, which were in good agreement with the experimental data. Under shear strain, however, the models exhibited different behaviors, with the SVE model showing much closer response to the experimental observations. Moreover, the SVE model displayed a significantly better agreement with the reports of the experiments at high strain rates. The results suggest that the randomized fiber architecture has a great influence on the validity of the micromechanical models of white matter, with a distinguished impact on the model's response to shear deformation and high strain rates. Moreover, it can provide a more detailed presentation of the localized responses of the tissue substructures, including the stress concentrations around the low caliber axonal tracts, which is critical for studying the axonal injury mechanisms.

Crashworthiness topology optimization of thin-walled square tubes, using modified Bidirectional Evolutionary Structural Optimization approach

Abstract In this study, topology optimization of a thin-walled square tube subjected to an axial crushing load was carried out to enhance its crashworthiness performance, utilizing the modified Bidirectional Evolutionary Structural Optimization (BESO) procedure. In this way, by systematic searching, topology optimization finds the best material layout for the structure to satisfy the objective function. In each iteration, a new pattern of material-void through the tube walls can trigger various folding mechanisms. Thus, the energy absorption history trend might not be smooth and the ultimate pattern proposed by the algorithm is less likely to be the optimal one. With an emphasis on the BESO hypothesis regarding direct removal and addition of elements, the modified BESO algorithm excavated the optimal design in two steps. First, material-void patterns were produced, considering specific energy absorption as the element efficiency criterion. Then, the pattern with the least material usage which satisfies an energy absorption constraint was selected as the optimal design. Such an optimum layout also boosts the tube performance respecting peak crushing force, since the embedded voids through the structure serve as a crush initiator. The optimization code was developed in MATLAB, which was automatically integrated with ABAQUS software performing the nonlinear crushing analysis. To validate the finite element model, an experimental investigation was carried out on a simple square tube. Having performed the topology optimization and some fine-tuning process, the topologically optimized tube was constructed and experimentally tested. Results showed 16.21% weight reduction enriched with 36.57% enhancement in the peak crushing force by sacrificing less than 3.5% energy absorption, which represents substantial improvements from a crashworthiness viewpoint. The obtained interesting results showed the high potential of the BESO algorithm for the design of thin-walled structures under large deformation and out-of-plane buckling.

Optimizing optogenetic stimulation protocols in auditory corticofugal neurons based on closed-loop spike feedback

Objective. Optogenetics provides a means to probe functional connections between brain areas. By activating a set of presynaptic neurons and recording the activity from a downstream brain area, one can establish the sign and strength of a feedforward connection. One challenge is that there are virtually limitless patterns that can be used to stimulate a presynaptic brain area. Functional influences on downstream brain areas can depend not just on whether presynaptic neurons were activated, but how they were activated. Corticofugal axons from the auditory cortex (ACtx) heavily innervate the auditory tectum, the inferior colliculus (IC). Here, we sought to determine whether different modes of corticocollicular activation could titrate the strength of feedforward modulation of sound processing in IC neurons. Approach. We used multi-channel electrophysiology and optogenetics to record from multiple regions of the IC in awake head-fixed mice while optogenetically stimulating ACtx neurons expressing Chronos, an ultra-fast channelrhodopsin. To identify cortical activation patterns associated with the strongest effects on IC firing rates, we employed a closed-loop evolutionary optimization procedure that tailored the voltage command signal sent to the laser based on spike feedback from single IC neurons. Main results. Within minutes, our evolutionary search procedure converged on ACtx stimulation configurations that produced more effective and widespread enhancement of IC unit activity than generic activation parameters. Cortical modulation of midbrain spiking was bi-directional, as the evolutionary search procedure could be programmed to converge on activation patterns that either suppressed or enhanced sound-evoked IC firing rate. Significance. This study introduces a closed-loop optimization procedure to probe functional connections between brain areas. Our findings demonstrate that the influence of descending feedback projections on subcortical sensory processing can vary both in sign and degree depending on how cortical neurons are activated in time.

Crop yield simulation optimization using precision irrigation and subsurface water retention technology

Maximizing crop production with minimal resources such as water and energy is the primary focus of sustainable agriculture. Subsurface water retention technology (SWRT) is a stable approach that preserves water in sandy soils using water saving membranes. An optimal use of SWRT depends on its shape, location and other factors. In order to predict crop yield for different irrigation schedule, we require at least two computational processes: (i) a crop growth modeling process and (ii) a water and nutrient permeation process through soil to the root system. Validation of software parameters to suit properties of specific field becomes increasingly hard since they involve a coordination with field data and coordination between two software. In this paper, we propose a computationally fast approach that utilizes HYDRUS-2D software for water and nutrient flow simulation and DSSAT crop simulation software with an evolutionary multi-objective optimization (EMO) procedure in a coordinated manner to minimize water utilization and maximize crop yield prediction. Our proposed method consists of training one-dimensional crop model (DSSAT) on data generated by two dimensional model calibrates and validates (HYDRUS-2D), that accounts for water accumulation in the SWRT membranes. Then we used DSSAT model to find the best irrigation schedules for maximizing crop yield with the highest plant water use efficiency (Tambussi et al., 2007; Blum, 2009) using for the EMO methodology. The optimization procedure minimizes water usage with the help of rainfall water and increases corn yield prediction as much as six times compare to a non-optimized and random irrigation schedule without any SWRT membrane. Our framework also demonstrates an integration of latest computing software and hardware technologies synergistically to facilitate better crop production with minimal water requirement.

Application of evolutionary structural optimization based on the boundary element method using initial stress fields

This paper presents the application of the topological optimization in plane elasticity problems applying the boundary element method (BEM) coupled with the evolutionary structural optimization (ESO) procedure by using initial stress fields as the new strategy to create cavities in the topological optimization domain. In this approach, in the domain region, where must be removed in the heuristic process, a stress field is added that is equal to and of opposite sign in the initial elastic stress formulation resulting in null domain stresses. Thus, a virtual cavity is created, avoiding the introduction of elements in the domain of the structure or other cumbersome strategy integrated in the formulation for considering the void region in BEM. The advantages of the present approach, as compared to other existing methods, are that, firstly, during the iterative process, there is no need to remesh and recalculate the boundary equations at each iteration once the introduction of the initial stress - to simulate each void region - is computed in the right-hand side vector of the final algebraic equation and, secondly, there is a significant reduction in the computational cost. Numerical examples are presented and compared to others available in literature, showing the robustness and efficiency of the proposed algorithm.

A Computationally Fast Convergence Measure and Implementation for Single-, Multiple-, and Many-Objective Optimization

A previous study suggested a Karush–Kuhn–Tucker proximity measure (KKTPM) that is able to identify relative closeness of any point from the theoretical optimum point without actually knowing the exact location of the optimum point. However, the drawback of the KKTPM metric is that it requires a new optimization problem to be solved for each solution to find its convergence measure. In this paper, we propose a number of approximate formulations of the KKTPM measure by studying its calculation procedure so that the KKTPM measure can be computed in a computationally fast manner and without solving the inherent optimization problem. The approximate KKTPM values are evaluated in comparison with the original exact optimization-based KKTPM value on standard single-objective, multiobjective, and many-objective optimization problems. In all cases, our proposed “estimated” approximate method is found to achieve a strong correlation of KKTPM values with the exact values, and achieve such results in two or three orders of magnitude smaller computational time. We also present a parser-based KKTPM computational procedure, which can be used independently or in conjunction with an evolutionary multiobjective optimization procedure.

Fast Adaptive Evolutionary PM Traction Motor Optimization Based on Electric Vehicle Drive Cycle

This paper introduces an evolutionary optimization procedure for the design of permanent-magnet motors (PMMs) for electric vehicle (EV) applications, considering a specific drive cycle with multiple operating points. For the purposes of the analysis, the New European Drive Cycle (NEDC) has been employed with two alternative PMM configurations. Energy distribution over the NEDC for a small passenger's EV has been calculated and the equivalent multiple operating points have been extracted, using appropriate weights, in order to maintain an equal energy consumption basis, resulting in reduced computational cost. The proposed optimization technique is constituted of an adaptive differential evolution (DE) algorithm involving dynamic variation of the mutation factor, combined with finite-element (FE) and circuit models. The procedure is based on the precise calculation of the two axes input current components for each candidate solution and operating condition. The methodology introduced presents stable and fast convergence characteristics and has been applied to optimize the geometry of both surface-mounted and interior PMM configurations. The proposed motor is based on the thorough tradeoff among the two alternative optimized geometries and has been validated through measurements on a prototype.

Derived heuristics-based consistent optimization of material flow in a gold processing plant

ABSTRACTMaterial flow in a chemical processing plant often follows complicated control laws and involves plant capacity constraints. Importantly, the process involves discrete scenarios which when modelled in a programming format involves if–then–else statements. Therefore, a formulation of an optimization problem of such processes becomes complicated with nonlinear and non-differentiable objective and constraint functions. In handling such problems using classical point-based approaches, users often have to resort to modifications and indirect ways of representing the problem to suit the restrictions associated with classical methods. In a particular gold processing plant optimization problem, these facts are demonstrated by showing results from MATLAB®'s well-known fmincon routine. Thereafter, a customized evolutionary optimization procedure which is capable of handling all complexities offered by the problem is developed. Although the evolutionary approach produced results with comparatively less variance over multiple runs, the performance has been enhanced by introducing derived heuristics associated with the problem. In this article, the development and usage of derived heuristics in a practical problem are presented and their importance in a quick convergence of the overall algorithm is demonstrated.

A Unified Evolutionary Optimization Procedure for Single, Multiple, and Many Objectives

Traditionally, evolutionary algorithms (EAs) have been systematically developed to solve mono-, multi-, and many-objective optimization problems, in this order. Despite some efforts in unifying different types of mono-objective evolutionary and non-EAs, researchers are not interested enough in unifying all three types of optimization problems together. Such a unified algorithm will allow users to work with a single software enabling one-time implementation of solution representation, operators, objectives, and constraints formulations across several objective dimensions. For the first time, we propose a unified evolutionary optimization algorithm for solving all three classes of problems specified above, based on the recently proposed elitist, guided nondominated sorting procedure, developed for solving many-objectives problems. Using a new niching-based selection procedure, our proposed unified algorithm automatically degenerates to an efficient equivalent population-based algorithm for each class. No extra parameters are needed. Extensive simulations are performed on unconstrained and constrained test problems having single-, two-, multi-, and many-objectives and on two engineering optimization design problems. Performance of the unified approach is compared to suitable population-based counterparts at each dimensional level. Results amply demonstrate the merit of our proposed unified approach and motivate similar studies for a richer understanding of the development of optimization algorithms.

Robust inverse identification of the effective three-dimensional elastic behaviour of a piezoceramic patch bonded to a multilayer unidirectional fibre composite

The effective three-dimensional elastic behaviour of a rectangular piezoceramic patch centrally surface-bonded to a free multilayer unidirectional carbon-fibre reinforced plastic composite plate is inversely identified from three potential ones: orthotropic, quasi transversely isotropic (QTI) or transversely isotropic. This is reached through minimizing the finite element-experimental frequency relative deviations of the first eight short-circuit modes of the smart composite structure using a robust multi-objective evolutionary optimization procedure. The latter combines full factorial design of experiments (DoE)-based surface response meta-modelling of the frequency dependence on the patch’s elastic engineering constants and a non-sorting genetic algorithm of second generation. The inverse identification robustness comes from considering large uncertainties (±20%) of the design parameters nominal (initial) values. DoE-based sensitivities of the considered frequencies to the investigated piezoceramic patch’s elastic behaviour engineering constants are analyzed in order to identify the most influent design parameters. The latter are used for reducing the DoE plans and corresponding finite element computations. It is found that the bonded patch’s effective elastic behaviour is QTI (or orthotropic) when all (or the most influent) engineering constants are optimized.

Design of the lower chassis of a monorail personal rapid transit (MPRT) car using the evolutionary structural optimization (ESO) method

The Evolutionary Structural Optimization (ESO) procedure was applied to the design of the lower chassis of a monorail personal rapid transit (MPRT) car. As part of the early-stage development effort, ESO was used to identify a good topology of the lower chassis structure, which is effective in material usage, with lowly-stressed material removed. The procedure started with building a three-dimensional finite element model of the topology that occupies the design envelop, and lowly stressed elements were removed step by step during the ESO procedure. Multiple load cases concerning acceleration, deceleration, left turn, and right turn were analyzed separately, and a simple procedure dealing with multiple load cases was adopted. After 14 calculation increments, 80 % of the initial material was removed. The resulting topology reveals a reasonable frame structure with rounded outer corners, triangular cantilever supports, and Michell style beam structures, suitable as a starting reference for the structure design of a MPRT.

Evolutionary optimization of compact dielectric lens for farfield sub-wavelength imaging.

The resolution of conventional optical lenses is limited by diffraction. For decades researchers have made various attempts to beat the diffraction limit and realize subwavelength imaging. Here we present the approach to design modified solid immersion lenses that deliver the subwavelength information of objects into the far field, yielding magnified images. The lens is composed of an isotropic dielectric core and anisotropic or isotropic dielectric matching layers. It is designed by combining a transformation optics forward design with an inverse design scheme, where an evolutionary optimization procedure is applied to find the material parameters for the matching layers. Notably, the total radius of the lens is only 2.5 wavelengths and the resolution can reach λ/6. Compared to previous approaches based on the simple discretized approximation of a coordinate transformation design, our method allows for much more precise recovery of the information of objects, especially for those with asymmetric shapes. It allows for the far-field subwavelength imaging at optical frequencies with compact dielectric devices.