Differential Evolutions Research Articles

A constrained multi-objective evolutionary algorithm based on fitness landscape indicator

Constrained multi-objective optimization problems (CMOPs) with constraints in both the decision and objective space are shown to be great challenges to be solved. Considering the different requirements of different problems on resource allocation of exploration and exploitation, this paper proposes a new constrained multi-objective evolutionary algorithm based on a novel fitness landscape indicator. The indicator regards the fitness landscape and evolutionary generation among the population to determine the selection of the offspring generation mechanism. The proposed algorithm uses the new indicator to select different differential evolutions during the evolutionary process to balance exploration and exploitation. Numerical experiments on three test suites and three practical examples compared with six existing algorithms show the proposed algorithm can effectively deal with different types of CMOPs, especially in CMOPs with constraints in both the decision and objective spaces.

High-resolution diffusion magnetic resonance imaging and spatial-transcriptomic in developing mouse brain

Brain development is a highly complex process regulated by numerous genes at the molecular and cellular levels. Brain tissue exhibits serial microstructural changes during the development process. High-resolution diffusion magnetic resonance imaging (dMRI) affords a unique opportunity to probe these changes in the developing brain non-destructively. In this study, we acquired multi-shell dMRI datasets at 32 µm isotropic resolution to investigate the tissue microstructure alterations, which we believe to be the highest spatial resolution dMRI datasets obtained for postnatal mouse brains. We adapted the Allen Developing Mouse Brain Atlas (ADMBA) to integrate quantitative MRI metrics and spatial transcriptomics. Diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), and neurite orientation dispersion and density imaging (NODDI) metrics were used to quantify brain development at different postnatal days. We demonstrated that the differential evolutions of fiber orientation distributions contribute to the distinct development patterns in white matter (WM) and gray matter (GM). Furthermore, the genes enriched in the nervous system that regulate brain structure and function were expressed in spatial correlation with age-matched dMRI. This study is the first one providing high-resolution dMRI, including DTI, DKI, and NODDI models, to trace mouse brain microstructural changes in WM and GM during postnatal development. This study also highlighted the genotype-phenotype correlation of spatial transcriptomics and dMRI, which may improve our understanding of brain microstructure changes at the molecular level.

Evolution in key indicators of maternal and child health across the wealth gradient in 41 sub-Saharan African countries, 1986–2019

BackgroundAggregate trends can be useful for summarizing large amounts of information, but this can obscure important distributional aspects. Some population subgroups can be worse off even as averages climb, for example. Distributional information can identify health inequalities, which is essential to understanding their drivers and possible remedies.MethodsUsing publicly available Demographic and Health Survey (DHS) data from 41 sub-Saharan African countries from 1986 to 2019, we analyzed changes in coverage for eight key maternal and child health indicators: first dose of measles vaccine (MCV1); Diphtheria-Pertussis-Tetanus (DPT) first dose (DPT1); DPT third dose (DPT3); care-seeking for diarrhea, acute respiratory infections (ARI), or fever; skilled birth attendance (SBA); and having four antenatal care (ANC) visits. To evaluate whether coverage diverged or converged over time across the wealth gradient, we computed several dispersion metrics including the coefficient of variation across wealth quintiles. Slopes and 5-year moving averages were computed to identify overall long-term trends.ResultsAverage coverage increased for all quintiles and indicators, although the range and the speed at which they increased varied widely. There were small changes in the wealth-related gap for SBA, ANC, and fever. The wealth-related gap of vaccination-related indicators (DPT1, DPT3, MCV1) decreased over time. Compared to 2017, the wealth-gap between richest and poorest quintiles in 1995 was 7 percentage points larger for ANC and 17 percentage points larger for measles vaccination.ConclusionsMaternal and child health indicators show progress, but the distributional effects show differential evolutions in inequalities. Several reasons may explain why countries had smaller wealth-related gap trends in vaccination-related indicators compared to others. In addition to service delivery differences, we hypothesize that the allocation of development assistance for health, the prioritization of vaccine-preventable diseases on the global agenda, and indirect effects of structural adjustment programs on health system-related indicators might have played a role.

Learning Adaptive Differential Evolution by Natural Evolution Strategies

Adaptive parameter control is critical in the design and application of evolutionary algorithm (EA), so does in differential evolution. In the past decade, many adaptive evolutionary algorithms have been proposed, in which online information collected until current generation during the evolutionary search procedure is used to determine the algorithmic parameters for the next generation. Recent studies often assume that the algorithmic parameters follow some distributions, while the distributions' parameters (called hyper-parameters) are updated by the collected information. Performances of these adaptive EAs depend highly on the hyper-parameters. Notice that the experiences obtained from optimizing some related problems could provide useful guidelines on how to adaptively control the distributions' parameters. However, few existing studies sufficiently used such experiences. To fill the gap, we propose a general framework for adaptive parameter control by modeling its evolution procedure as a Markov decision process. In the framework, a neural network is employed to act as the controller. The natural evolution strategies is applied to train the neural network. The proposed framework is applied on two well-known differential evolutions (DEs), namely JADE and LSHADE. By incorporating the learned controller, two DEs, named JADE/AC and LSHADE/AC, are formed. Experimental results on the CEC 2018 benchmark suite show that in general JADE/AC and LSHADE/AC perform significantly better than their counterparts. Moreover, in comparison with some well-known EAs including three suggested best DEs in a review paper (including LSHADE, cDE and CoBiDE), the championship algorithm in the CEC 2018 competitions, a recently-developed learnable DE and recently proposed DEs, our study shows that LSHADE/AC performs the best amongst them without sacrificing much computation time.

Efficient computational stochastic framework for performance optimization of E-waste management plant

PurposeReliability and maintainability are the key system effectiveness measures in process and manufacturing industries, and treatment plants, especially in E-waste management plants. The present work is proposed with a motto to develop a stochastic framework for the e-waste management plant to optimize its availability integrated with reliability, availability, maintainability, and dependability (RAMD) measures and Markovian analysis to estimate the steady-state availability of the E-waste management plant. In the analysis an effort is also made to identify the best performing algorithm for availability optimization of the e-waste plant. MethodologyA stochastic model for a particular plant is developed and its availability is optimized using various metaheuristic approaches like a genetic algorithm (GA), particle swarm optimization (PSO), and differential evolutions (DE). The most sensitive component is identified using RAMD methodology while the effect of deviation in various failure and repair rates are observed by the proposed model. The failure and repair rates follow an exponential distribution. All time-dependent random variables are statistically independent. Originality/NoveltiesA novel stochastic model is presented for an e-waste management plant and optimum availability is obtained using metaheuristic approaches. The proposed methodology is not so far discussed in the reliability analysis of process industries. FindingsThe numerical results of the proposed model compared to identify the most efficient algorithm. It is observed that genetic algorithm provides the maximum value (0.92330969) of availability at a population size 2500 after 500 iterations. PSO algorithm attained the maximum value (0.99996744) of availability just after 50 iterations and 100 population size. So, its rate of convergence is faster than GA. The optimum value of availability is 0.99997 using differential evolution after 500 iterations and population size of more than 1000. These findings are very beneficial for system designers. Practical ImplicationsThe proposed methodology can be utilized to find the reliability measures of other process industries.

Directional mutation and crossover for immature performance of whale algorithm with application to engineering optimization

AbstractIn recent years, a range of novel and pseudonovel optimization algorithms has been proposed for solving engineering problems. Swarm intelligence optimization algorithms (SIAs) have become popular methods, and the whale optimization algorithm (WOA) is one of the highly discussed SIAs. However, regardless of novelty concerns about this method, the basic WOA is a weak method compared to top differential evolutions and particle swarm variants, and it suffers from the problem of poor initial population quality and slow convergence speed. Accordingly, in this paper, to increase the diversity of WOA versions and enhance the performance of WOA, a new WOA variant, named LXMWOA, is proposed, and based on the Lévy initialization strategy, the directional crossover mechanism, and the directional mutation mechanism. Specifically, the introduction of the Lévy initialization strategy allows initial populations to be dynamically distributed in the search space and enhances the global search capability of the WOA. Meanwhile, the directional crossover mechanism and the directional mutation mechanism can improve the local exploitation capability of the WOA. To evaluate its performance, using a series of functions and three models of engineering optimization problems, the LXMWOA was compared with a broad array of competitive optimizers. The experimental results demonstrate that the LXMWOA is significantly superior to its exploration and exploitation capability peers. Therefore, the proposed LXMWOA has great potential to be used for solving engineering problems.

Illumination correction with optimized kernel extreme learning machine based on improved marine predators algorithm

AbstractAiming at the problem of poor image illumination correction accuracy, a kernel extreme learning machine optimized based on the differential evolution‐improved marine predators algorithm is proposed to estimate the scene illumination information and restore the image. First, in order to solve the problem of randomization of the initial population of the marine predators algorithm, differential evolutions is used to provide a set of suitable initial populations to the algorithm. Then, an improved algorithm is used to optimize the weight and bias of the kernel extreme learning machine to solve the problem of the randomness of the weight and bias, so that the learning machine converges to the global optimal value and avoids the unstable predictions. Finally, after obtaining the predicted illumination information, the image model is corrected to the image effect under standard illumination through diagonal transformation. It can be seen from the experimental results that the best predictive value of the differential evolution marine predator algorithm learning machine is 0.0135915, and the quasi‐bias is only 0.001687. Compared with traditional illumination estimation algorithms such as random vector functional link and extreme learning machine, the differential evolution marine predator algorithm learning machine algorithm proposed in this article has better stability, higher accuracy of calculated predicted values, and better image restoration effect.

Differential evolution and the influencing factors of low-maturity terrestrial shale with different types of kerogen: A case study of a Jurassic shale from the northern margin of Qaidam Basin，China

The Jurassic terrestrial shale on the northern margin of Qaidam Basin is characterized by high contents of organic matter but low maturity resulting in a lack of further research on shale gas in this area. To better understanding the shale gas potential of organic matter with different types, we conducted thermal maturity experiment of hydrocarbon generation from different kerogen types of low-mature shales under closed conditions. The results show that type II and type III kerogen have experienced similar hydrocarbon generation stages, but they differ in the hydrocarbon generation interval and evolution process between liquid hydrocarbon and gaseous hydrocarbon. Compared with Type III kerogen, type II kerogen is characterized by a low initial temperature at each evolutionary stage and wide temperature range, which caused the overall evolution of type III Kerogen lagged behind that of type II kerogen. The differential evolutions mainly result from the differences in hydrocarbon generation mechanism, hydrocarbon generation activation energy and kerogen macerals among different kerogen types. We summarized the evolution model of type II and type III Kerogen based on the characteristics of kerogen in hydrocarbon generation, carbon isotope change, pore development and other aspects. This work can provide theoretical and data support for reconstructing the hydrocarbon generation process of terrestrial shale gas, investigating the hydrocarbon generation mechanism, and predicting the hydrocarbon resources of terrestrial shale oil and gas on the northern margin of Qaidam basin and even China.

The Use of Evolutionary Methods for the Determination of a DC Motor and Drive Parameters Based on the Current and Angular Speed Response

Determination of the seven parameters of a Direct Current (DC) motor and drive is presented, based on the speed and current step responses. The method is extended for the motor and drive parameter determination in the case of a controlled drive. The influence of a speed controller on the responses is considered in the motor model with the use of the measured voltage. Current limitation of the supply unit is also considered in the DC motor model. For parameter determination, a motor model is used, which is determined with two coupled differential equations. Euler’s first-order and Runge–Kutta fourth-order methods are used for the motor model simulations. For parameter determination, evolutionary methods are used and compared to each other. Methods used are Genetic Algorithm, Differential Evolutions with two strategies, Teaching–Learning-Based Optimization, and Artificial Bee Colony. To improve results, deviation of the motor model simulation time is used and Memory Assistance with three different approaches is analyzed to shorten the calculation time. The tests showed that Differential Evolution (DE)/rand/1/exp is the most appropriate for the presented problem. The division of the motor model simulation time improves the results. For the presented problem, short-term memory assistance can be suggested for calculation time reduction.

A Novel Hybrid Intelligent Prediction Model for Valley Deformation: A Case Study in Xiluodu Reservoir Region, China

The narrowing deformation of reservoir valley during the initial operation period threatens the long-term safety of the dam, and an accurate prediction of valley deformation (VD) remains a challenging part of risk mitigation. In order to enhance the accuracy of VD prediction, a novel hybrid model combining Ensemble empirical mode decomposition based interval threshold denoising (EEMD-ITD), Differential evolutions—Shuffled frog leaping algorithm (DE-SFLA) and Least squares support vector machine (LSSVM) is proposed. The non-stationary VD series is firstly decomposed into several stationary subseries by EEMD; then, ITD is applied for redundant information denoising on special sub-series, and the denoised deformation is divided into the trend and periodic deformation components. Meanwhile, several relevant triggering factors affecting the VD are considered, from which the input features are extracted by Grey relational analysis (GRA). After that, DE-SFLA-LSSVM is separately performed to predict the trend and periodic deformation with the optimal inputs. Ultimately, the two individual forecast components are reconstructed to obtain the final predicted values. Two VD series monitored in Xiluodu reservoir region are utilized to verify the proposed model. The results demonstrate that: (1) Compared with Discrete wavelet transform (DWT), better denoising performance can be achieved by EEMD-ITD; (2) Using GRA to screen the optimal input features can effectively quantify the deformation response relationship to the triggering factors, and reduce the model complexity; (3) The proposed hybrid model in this study displays superior performance on some compared models (e.g., LSSVM, Backward Propagation neural network (BPNN), and DE-SFLA-BPNN) in terms of forecast accuracy.

New few parameters differential evolution algorithm with application to structural identification

Abstract Differential evolution algorithm (DEA) is a stochastic, population-based global optimization method. In this paper, we propose new schemes for both mutation and crossover operators in order to enhance the performances of the standard DEA. The advantage of these proposed operators is that they are “parameters-less”, without a tuning phase of algorithm parameters that is often a disadvantage of DEA. Once the modified differential evolutions are presented, a large comparative analysis is performed with the aim to assess both correctness and efficiency of the proposed operators. Advantages of proposed DEA are used in an important task of modern structural engineering that is mechanical identification under external dynamic loads. This is because of the importance of using a “parameters-less” algorithm in identification problems whose characteristics typically vary strongly case by case, needing of a continuous set up of the algorithm proposed. This important advantage of proposed optimizers, in front of other identification algorithms, is used to develop a computer code suitable for the automatic identification of a simple supported beam subject to an impact load, that has been tested both using numerical simulations and real standard tests dynamic. The results point out that this algorithm is an interesting candidate for standard applications in structural identification problems.

Macromolecular evolution and structural defects in tectonically deformed coals

Here, the differential macromolecular evolutions and the structural defects in various TDCs (tectonically deformed coals) were profoundly investigated utilizing the 13C NMR, FTIR, Raman, and DFT (density function theory) calculations. The increasing aromatics provides evidences for advance evolution for aromatic clusters induced by dynamic metamorphism. The variations of fal∗ (non-protonated carbons) and falH (CH or CH2) indicates that the brittle could promote the aliphatic carbon diversifications while ductile deformation could significantly promote the loss of aliphatic carbons. The I2 (=A900–700/A3000–2800) gradually increases while the I3 (=A1703+1745/A1618) decreases. The comparisons of the D1 peak in TDCs with those in perfect- and defective graphene indicated the existences of the structural defects in TDCs. The ductile TDCs have the lowest D1 peak positions, indicating that ductile deformation can promote the macromolecular disorder degrees to the maximum extent. The gradual increase of ID1/IG and the good linear relationship (R2 = 0.90) between ID1/IG and AD1/AG indicated the gradual increasing content of structural defects with the enhancement of the tectonic deformation. The geological conditions and the Raman results indicated the existences of the Stone-Wales defect (SW) and vacancy-like defects, including the single vacancy (SV), double vacancies (DV), and multi vacancies (MV1 and MV2) in TDCs. The evolution paths of DV (formation energy, Ef: 11.68 eV) → MV1 (Ef: 9.74 eV) → MV2 (Ef: 18.34 eV) and initial structures → SW defects have witnessed the increasing defects and disorder degrees with the enhancement of the tectonic deformation without damaging the continuity of coal matrix structures, which macroscopically manifests as ductile deformation. However, the evolution paths of initial structure → DV (Ef: 11.68 eV) and initial structure → SV (Ef: 9.08 eV) have damaged the continuity by missing carbons, which are consistent with the brittle TDCs.

Composite differential evolution algorithm for SHM with low carrier ratio

This study presents a new method of switching angle solution based on composite differential evolutions (CoDE) in selective harmonic mitigation pulse width modulation (SHMPWM). The method can effectively improve the global searching ability and convergence rate of the solution by the combination of multiple composite trial vectors and control parameter settings. Its great generality makes itself applicable to selective harmonic elimination PWM and synchronous harmonic optimum PWM as well. This study introduces the basic principles of SHMPWM and CoDE, constructs the constraint and objective functions by means of penalty, and gives detailed solution steps. After getting the switching angle solutions from comparative studies including different switching angle numbers, different modulation degrees, or different optimised PWM methods, the experimental platform finally has been designed and carried out to verify the accuracy and generality of the proposed method.

Tectono‐stratigraphic response of the Sandino Forearc Basin (N‐Costa Rica and W‐Nicaragua) to episodes of rough crust and oblique subduction

AbstractThe southern Central American active margin is a world‐class site where past and present subduction processes have been extensively studied. Tectonic erosion/accretion and oblique/orthogonal subduction are thought to alternate in space and time along the Middle American Trench. These processes may cause various responses in the upper plate, such as uplift/subsidence, deformation, and volcanic arc migration/shut‐off. We present an updated stratigraphic framework of the Late Cretaceous–Cenozoic Sandino Forearc Basin (SFB) which provides evidence of sedimentary response to tectonic events. Since its inception, the basin was predominantly filled with deep‐water volcaniclastic deposits. In contrast, shallow‐water deposits appeared episodically in the basin record and are considered as tectonic event markers. The SFB stretches for about 300 km and varies in thickness from 5 km (southern part) to about 16 km (northern part). The drastic, along‐basin, thickness variation appears to be the result of (1) differential tectonic evolutions and (2) differential rates of sediment supply. (1) The northern SFB did not experience major tectonic events. In contrast, the reduced thickness of the southern SFB (5 km) is the result of at least four uplift phases related to the collision/accretion of bathymetric reliefs on the incoming plate: (i) the accretion of a buoyant oceanic plateau (Nicoya Complex) during the middle Campanian; (ii) the collision of an oceanic plateau (?) during the late Danian–Selandian; (iii) the collision/accretion of seamounts during the late Eocene–early Oligocene; (iv) the collision of seamounts and ridges during the Pliocene–Holocene. (2) The northwestward thickening of the SFB may have been enhanced by high sediment supply in the Fonseca Gulf area which reflects sourcing from wide, high relief drainage basins. In contrast, sedimentary input has possibly been lower along the southern SFB, due to the proximity of the narrow, lowland isthmus of southern Central America. Moreover, two phases of strongly oblique subduction affected the margin, producing strike‐slip faulting in the forearc basin: (1) prior to the Farallon Plate breakup, an Oligocene transpressional phase caused deformation and uplift of the basin depocenter, triggering shallowing‐upward of the Nicaraguan Isthmus in the central and northern SFB; (2) a Pleistocene–Holocene transtensional phase drives the NW‐directed motion of a forearc sliver and reactivation of the graben‐bounding faults of the late Neogene Nicaraguan Depression. We discuss arguments in favour of a Pliocene development of the Nicaraguan Depression and propose that the Nicaraguan Isthmus, which is the apparent rift shoulder of the depression, represents a structure inherited from the Oligocene transpressional phase.

Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems

This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method for solving multi-objective problems. Most of the multi-objective optimization algorithms use different search techniques inspired by different optimization techniques such as genetic algorithms, differential evolutions, particle swarm optimization, cuckoo search etc., but search techniques of recently developed metaheuristics have hardly been investigated. Non-dominated moth-flame optimization algorithm (NS-MFO) is based on the search technique of moth-flame optimization algorithm (MFO) algorithm and utilizes the elitist non-dominated sorting and crowding distance approach for obtaining different non domination levels and to preserve the diversity among the optimal set of solutions respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems and multi-objective engineering design problems with distinctive features. It is shown in this paper that this method effectively generates the Pareto front and also, this method is easy to implement and algorithmically simple.

Lithium response in bipolar disorders and core clock genes expression

Objectives: We examine whether the lithium response is associated with changes in the expression of core clock genes.Methods: The effect of a therapeutic concentration of lithium (1 mM) on the expression levels of 17 circadian genes was examined in lymphoblastoid cell lines (LCLs) derived from two well-characterized groups of bipolar disorder patients, defined as lithium non-responders (NR, n = 20) or excellent responders (ER, n = 16). Quantitative real-time PCR (qRT-PCR) was conducted at 2, 4 and 8 days (d2, d4 and d8) with and without lithium exposure.Results: At d2, in ER only, BHLHE41, RORA, PER1, ARNTL, CRY2, BHLHE40 and CSNK1D were upregulated, whereas NR1D1 was downregulated. At d4, in ER only, CRY1 was downregulated. At d8, in NR only, GSK3β was upregulated and DBP, TIMELESS and CRY1 were downregulated. Significant Group × Lithium interactions existed for NR1D1 at d2 (P = 0.02), and CRY1 at d4 (P = 0.02). Longitudinal analyses showed differential temporal evolutions between NR and ER (significant Time × Group interaction) for PER3, NR1D1, DBP, RORA, CSNK1D and TIMELESS; and a significant Time × Lithium interaction for NR1D1. Coexpression data analyses suggested distinct groups of circadian genes concurrently modulated by lithium.Conclusions: In LCLs, lithium influences expression of circadian genes with differences in amplitude and kinetics according to the patient’s lithium response status.

Discrete differential evolutions for the discounted {0-1} knapsack problem

This paper first proposes a discrete differential evolution algorithm for discounted {0-1} knapsack problems (D{0-1}KP) based on feasible solutions represented by the 0-1 vector. Subsequently, based on two encoding mechanisms of transforming a real vector into an integer vector, two new algorithms for solving D{0-1}KP are given through using integer vectors defined on {0, 1, 2, 3}n to represent feasible solutions of the problem. Finally, the paper conducts a comparative study on the performance between our proposed three discrete differential evolution algorithms and those developed by common genetic algorithms for solving several types of large scale D{0-1}KP problems. The paper confirms the feasibility and effectiveness of designing discrete differential evolution algorithms for D{0-1}KP by encoding conversion approaches.

Discrete differential evolutions for the discounted {0-1} knapsack problem

This paper first proposes a discrete differential evolution algorithm for discounted {0-1} knapsack problems (D{0-1}KP) based on feasible solutions represented by the 0-1 vector. Subsequently, based on two encoding mechanisms of transforming a real vector into an integer vector, two new algorithms for solving D{0-1}KP are given through using integer vectors defined on {0, 1, 2, 3}n to represent feasible solutions of the problem. Finally, the paper conducts a comparative study on the performance between our proposed three discrete differential evolution algorithms and those developed by common genetic algorithms for solving several types of large scale D{0-1}KP problems. The paper confirms the feasibility and effectiveness of designing discrete differential evolution algorithms for D{0-1}KP by encoding conversion approaches.

Improved simple optimization (SOPT) algorithm for unconstrained non-linear optimization problems

Summary In the recent years, population based meta-heuristic are developed to solve non-linear optimization problems. These problems are difficult to solve using traditional methods. Simple optimization (SOPT) algorithm is one of the simple and efficient meta-heuristic techniques to solve the non-linear optimization problems. In this paper, SOPT is compared with some of the well-known meta-heuristic techniques viz. Artificial Bee Colony algorithm (ABC), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Differential Evolutions (DE). For comparison, SOPT algorithm is coded in MATLAB and 25 standard test functions for unconstrained optimization having different characteristics are run for 30 times each. The results of experiments are compared with previously reported results of other algorithms. Promising and comparable results are obtained for most of the test problems. To improve the performance of SOPT, an improvement in the algorithm is proposed which helps it to come out of local optima when algorithm gets trapped in it. In almost all the test problems, improved SOPT is able to get the actual solution at least once in 30 runs.

Empirical investigations into the exponential crossover of differential evolutions

Since the introduction in 1995, Differential evolution (DE) has drawn the attention of many researchers all over the world. Even though binomial (uniform) and exponential (modular two-point) crossover operators have been proposed simultaneously, binomial crossover has been more frequently used. Recently, the exponential crossover operator demonstrated superior performance over the binomial operator when solving complex high dimensional problems. We observe that the commonly used definition of exponential crossover operator does not scale impractically with the dimensionality of the problem being solved. Motivated by these observations, in this research, we investigate the performance of the current exponential crossover operator (EXP) and demonstrate its deficiencies. Consequently, a linearly scalable exponential crossover operator (LS-EXP) based on a number of consecutive dimensions to crossover is defined. Our numerical results on the most recent benchmark problems with dimensions ranging from 50 to 1000 show superior performance of the LS-EXP over the current exponential crossover operator, EXP.