Appropriate Combination of Crossover Operator and Mutation Operator in Genetic Algorithms for the Travelling Salesman Problem

Genetic algorithms(GAs)are very good metaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems.AsimpleGAbeginswith a set of solutions represented by a population of chromosomes and then uses the idea of survival of the fittest in the selection process to select some fitter chromosomes.It uses a crossover operator to create better offspring chromosomes and thus,converges the population.Also,it uses a mutation operator to explore the unexplored areas by the crossover operator,and thus,diversifies the GA search space.A combination of crossover and mutation operators makes the GA search strong enough to reach the optimal solution.However,appropriate selection and combination of crossover operator and mutation operator can lead to a very good GA for solving an optimization problem.In this present paper,we aim to study the benchmark traveling salesman problem(TSP).We developed several genetic algorithms using seven crossover operators and six mutation operators for the TSP and then compared them to some benchmark TSPLIB instances.The experimental studies show the effectiveness of the combination of a comprehensive sequential constructive crossover operator and insertion mutation operator for the problem.The GA using the comprehensive sequential constructive crossover with insertion mutation could find average solutions whose average percentage of excesses from the best-known solutions are between 0.22 and 14.94 for our experimented problem instances.

Absence of BCS–BEC crossover in FeSe_(0.45)Te_(0.55) superconductor

In iron-based superconductor Fe(Se,Te), a flat band-like feature near the Fermi level was observed around the Brillouin zone center in the superconducting state. It is under debate whether this is the evidence on the presence of the BCS–BEC[Bardeen–Cooper–Schrieffer(BCS), Bose–Einstein condensation(BEC)] crossover in the superconductor. High-resolution laser-based angle-resolved photoemission measurements are carried out on high quality single crystals of FeSe_(0.45)Te_(0.55) superconductor to address the issue. By employing different polarization geometries, we have resolved and isolated the dyz band and the topological surface band, making it possible to study their superconducting behaviors separately. The dyz band alone does not form a flat band-like feature in the superconducting state and the measured dispersion can be well described by the BCS picture. We find that the flat band-like feature is formed from the combination of the dyz band and the topological surface state band in the superconducting state. These results reveal the origin of the flat band-like feature and rule out the presence of BCS-BEC crossover in Fe(Se,Te) superconductor.

Genomic features of meiotic crossovers in diploid potato

Meiotic recombination plays an important role in genome evolution and crop improvement.Potato(Solanum tuberosum L.)is the most important tuber crop in the world,but research about meiotic recombination in potato is limited.Here,we resequenced 2163 F2 clones derived from five different genetic backgrounds and identified 41945 meiotic crossovers.Some recombination suppression in euchromatin regions was associated with large structural variants.We also detected five shared crossover hotspots.The number of crossovers in each F2 individual from the accession Upotato 1 varied from 9 to 27,with an average of 15.5,78.25%of which were mapped within 5 kb of their presumed location.We show that 57.1%of the crossovers occurred in gene regions,with poly-A/T,poly-AG,AT-rich,and CCN repeats enriched in the crossover intervals.The recombination rate is positively related with gene density,SNP density,Class II transposon,and negatively related with GC density,repeat sequence density and Class I transposon.This study deepens our understanding of meiotic crossovers in potato and provides useful information for diploid potato breeding.

Genetic Crossover Operators for the Capacitated Vehicle Routing Problem

We study the capacitated vehicle routing problem(CVRP)which is a well-known NP-hard combinatorial optimization problem(COP).The aim of the problem is to serve different customers by a convoy of vehicles starting from a depot so that sum of the routing costs under their capacity constraints is minimized.Since the problem is very complicated,solving the problem using exact methods is almost impossible.So,one has to go for the heuristic/metaheuristic methods and genetic algorithm(GA)is broadly applied metaheuristic method to obtain near optimal solution to such COPs.So,this paper studies GAs to find solution to the problem.Generally,to solve a COP,GAs start with a chromosome set named initial population,and then mainly three operators-selection,crossover andmutation,are applied.Among these three operators,crossover is very crucial in designing and implementing GAs,and hence,numerous crossover operators were developed and applied to different COPs.There are two major kinds of crossover operators-blind crossovers and distance-based crossovers.We intend to compare the performance of four blind crossover and four distance-based crossover operators to test the suitability of the operators to solve the CVRP.These operators were originally proposed for the standard travelling salesman problem(TSP).First,these eight crossovers are illustrated using same parent chromosomes for building offspring(s).Then eight GAs using these eight crossover operators without any mutation operator and another eight GAs using these eight crossover operators with a mutation operator are developed.These GAs are experimented on some benchmark asymmetric and symmetric instances of numerous sizes and various number of vehicles.Our study revealed that the distance-based crossovers are much superior to the blind crossovers.Further,we observed that the sequential constructive crossover with and without mutation operator is the best one for theCVRP.This estimation is validated by Student’s t-test at 95%confidence level.We further determined a comparative rank of the eight crossovers for the CVRP.

Saturated absorption spectrum of cesium micrometric-thin cell with suppressed crossover spectral lines

Micrometric-thin cells(MCs)with alkali vapor atoms have been valuable for research and applications of hyperfine Zeeman splitting and atomic magnetometers under strong magnetic fields.We theoretically and experimentally study the saturated absorption spectra using a 100-μm cesium MC,where the pump and probe beams are linearly polarized with mutually perpendicular polarizations,and the magnetic field is along the pump beam.Because of the distinctive thin chamber of the MC,crossover spectral lines in saturated absorption spectra are largely suppressed leading to clear splittings of hyperfine Zeeman transitions in experiments,and the effect of spatial magnetic field gradient is expected to be reduced.A calculation method is proposed to achieve good agreements between theoretical calculations and experimental results.This method successfully explains the suppression of crossover lines in MCs,as well as the effects of magnetic field direction,propagation and polarization directions of the pump/probe beam on saturated absorption spectrum.The saturated absorption spectrum with suppressed crossover lines is used for laser frequency stabilization,which may provide the potential value of MCs for high spatial resolution strong-field magnetometry with high sensitivity.

品牌联合视角下的“CROSSOVER”(酷越)

"crossover"思想已经成为一种崭新的现代企业经营理念,代表一种新锐的生活态度和审美方式的融合。在实施"crossover"策略时,关键要在原来的品牌基础上形成新的超越,创造新的魅力,才能吸引更多消费者的关注。

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas-Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.

D-Dimensional Dirac Fermions BEC-BCS Crossover Thermodynamics

An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentzvector condensation effects on the equation of state of the strongly interacting fermions system.The interior quantumfluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized ThomsonProblem counterterm background.The general analytical formulas for the d-dimensional thermodynamics are given nearthe unitary limit region,In the non-relativistic limit for d=3,the universal dimensionless coefficientε=4/9 andenergy gap △/ε_f=5/18 are reasonably consistent with the existing theoretical and experimental results.In the unitarylimit for d=2 and T=0,the universal coefficient can even approach the extreme occasion ξ=0 corresponding to theinfinite effective fermion mass m~*=∞,which can be mapped to the strongly coupled two-dimensional electrons and isquite similar to the three-dimensional Bose-Einstein condensation of ideal boson gas.Instead,for d=1,the universalcoefficient ξ is negative,implying the non-existence of phase transition from superfluidity to normal state.The solutionsmanifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.

Does crossover innervation really affect the clinical outcome？ A comparison of outcome between unilateral and bilateral digital nerve repair

Digital nerve injuries are the mostly detected nerve injury in the upper extremity. However, since the clinical phenomenon of crossover innervation at some degree from uninjured digital nerve to the in- jured side occurs after digital nerve injuries is sustained, one could argue that this concept might even result in the overestimation of the outcome of the digital nerve repair. With this knowledge in mind, this study aimed to present novel, pure, focused and valuable clinical data by comparing the outcomes of bilateral and unilateral digital nerve repair. A retrospective review of 28 fingers with unilateral or bilateral digital nerve repair using end-to-end technique in 19 patients within 2 years was performed. Weber＇s two-point discrimination, sharp/dull discrimination, warm/cold sensation and Visual Analog Scale scoring were measured at final 12-month follow ups in all patients. There was no significant difference in recovery of sensibility after unilateral and bilateral digital nerve repairs. Though there is crossover innervation microscopically, it is not important in the clinical evaluation period. According to clinical findings from this study, crossover innervations appear to be negligible in the estimation of outcomes of digital neurorrhaphy.

The TBD method for dim targets based on multi-level crossover and matching operator

In order to improve the tracking performance in this paper following TBD(Track before Detection) framework multi-level crossover and matching operator is presented.In data association stage the greedy principle is adopted to handle time complexity in DPA and at the same time crossover mathing operator is given to construct candidate trajectory.In addition the corresponding strategy is introduced in preprocessing and postprocessing to remove clutter and suppress false alarm rate.By the experimental comparison and analysis it can be found that the method is more perfer to strengthen the tracking performance of targets with SNR < 2.0 dB.

Superconductivity of the FeSe/SrTiO3 Interface in View of BCS–BEC Crossover

In paired Fermi systems,strong many-body effects exhibit in the crossover regime between the Bardeen–Cooper–Schrieffer(BCS)and the Bose–Einstein condensation(BEC)limits.The concept of the BCS–BEC crossover,which is studied intensively in the research field of cold atoms,has been extended to condensed matters.Here by analyzing the typical superconductors within the BCS–BEC phase diagram,we find that FeSe-based superconductors are prone to shift their positions in the BCS–BEC crossover regime by charge doping or substrate substitution,since their Fermi energies and the superconducting gap sizes are comparable.Especially at the interface of single-layer FeSe on SrTiO3 substrate,the superconductivity is relocated closer to the crossover unitary than other doped FeSe-based materials,indicating that the pairing interaction is effectively modulated.We further show that hole-doping can drive the interfacial system into the phase with possible pre-paired electrons,demonstrating its flexible tunability within the BCS–BEC crossover regime.

Investigation of the Spin Crossover Complex [Fe(bapbpy)(NCS)_2 ] in Its Low-spin and Highspin State by DFT/TD-DFT/BS-DFT Calculations

The spin crossover（SCO） compound [Fe（bapbpy）（NCS）2],where bapbpy contains two fused N,N-bis（2-pyridyl）amines,has been studied by DFT/TD-DFT/BS-DFT methods.Several density functionals and basis sets were used in the calculation to obtain optimized geometries of the compound in the low-（LS） and high-spin（HS） states.The vibrational modes and IR spectra,spin splitting energies,excited states and UV/Vis absorption spectra were obtained.The structural parameters of the calculated isolated complex are in good agreement with the X-ray data.We investigate three dimers of [Fe（bapbpy）（NCS）2] complex for their magnetic properties.It has been found that the complex（1,3） has ferromagnetic character while the others are antiferromagnetic in nature by using a broken symmetry approach in the DFT framework（BS-DFT） with support from the coupling constant values（J） and spin density plots.

A Wideband E-Plane Crossover Coupler for Terahertz Applications

In this paper,a new approach to design terahertz(THz)E-plane crossover coupler is reported.By cascading two symmetrical septum polarizers,a simple structure with wide operating bandwidth and high isolation performance is achieved.The working principle is explained by operating waveguide modes.To simplify the optimization process,the scattering matrix(S-matrix)of the crossover is calculated.Two prototypes loaded and unloaded electromagnetic band gap(EBG)are fabricated and measured.The electrical contact problem at assembly plane is eliminated by the prototype loaded EBG.A measured bandwidth of 17.3%from 92.5 to 110 GHz for reflection and isolation coefficients<-15 dB and transmission coefficient>-2 dB is achieved.

Differential Evolution Algorithm Based on Ensemble of Constraint Handling Techniques and Multi-Population Framework

Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differential evolution algorithm?based on ensemble of constraint handling techniques and multi-population?framework, called ECMPDE. First, handling three improved variants of differential evolution algorithms are dynamically matched with two constraint handling techniques through the constraint allocation mechanism. Each combination includes three variants with corresponding constraint handling technique?and these combinations are in the set. Second, the population is divided into three smaller subpopulations and one larger reward subpopulation. Then a combination with three constraint algorithms is randomly selected from the set, and the three constraint algorithms are run in three sub-populations respectively. According to the improvement of fitness value, the optimal constraint?algorithm is selected to run on the reward sub-population, which can share?information and close cooperation among populations. In order to verify the effectiveness of the proposed algorithm, 12 standard constraint optimization problems?and 10 engineering constraint optimization problems are tested. The experimental results show that ECMPDE is an effective algorithm for solving constraint optimization problems.

An Improved Genetic Algorithm with Quasi-Gradient Crossover

The convergence of genetic algorithm is mainly determined by its core operation crossover operation. When the objective function is a multiple hump function, traditional genetic algorithms are easily trapped into local optimum, which is called premature conver- gence. In this paper, we propose a new genetic algorithm with improved arithmetic crossover operation based on gradient method. This crossover operation can generate offspring along quasi-gradient direction which is the Steepest descent direction of the value of objective function. The selection operator is also simplified, every individual in the population is given an opportunity to get evolution to avoid complicated selection algorithm. The adaptive mutation operator and the elitist strategy are also applied in this algorithm. The case 4 indicates this algorithm can faster converge to the global optimum and is more stable than the conventional genetic algorithms.

Hybrid Chaotic Salp Swarm with Crossover Algorithm for Underground Wireless Sensor Networks

Resource management in Underground Wireless Sensor Networks(UWSNs)is one of the pillars to extend the network lifetime.An intriguing design goal for such networks is to achieve balanced energy and spectral resource utilization.This paper focuses on optimizing the resource efficiency in UWSNs where underground relay nodes amplify and forward sensed data,received from the buried source nodes through a lossy soil medium,to the aboveground base station.A new algorithm called the Hybrid Chaotic Salp Swarm and Crossover(HCSSC)algorithm is proposed to obtain the optimal source and relay transmission powers to maximize the network resource efficiency.The proposed algorithm improves the standard Salp Swarm Algorithm(SSA)by considering a chaotic map to initialize the population along with performing the crossover technique in the position updates of salps.Through experimental results,the HCSSC algorithm proves its outstanding superiority to the standard SSA for resource efficiency optimization.Hence,the network’s lifetime is prolonged.Indeed,the proposed algorithm achieves an improvement performance of 23.6%and 20.4%for the resource efficiency and average remaining relay battery per transmission,respectively.Furthermore,simulation results demonstrate that the HCSSC algorithm proves its efficacy in the case of both equal and different node battery capacities.

Single-layer graphene as a highly selective barrier for vanadium crossover with high proton selectivity

We report near-zero crossover for vanadium cross-permeation through single-layer graphene immobilized at the interface of two Nafion?polymer electrolyte membranes.Vanadium ion diffusion and migration,including proton mobility through membrane composites,were studied with and without graphene under diffusion and migration conditions.Single-layer graphene was found to effectively inhibit vanadium ion diffusion and migration under specific conditions.The single-layer graphene composites also enabled remarkable ion transmission selectivity improvements over pure Nafion membranes,with proton transport being four orders of magnitude faster than vanadium ion transport.Resistivity values of 0.02±0.005Ωcm^(2) for proton and 223±4Ωcm^(2) for vanadium ion through single atomic layer graphene are reported.This high selectivity may have significant impact on flow battery applications or for other electrochemical devices where proton conductivity is required,and transport of other species is detrimental.Our results emphasize that crossover may be essentially completely eliminated in some cases,enabling for greatly improved operational viability.

Composition of Web Services of Multi-Population Adaptive Genetic Algorithm Based on Cosine Improvement

Web quality of service (QoS) awareness requires not only the selection of specific services to complete specific tasks, but also the comprehensive quality of service of the whole web service composition. How to select the web service composition with the highest comprehensive QoS is a NP hard problem. In this paper, an improved multi population genetic algorithm is proposed. Cosine adaptive operator is added to the algorithm to avoid premature algorithm caused by improper genetic operator and the disadvantage of destroying excellent individuals in later period. Experimental results show that compared with the common genetic algorithm and multi population genetic algorithm, this algorithm has the advantages of shorter time consumption and higher accuracy, and effectively avoids the loss of effective genes in the population.

Crossover from 2-dimensional to 3-dimensional aggregations of clusters on square lattice substrates

A Monte Carlo study on the crossover from 2-dimensional to 3-dimensional aggregations of clusters is presented. Based on the traditional cluster-cluster aggregation （CCA） simulation, a modified growth model is proposed. The clusters （including single particles and their aggregates） diffuse with diffusion step length 1 （1≤l≤7） and aggregate on a square lattice substrate. If the number of particles contained in a cluster is larger than a critical size Sc, the particles at the edge of the cluster have a possibility to jump onto the upper layer, which results in the crossover from 2-dimensional to 3-dimensional aggregations. Our simulation results are in good agreement with the experimental findings.

Power Analysis and Sample Size Determination for Crossover Trials with Application to Bioequivalence Assessment of Topical Ophthalmic Drugs Using Serial Sampling Pharmacokinetic Data

Objective To develop methods for determining a suitable sample size for bioequivalence assessment of generic topical ophthalmic drugs using crossover design with serial sampling schemes.Methods The power functions of the Fieller-type confidence interval and the asymptotic confidence interval in crossover designs with serial-sampling data are here derived.Simulation studies were conducted to evaluate the derived power functions.Results Simulation studies show that two power functions can provide precise power estimates when normality assumptions are satisfied and yield conservative estimates of power in cases when data are log-normally distributed.The intra-correlation showed a positive correlation with the power of the bioequivalence test.When the expected ratio of the AUCs was less than or equal to 1, the power of the Fieller-type confidence interval was larger than the asymptotic confidence interval.If the expected ratio of the AUCs was larger than 1, the asymptotic confidence interval had greater power.Sample size can be calculated through numerical iteration with the derived power functions.Conclusion The Fieller-type power function and the asymptotic power function can be used to determine sample sizes of crossover trials for bioequivalence assessment of topical ophthalmic drugs.