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.

Suppression of current-induced membrane discharge of bipolar membranes by regulating ion crossover transport

Bipolar membranes(BPMs)exhibit the unique capability to regulate the operating environment of electrochemical system through the water dissociation-combination processes.However,the industrial utilization of BPMs is limited by instability and serious energy consumption.The current-induced membrane discharge(CIMD)at high-current conditions has a negative influence on the performance of anion-exchange membranes,but the underlying ion transport mechanisms in the BPMs remain unclear.Here,the CIMD-coupled Poisson-Nernst-Planck(PNP)equations are used to explore the ion transport mechanisms in the BPMs for both reverse bias and forward bias at neutral and acid-base conditions.It is demonstrated that the CIMD effect in the reverse-bias mode can be suppressed by enhancing the diffusive transport of salt counter-ions(Na^(+)and Cl^(−))into the BPMs,and that in the forward-bias mode with acid-base electrolytes can be suppressed by matching the transport rate of water counter-ions(H_(3)O^(+)and OH^(−)).Suppressing the CIMD can promote the water dissociation in the reverse-bias mode,as well as overcome the plateau of limiting current density and reduce the interfacial blockage of salt co-ions(Cl^(−))in the anion-exchange layer in the forward-bias mode with acid-base electrolytes.Our work highlights the importance of regulating ion crossover transport on improving the performance of BPMs.

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.

Solving the Generalized Traveling Salesman Problem Using Sequential Constructive Crossover Operator in Genetic Algorithm

The generalized travelling salesman problem(GTSP),a generalization of the well-known travelling salesman problem(TSP),is considered for our study.Since the GTSP is NP-hard and very complex,finding exact solutions is highly expensive,we will develop genetic algorithms(GAs)to obtain heuristic solutions to the problem.In GAs,as the crossover is a very important process,the crossovermethods proposed for the traditional TSP could be adapted for the GTSP.The sequential constructive crossover(SCX)and three other operators are adapted to use in GAs to solve the GTSP.The effectiveness of GA using SCX is verified on some GTSP Library(GTSPLIB)instances first and then compared against GAs using the other crossover methods.The computational results show the success of the GA using SCX for this problem.Our proposed GA using SCX,and swap mutation could find average solutions whose average percentage of excesses fromthe best-known solutions is between 0.00 and 14.07 for our investigated instances.

Game Theory Optimization via Diverse Genetic Crossover Intelligence

Game theory is explored via a maze application where combinatorial optimization occurs with the objective of traversing through a defined maze with an aim to enhance decision support and locate the optimal travel sequence while minimizing computation time. This combinatorial optimization approach is initially demonstrated by utilizing a traditional genetic algorithm (GA), followed by the incorporation of artificial intelligence utilizing embedded rules based on domain-specific knowledge. The aim of this initiative is to compare the results of the traditional and rule-based optimization approaches with results acquired through an intelligent crossover methodology. The intelligent crossover approach encompasses a two-dimensional GA encoding where a second chromosome string is introduced within the GA, offering a sophisticated means for chromosome crossover amongst selected parents. Additionally, parent selection intelligence is incorporated where the best-traversed paths or population members are retained and utilized as potential parents to mate with parents selected within a traditional GA methodology. A further enhancement regarding the utilization of saved optimal population members as potential parents is mathematically explored within this literature.

Genetic Optimization via Diverse Crossover Intelligence

An intelligent crossover methodology within the genetic algorithm (GA) is explored within both mathematical and finite element arenas improving both design and solution convergence time. This improved intelligent crossover outperforms the traditional genetic algorithm combined with a rule-based approach utilizing domain specific knowledge developed by Webb, et al. [1]. The encoding of the improved crossover consists of two chromosome strings within the genetic algorithm where the first string represents the design or solution string, and the second string represents chromosome crossover string intelligence. This improved crossover methodology saves the best population members or designs evaluated from each generation and applies crossover chromosome intelligence to the best saved population members paired with globally selected parents. Enhanced features of this crossover methodology employ the random selection of the best designs from the prior generation as a potential parent coupled with alternating intelligence pairing methods. In addition to this approach, two globally selected parents possess the ability to mate utilizing crossover chromosome string intelligence maintaining the integrity of a global GA search. Overall, the final population following crossover employs both global and best generation design chromosome strings to maximize creativity while enhancing the solution search. This is a modification to a conventional GA that can be translated into GA encoding. This technique is explored initially through a Base 10 mathematical application followed by the examination of plate structural optimization considering stress and displacement constraints. Results from crossover intelligence are compared with the conventional genetic algorithm and from Webb, et al. [1] which illustrates the outcome of a two phase genetic optimization algorithm.

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.

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.

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.

Auto-parametric resonance of a continuous-beam-bridge model under two-point periodic excitation:an experimental investigation and stability analysis

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.

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.

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.

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.

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.

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.