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 and Correlation Analysis of Grain Characters in Three-line Hybrid Rice

Abst[Objective] This study was to understand the genetic dynamics of three-line hybrid rice, and explore the respective effect of sterile line and restoring line on grain characters of hybrid rica. [Method] Four three-line stedle lines and 27 restoring lines（cultivars） commonly culti- vated in Central China region were regarded as expadmental materials to conduct 4 x27NCII cross design, and the grain characters of three-line hybrid rico were analyzed at genetic and correlation levels. [ Result] Four characters of grain length, grain width, 1 000-grain weight and length- width ratio play the leading role in additive gene effect; these four characters were simultaneously influenced by male parent and female parent, but the effect from male parent was relatively larger. The grain length, grain width, 1 000-grain weight and length-width ratio all have high brood hedtabUities（ respectively 99.65%, 98.31%, 95.27% and 98.81% ）. Correlation analysis showed that grain length was positively correlated with 1 000-grain weight and length-width ratio at extremely significant level; 1 000-grain weight was positively correlated with grain length and length- width ratio at extremely significant level, and was insignificantly correlated with grain width; grain width was negatively correlated with grain length and length-width ratio at extremely significant level. Path analysis showed that the direct path coefficients of grain length, grain width and 1 0（30- grain weight to length-width ratio were 0.624 6, -0.555 9 and -0.015 8, respectively. [ Conclusion] This study systematically analyzed the effects of stedle line and restoring line on grain characters of hybrid rice, which provided theoretical basis for breeding high quality and yield hy- brid dce.

Reproduction of the Three-line Genic Male Sterile Line Parent Mian 7MB-1 （Brasscia Napus L.） and Seed Production of F1 Based on Somatic Tissue Culture

[Objective] The aim was to study the reproduction of the three-line genic male sterile （GMS） lineparent Mian7MB-1 （B. NapusL.） and the seed production of F1 through somatic tissue culture. [Methed] Through hybridization, a new breeding material Mian 7MB-1 in three-line genic temporary maintainer line propagated by tissue culture was used to improve the sterile plant rate of rapeseed in dual-purpose recessive GMS line, such as Mian 7AB type, S45AB type, and etc. And then the variety comparative test was performed. [Result] In order to avoid some fertility restoration phenomena occurring during the process of self-reproduction, Mian 7AB was propagated in bulk with somatic tissue culture of temporary maintainer line plant stem. The propagated temporary maintainer line seedlings were applied to the breeding and seed production of net room male sterile line parent, promoting the sterile plant rate of the male sterile line parent to 91.7% -93.5%. The male sterile line parents per hectare were enough for the seed production of hybrid F1 in 7 500 -15 000 hm^2. [ Conclusion ] Compared with the original dual-purpose GMS line, the seed production ultilizing male sterile line with high sterile plant rate greatly reduced the labor, significantly improved the seed yield, ensuring the seed quality and forming a perfect breeding and seed production system.

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。

Technical Specification for Producing Hybrid Pepper Seed Using Three-line Male Sterility

This paper described the whole process of three line hybrid pepper seed production in detail, including requirement of the seed production base, parent culti- vation, field management, and specified the key operation techniques in seed pro- duction, such as parental impurity removal to preserve pure state, pollen collection, pollination and seed collecting essentials. This specification is of guiding significance for the production of hybrid pepper seed and ensuring the purity of hybrid pepper seed.

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.

Studies on the Developmental Genetics of Tiller Number in Three-line Indica Hybrid Rice

Following NCI design, the developmental genetic behavior of tiller number (TN) in three-line indica hybrid rice was studied using additive-dominance developmental genetic models and the corresponding statistical methods. The results showed that dominance effects were predominant for TN. The expression of those additive effects were affected by environment and genotype interaction, but the expression of dominance effects were not affected. Heterosis was the strongest in the middle developmental periods of TN. Additive effects and dominance effects were selectively expressed throughout in the entire tillering developmental stage. Analysis of genetic correlation between TN at different stages and the productive panicles indicated that a close correlation appeared earlier in the populations with higher heterosis than in those with less heterosis. Utilization of heterosis at the middle tillering stage might enhance the final biomass but reduce the percentage of productive panicles.

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.

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.

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.