GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

Optimization of dynamic aperture by using non-dominated sorting genetic algorithm-Ⅱ in a diffraction-limited storage ring with solenoids for generating round beam

Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing the number of photons getting discarded and better phase space match between photon and electron beam.Conventional methods of obtaining round beam inescapably results in a reduction of dynamic aperture(DA).In order to recover the DA as much as possible for improving the injection efficiency,the DA optimization by using Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ)to generate round beam,particularly to one of the designed lattice of the High Energy Photon Source(HEPS)storage ring,are presented.Method According to the general unconstrained model of NSGA-Ⅱ,we modified the standard model by using parallel computing to optimize round beam lattices with errors,especially for a strong coupling,such as solenoid scheme.Results and conclusion The results of numerical tracking verify the correction of the theory framework of solenoids with fringe fields and demonstrates the feasibility on the HEPS storage ring with errors to operate in round beam mode after optimizing DA.

Multi-objective optimization of the cathode catalyst layer micro-composition of polymer electrolyte membrane fuel cells using a multi-scale,two-phase fuel cell model and data-driven surrogates

Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.

Orbit Design for Responsive Space Using Multiple-objective Evolutionary Computation

Responsive orbits have exhibited advantages in emergencies for their excellent responsiveness and coverage to targets.Generally,there are several conflicting metrics to trade in the orbit design for responsive space.A special multiple-objective genetic algorithm,namely the Nondominated Sorting Genetic AlgorithmⅡ(NSGAⅡ),is used to design responsive orbits.This algorithm has considered the conflicting metrics of orbits to achieve the optimal solution,including the orbital elements and launch programs of responsive vehicles.Low-Earth fast access orbits and low-Earth repeat coverage orbits,two subtypes of responsive orbits,can be designed using NSGAI under given metric tradeoffs,number of vehicles,and launch mode.By selecting the optimal solution from the obtained Pareto fronts,a designer can process the metric tradeoffs conveniently in orbit design.Recurring to the flexibility of the algorithm,the NSGAI promotes the responsive orbit design further.

Multi-objective Dimensional Optimization of a 3-DOF Translational PKM Considering Transmission Properties

Multi-objective dimensional optimization of parallel kinematic manipulators(PKMs) remains a challenging and worthwhile research endeavor. This paper presents a straightforward and systematic methodology for implementing the structure optimization analysis of a 3-prismatic-universal-universal(PUU) PKM when simultaneously considering motion transmission, velocity transmission and acceleration transmission. Firstly, inspired by a planar four-bar linkage mechanism, the motion transmission index of the spatial parallel manipulator is based on transmission angle which is defined as the pressure angle amongst limbs. Then, the velocity transmission index and acceleration transmission index are derived through the corresponding kinematics model. The multi-objective dimensional optimization under specific constraints is carried out by the improved non-dominated sorting genetic algorithm(NSGA Ⅱ), resulting in a set of Pareto optimal solutions. The final chosen solution shows that the manipulator with the optimized structure parameters can provide excellent motion, velocity and acceleration transmission properties.