Modified Differential Evolution Algorithm for Solving Dynamic Optimization with Existence of Infeasible Environments

Dynamic constrained optimization is a challenging research topic in which the objective function and/or constraints change over time.In such problems,it is commonly assumed that all problem instances are feasible.In reality some instances can be infeasible due to various practical issues,such as a sudden change in resource requirements or a big change in the availability of resources.Decision-makers have to determine whether a particular instance is feasible or not,as infeasible instances cannot be solved as there are no solutions to implement.In this case,locating the nearest feasible solution would be valuable information for the decision-makers.In this paper,a differential evolution algorithm is proposed for solving dynamic constrained problems that learns from past environments and transfers important knowledge from them to use in solving the current instance and includes a mechanism for suggesting a good feasible solution when an instance is infeasible.To judge the performance of the proposed algorithm,13 well-known dynamic test problems were solved.The results indicate that the proposed algorithm outperforms existing recent algorithms with a margin of 79.40%over all the environments and it can also find a good,but infeasible solution,when an instance is infeasible.

Dynamic Optimization Method on Electromechanical Coupling System by Exponential Inertia Weight Particle Swarm Algorithm

Dynamic optimization of electromechanical coupling system is a significant engineering problem in the field of mechatronics. The performance improvement of electromechanical equipment depends on the system design parameters. Aiming at the spindle unit of refitted machine tool for solid rocket, the vibration acceleration of tool is taken as objective function, and the electromechanical system design parameters are appointed as design variables. Dynamic optimization model is set up by adopting Lagrange-Maxwell equations, Park transform and electromechanical system energy equations. In the procedure of seeking high efficient optimization method, exponential function is adopted to be the weight function of particle swarm optimization algorithm. Exponential inertia weight particle swarm algorithm（EPSA）, is formed and applied to solve the dynamic optimization problem of electromechanical system. The probability density function of EPSA is presented and used to perform convergence analysis. After calculation, the optimized design parameters of the spindle unit are obtained in limited time period. The vibration acceleration of the tool has been decreased greatly by the optimized design parameters. The research job in the paper reveals that the problem of dynamic optimization of electromechanical system can be solved by the method of combining system dynamic analysis with reformed swarm particle optimizati on. Such kind of method can be applied in the design of robots, NC machine, and other electromechanical equipments.

Decision-Making Model for Farmer Choosing Land Use Based upon Dynamic Optimization Theory

Using the dynamic optimization theory, we described a decision-making model for farmer choosing land use when there are several different kinds of uses for land. To obtain an empirical model that could be easily applied, decision rules for farmer with a single static expectation were given.

Multi-Objective Multi-Variable Large-Size Fan Aerodynamic Optimization by Using Multi-Model Ensemble Optimization Algorithm

The constrained multi-objective multi-variable optimization of fans usually needs a great deal of computational fluid dynamics(CFD)calculations and is time-consuming.In this study,a new multi-model ensemble optimization algorithm is proposed to tackle such an expensive optimization problem.The multi-variable and multi-objective optimization are conducted with a new flexible multi-objective infill criterion.In addition,the search direction is determined by the multi-model ensemble assisted evolutionary algorithm and the feature extraction by the principal component analysis is used to reduce the dimension of optimization variables.First,the proposed algorithm and other two optimization algorithms which prevail in fan optimizations were compared by using test functions.With the same number of objective function evaluations,the proposed algorithm shows a fast convergency rate on finding the optimal objective function values.Then,this algorithm was used to optimize the rotor and stator blades of a large axial fan,with the efficiencies as the objectives at three flow rates,the high,the design and the low flow rate.Forty-two variables were included in the optimization process.The results show that compared with the prototype fan,the total pressure efficiencies of the optimized fan at the high,the design and the low flow rate were increased by 3.35%,3.07%and 2.89%,respectively,after CFD simulations for 500 fan candidates with the constraint for the design pressure.The optimization results validate the effectiveness and feasibility of the proposed algorithm.

A strategy for lightweight designing of a railway vehicle car body including composite material and dynamic structural optimization

Rolling stock manufacturers are finding structural solutions to reduce power required by the vehicles,and the lightweight design of the car body represents a possible solution.Optimization processes and innovative materials can be combined in order to achieve this goal.In this framework,we propose the redesign and optimization process of the car body roof for a light rail vehicle,introducing a sandwich structure.Bonded joint was used as a fastening system.The project was carried out on a single car of a modern tram platform.This preliminary numerical work was developed in two main steps:redesign of the car body structure and optimization of the innovated system.Objective of the process was the mass reduction of the whole metallic structure,while the constraint condition was imposed on the first frequency of vibration of the system.The effect of introducing a sandwich panel within the roof assembly was evaluated,focusing on the mechanical and dynamic performances of the whole car body.A mass saving of 63%on the optimized components was achieved,corresponding to a 7.6%if compared to the complete car body shell.In addition,a positive increasing of 17.7%on the first frequency of vibration was observed.Encouraging results have been achieved in terms of weight reduction and mechanical behaviour of the innovated car body.

WiFi6 Dynamic Channel Optimization Method for Fault Tolerance in Power Communication Network

As the scale of power networks has expanded,the demand for multi-service transmission has gradually increased.The emergence of WiFi6 has improved the transmission efficiency and resource utilization of wireless networks.However,it still cannot cope with situations such as wireless access point(AP)failure.To solve this problem,this paper combines orthogonal fre-quency division multiple access(OFDMA)technology and dynamic channel optimization technology to design a fault-tolerant WiFi6 dynamic resource optimization method for achieving high quality wireless services in a wirelessly covered network even when an AP fails.First,under the premise of AP layout with strong coverage over the whole area,a faulty AP determination method based on beacon frames(BF)is designed.Then,the maximum signal-to-interference ratio(SINR)is used as the principle to select AP reconnection for the affected users.Finally,this paper designs a dynamic access selection model(DASM)for service frames of power Internet of Things(IoTs)and a schedul-ing access optimization model(SAO-MF)based on multi-frame transmission,which enables access optimization for differentiated services.For the above mechanisms,a heuristic resource allocation algorithm is proposed in SAO-MF.Simulation results show that the method can reduce the delay by 15%and improve the throughput by 55%,ensuring high-quality communication in power wireless networks.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

Suitable region of dynamic optimal interpolation for efficiently altimetry sea surface height mapping

The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).

Dynamic Manipulability and Optimization of a Two DOF Parallel Mechanism

The dynamic dexterity is an important issue for manipulator design, some indices were proposed for analyzing dynamic dexterity, but they can evaluate the dynamic performance just at one pose in the workspaee of the manipulator, and can＇t be applied to dynamic design expediently. Much work has been done in the kinematic optimization, but the work in the dynamic optimization is much less. A global dynamic condition number index is proposed and applied to the dynamic optimization design the parallel manipulator. This paper deals with the dynamic manipulability and dynamic optimization of a two degree-of-freedom （DOF） parallel manipulator. The particular velocity and particular angular velocity matrices of each moving part about the part＇s pivot point are derived fi＇om the kinematic formulation of the manipulator, and the inertial force and inertial movement are obtained utilizing Newton-Euler formulation, then the inverse dynamic model of the parallel manipulator is proposed based on the virtual work principle. The general inertial ellipsoid and dynamic manipulability ellipsoid are applied to evaluate the dynamic performance of the manipulator, a global dynamic condition number index based on the condition number of general inertial matrix in the workspace is proposed, and then the link lengths of the manipulator is redesigned to optimize the dynamic manipulability by this index. The dynamic manipulability of the origin mechanism and the optimized mechanism are compared, the result shows that the optimized one is much better. The global dynamic condition number index has good effect in evaluating the dynamic dexterity of the whole workspace, and is efficient in the dynamic optimal design of the parallel manipulator.

Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in Cloud Computing

The energy consumption in large-scale data centers is attracting more and more attention today with the increasing data center energy costs making the enhanced performance very expensive. This is becoming a bottleneck to further developments in terms of both scale and performance of cloud computing. Thus, the reduction of the energy consumption by data centers is becoming a key research topic in green IT and green computing. The web servers providing cloud service computing run at various speeds for different scenarios. By shifting among these states using speed scaling, the energy consumption is proportional to the workload, which is termed energy-proportionality. This study uses stochastic service decision nets to investigate energy-efficient speed scaling on web servers. This model combines stochastic Petri nets with Markov decision process models. This enables the model to dynamically optimize the speed scaling strategy and make performance evaluations. The model is graphical and intuitive enough to characterize complicated system behavior and decisions. The model is service-oriented using the typical service patterns to reduce the complex model to a simple model with a smaller state space. Performance and reward equivalent analyse substantially reduces the system behavior sub-net. The model gives the optimal strategy and evaluates performance and energy metrics more concisely.

Multiobjective evolutionary algorithm for dynamic nonlinear constrained optimization problems

A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.

Fuzzy Genetic Sharing for Dynamic Optimization

Recently,genetic algorithms(GAs) have been applied to multi-modal dynamic optimization(MDO).In this kind of optimization,an algorithm is required not only to find the multiple optimal solutions but also to locate a dynamically changing optimum.Our fuzzy genetic sharing(FGS) approach is based on a novel genetic algorithm with dynamic niche sharing(GADNS).FGS finds the optimal solutions,while maintaining the diversity of the population.For this,FGS uses several strategies.First,an unsupervised fuzzy clustering method is used to track multiple optima and perform GADNS.Second,a modified tournament selection is used to control selection pressure.Third,a novel mutation with an adaptive mutation rate is used to locate unexplored search areas.The effectiveness of FGS in dynamic environments is demonstrated using the generalized dynamic benchmark generator(GDBG).

Diploidy in evolutionary algorithms for dynamic optimization problems A best-chromosome-wins dominance mechanism

Purpose–In this work,the authors show the performance of the proposed diploid scheme(a representation where each individual contains two genotypes)with respect to two dynamic optimization problems,while addressing drawbacks the authors have identified in previous works which compare diploid evolutionary algorithms(EAs)to standard EAs.The paper aims to discuss this issue.Design/methodology/approach–In the proposed diploid representation of EA,each individual possesses two copies of the genotype.In order to convert this pair of genotypes to a single phenotype,each genotype is individually evaluated in relation to the fitness function and the best genotype is presented as the phenotype.In order to provide a fair and objective comparison,the authors make sure to compare populations which contain the same amount of genetic information,where the only difference is the arrangement and interpretation of the information.The two representations are compared using two shifting fitness functions which change at regular intervals to displace the global optimum to a new position.Findings–For small fitness landscapes the haploid(standard)and diploid algorithms perform comparably and are able to find the global optimum very quickly.However,as the search space increases,rediscovering the global optimum becomes more difficult and the diploid algorithm outperforms the haploid algorithm with respect to how fast it relocates the new optimum.Since both algorithms use the same amount of genetic information,it is only fair to conclude it is the unique arrangement of the diploid algorithm that allows it to explore the search space better.Originality/value–The diploid representation presented here is novel in that instead of adopting a dominance scheme for each allele(value)in the vector of values that is the genotype,dominance is adopted across the entire genotype in relation to its homologue.As a result,this representation can be extended across any alphabet,for any optimization function.

Power Flow Response Based Dynamic Topology Optimization of Bi-material Plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.

Dynamic Routing Optimization Algorithm for Software Defined Networking

Time and space complexity is themost critical problemof the current routing optimization algorithms for Software Defined Networking(SDN).To overcome this complexity,researchers use meta-heuristic techniques inside the routing optimization algorithms in the OpenFlow(OF)based large scale SDNs.This paper proposes a hybrid meta-heuristic algorithm to optimize the dynamic routing problem for the large scale SDNs.Due to the dynamic nature of SDNs,the proposed algorithm uses amutation operator to overcome the memory-based problem of the ant colony algorithm.Besides,it uses the box-covering method and the k-means clustering method to divide the SDN network to overcome the problemof time and space complexity.The results of the proposed algorithm compared with the results of other similar algorithms and it shows that the proposed algorithm can handle the dynamic network changing,reduce the network congestion,the delay and running times and the packet loss rates.

Dynamic Multi-objective Optimization of Chemical Processes Using Modified BareBones MOPSO Algorithm

Dynamic multi-objective optimization is a complex and difficult research topic of process systems engineering. In this paper,a modified multi-objective bare-bones particle swarm optimization( MOBBPSO) algorithm is proposed that takes advantage of a few parameters of bare-bones algorithm. To avoid premature convergence,Gaussian mutation is introduced; and an adaptive sampling distribution strategy is also used to improve the exploratory capability. Moreover, a circular crowded sorting approach is adopted to improve the uniformity of the population distribution.Finally, by combining the algorithm with control vector parameterization,an approach is proposed to solve the dynamic optimization problems of chemical processes. It is proved that the new algorithm performs better compared with other classic multiobjective optimization algorithms through the results of solving three dynamic optimization problems.

Cooperative Path Dynamic Planning Model of UCAV Team Based on Global Optimization Method

Cooperative path dynamic planning of a UCAV （unmanned combat air vehicle） team not only considers the capability of task requirement of single UCAV, but also considers the cooperative dynamic connection among members of the UCAV team. A cooperative path dynamic planning model of the UCAV team by applying a global optimization method is discussed in this paper and the corresponding model is built and analyzed. By the example simulation, the reasonable result acquired indicates that the model could meet dynamic planning demand under the circumstance of membership functions. The model is easy to be realized and has good practicability.

Central Force Optimization with Gravity <0, Elitism, and Dynamic Threshold Optimization: An Antenna Application, 6-Element Yagi-Uda Arrays

This paper investigates the effect of adding three extensions to Central Force Optimization when it is used as the Global Search and Optimization method for the design and optimization of 6-elementYagi-Uda arrays. Those extensions are Negative Gravity, Elitism, and Dynamic Threshold Optimization. The basic CFO heuristic does not include any of these, but adding them substantially improves the algorithm’s performance. This paper extends the work reported in a previous paper that considered only negative gravity and which showed a significant performance improvement over a range of optimized arrays. Still better results are obtained by adding to the mix Elitism and DTO. An overall improvement in best fitness of 19.16% is achieved by doing so. While the work reported here was limited to the design/optimization of 6- element Yagis, the reasonable inference based on these data is that any antenna design/optimization problem, indeed any Global Search and Optimization problem, antenna or not, utilizing Central Force Optimization as the Global Search and Optimization engine will benefit by including all three extensions, probably substantially.

A Hybrid Immigrants Scheme for Genetic Algorithms in Dynamic Environments

Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution（s） of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments.