Multi-objective optimization of membrane structures based on Pareto Genetic Algorithm

A multi-objective optimization method based on Pareto Genetic Algorithm is presented for shape design of membrane structures from a structural view point.Several non-dimensional variables are defined as optimization variables,which are decision factors of shapes of membrane structures.Three objectives are proposed including maximization of stiffness,maximum uniformity of stress and minimum reaction under external loads.Pareto Multi-objective Genetic Algorithm is introduced to solve the Pareto solutions.Consequently,the dependence of the optimality upon the optimization variables is derived to provide guidelines on how to determine design parameters.Moreover,several examples illustrate the proposed methods and applications.The study shows that the multi-objective optimization method in this paper is feasible and efficient for membrane structures;the research on Pareto solutions can provide explicit and useful guidelines for shape design of membrane structures.

MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.

Optimization of maintenance strategy for high-speed railwaycatenary system based on multistate model

A multi-objective optimization model considering both reliability and maintenance cost is proposed to solve the contradiction between reliability and maintenance cost in high-speed railway catenary system maintenance activities.The non-dominated sorting genetic algorithm 2(NSGA2)is applied to multi-objective optimization,and the optimization result is a set of Pareto solutions.Firstly,multistate failure mode analysis is conducted for the main devices leading to the failure of catenary,and then the reliability and failure mode of the whole catenary system is analyzed.The mathematical relationship between system reliability and maintenance cost is derived considering the existing catenary preventive maintenance mode to improve the reliability of the system.Secondly,an improved NSGA2(INSGA2)is proposed,which strengths population diversity by improving selection operator,and introduces local search strategy to ensure that population distribution is more uniform.The comparison results of the two algorithms before and after improvement on the zero-ductility transition(ZDT)series functions show that the population diversity is better and the solution is more uniform using INSGA2.Finally,the INSGA2 is applied to multi-objective optimization of system reliability and maintenance cost in different maintenance periods.The decision-makers can choose the reasonable solutions as the maintenance plans in the optimization results by weighing the relationship between the system reliability and the maintenance cost.The selected maintenance plans can ensure the lowest maintenance cost while the system reliability is as high as possible.

Multi-Objective Task Assignment for Maximizing Social Welfare in Spatio-Temporal Crowdsourcing

With the development of the Internet of Things(IoT),spatio-temporal crowdsourcing(mobile crowdsourcing)has become an emerging paradigm for addressing location-based sensing tasks.However,the delay caused by network transmission has led to low data processing efficiency.Fortunately,edge computing can solve this problem,effectively reduce the delay of data transmission,and improve data processing capacity,so that the crowdsourcing platform can make better decisions faster.Therefore,this paper combines spatio-temporal crowdsourcing and edge computing to study the Multi-Objective Optimization Task Assignment(MOO-TA)problem in the edge computing environment.The proposed online incentive mechanism considers the task difficulty attribute to motivate crowd workers to perform sensing tasks in the unpopular area.In this paper,the Weighted and Multi-Objective Particle Swarm Combination(WAMOPSC)algorithm is proposed to maximize both platform’s and crowd workers’utility,so as to maximize social welfare.The algorithm combines the traditional Linear Weighted Summation(LWS)algorithm and Multi-Objective Particle Swarm Optimization(MOPSO)algorithm to find pareto optimal solutions of multi-objective optimization task assignment problem as much as possible for crowdsourcing platform to choose.Through comparison experiments on real data sets,the effectiveness and feasibility of the proposed method are evaluated.

A structural design of multilevel decomposition and domain mapping

An integrated optimization design was described using multilevel decomposition technique on the base of the parametric distribution and independent axiom at the stages of lower level. Based on Pareto optimum solution, the detailed parameters at lower level can be defined into the independent axiom. The suspension design was used as the simulation example. In an axiomatic design for the optimization design, the uncoupled and decoupled designs between functional requirements and design parameters are generally needed. But using the design sensitivity(or screening) of design parameters, the approximate uncoupled design is developed on behalf of the decoupled and coupled designs. Successive design parameters were applied to the suspension of torsion beam axle. The structural performance increases by 18%. The kinematic and compliance performance increases by 6% within the feasible ranges.

Time variant multi-objective linear fractional interval-valued transportation problem

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.

Novel electromagnetism-like mechanism method for multiobjective optimization problems

As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.

Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games

In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.

The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces

In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.

Pareto optimal allocation of fault current limiter based on immune algorithm considering cost and mitigation effect

This paper presents a multi-objective Pareto optimal method for allocation of fault current limiters based on an immune algorithm, which takes into account two objectives of the cost and fault current mitigation effect. A sensitivity factor calculation method based on the rate of fault current mitigation is proposed to reduce the search space and improve the efficiency of the algorithm.In this approach, the objective functions related to the cost and fault current mitigation effect are established. A modified inversion operator based on equal cost is proposed to converge to global optimal solutions more effectively. The proposed algorithm is tested on the IEEE39-bus system, and obtains the Pareto optimal solutions,from which the user can select the most suitable solutions according to the preferences and relative importance of the objective functions. Simulation results are used to verify the proposed method.

Optimization of Roll Shifting Strategy of Alternately Rolling in Hot Strip Mill

An optimization solution to roll shifting strategy for alternately rolling campaign is presented. All the strips in a rolling campaign are divided into narrow strips and wide ones, and shifting position of narrow strips is obtained by the recursive method, and then shifting position of wide strips is optimized by NSGA-II which is a multiobjective genetic algorithm. For wide strips, a multi-objective optimization model of roll shifting strategy is pro posed, which takes 3 wear contour factors including edge smoothness, body smoothness and edge drop as optimization objectives. The Pareto optimal front of roll shifting strategy can be gained quickly by NSGA-II, which suggests a series of alternative solutions to roll shifting strategy. Analysis shows that the conflict exists among the 3 objectives. The final optimal solution is selected from the Pareto optimal solutions by the weighted-sum decision-making method. Industrial production proves the validity of the solution, and it can improve strip profile of alternately rolling, reduce strip edge wave, and extend the rolling miles of rolling campaigns.

A Power and Area Optimization Approach of Mixed Polarity Reed-Muller Expression for Incompletely Specified Boolean Functions

The power and area optimization of Reed-Muller （RM） circuits has been widely concerned. However, almost none of the exiting power and area optimization approaches can obtain all the Pareto optimal solutions of the original problem and are efficient enough. Moreover, they have not considered the don＇t care terms, which makes the circuit performance unable to be further optimized. In this paper, we propose a power and area optimization approach of mixed polarity RM expression （MPRM） for incompletely specified Boolean functions based on Non-Dominated Sorting Genetic Algorithm II （NSGA-II）. Firstly, the incompletely specified Boolean function is transformed into zero polarity incompletely specified MPRM （ISMPRM） by using a novel ISMPRM acquisition algorithm. Secondly, the polarity and allocation of don＇t care terms of ISMPRM is encoded as chromosome. Lastly, the Pareto optimal solutions are obtained by using NSGA-II, in which MPRM corresponding to the given chromosome is obtained by using a chromosome conversion algorithm. The results on incompletely specified Boolean functions and MCNC benchmark circuits show that a significant power and area improvement can be made compared with the existing power and area optimization approaches of RM circuits.

A multi-objective design method for seismic retrofitting of existing reinforced concrete frames using pin-supported rocking walls

Over the past several decades,a variety of technical ways have been developed in seismic retrofitting of existing reinforced concrete frames(RFs).Among them,pin-supported rocking walls(PWs)have received much attentions to researchers recently.However,it is still a challenge that how to determine the stiffness demand of PWs and assign the value of the drift concentration factor(DCF)for entire systems rationally and efficiently.In this paper,a design method has been exploited for seismic retrofitting of existing RFs using PWs(RF-PWs)via a multi-objective evolutionary algorithm.Then,the method has been investigated and verified through a practical project.Finally,a parametric analysis was executed to exhibit the strengths and working mechanism of the multi-objective design method.To sum up,the findings of this investigation show that the method furnished in this paper is feasible,functional and can provide adequate information for determining the stiffness demand and the value of the DCFfor PWs.Furthermore,it can be applied for the preliminary design of these kinds of structures.

MD Method in Solving Multiple Criteria Decision Problems Arising from Investment Systems

A new method(MD)to solve multiple objective 0-1 pogramming is given in this paper.It is very convenient for leaders to decide which plan is the beat in a set called Quasi-Pareto solution set as soon as possible. The effect is very good when it,is used in Fujian Province’s"eighth five-year plan".

Inefficiency of Centrally Planned Economies a Differential Game View

This paper presents a differential game model of centrally planned economics(CPEs). The Nash solution and Pareto solutions are derived.It concludes that CPEs is ineffident in the framework of game theory.