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.

A genetic algorithm for the pareto optimal solution set of multi-objective shortest path problem

Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.

Three-Objective Programming with Continuous Variable Genetic Algorithm

The subject area of multiobjective optimization deals with the investigation of optimization problems that possess more than one objective function. Usually, there does not exist a single solution that optimizes all functions simultaneously;quite the contrary, we have solution set that is called nondominated set and elements of this set are usually infinite. It is from this set decision made by taking elements of nondominated set as alternatives, which is given by analysts. Since it is important for the decision maker to obtain as much information as possible about this set, our research objective is to determine a well-defined and meaningful approximation of the solution set for linear and nonlinear three objective optimization problems. In this paper a continuous variable genetic algorithm is used to find approximate near optimal solution set. Objective functions are considered as fitness function without modification. Initial solution was generated within box constraint and solutions will be kept in feasible region during mutation and recombination.

A Hybrid Multi-Objective Evolutionary Algorithm for Optimal Groundwater Management under Variable Density Conditions

In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.

基于Pareto多目标遗传的LEO卫星网络多业务Qos路由算法

针对LEO卫星网络链路切换阻塞、流量分布不均、路由算法的负载均衡、以及卫星使用寿命期限问题,提出了一种基于Pareto多目标遗传的Qos路由算法。仿真结果表明,本文算法具有更低的呼叫阻塞率和流量分布指数,负载均衡性能较好并能有效减小卫星电池的放电深度,对于LEO卫星网络承载的多种业务类型,拥有更高的综合Qos。

Overview of multi-objective optimization methods

To assist readers to have a comprehensive understanding, the classical and intelligent methods roundly based on precursory research achievements are summarized in this paper. First, basic conception and description about multi-objective (MO) optimization are introduced. Then some definitions and related terminologies are given. Furthermore several MO optimization methods including classical and current intelligent methods are discussed one by one succinctly. Finally evaluations on advantages and disadvantages about these methods are made at the end of the paper.

Modal Analysis and Multi-objective Optimization of Pressurizing Pipeline

The pressurizing pipeline of hot press resonates under the excitation load,which poses a serious hidden danger to the safety of the equipment and the operator.In order to increase the natural frequency of the pressurizing pipeline,modal analysis of the pressurizing pipeline is carried out to study the mechanism of pipeline vibration and common vibration reduction measures.A method of increasing the natural frequency of the pressurizing pipeline was analyzed.The influence of pipeline clamp assembly stiffness,pipeline clamp number and pipeline clamp installation position on the mode of the pressurizing pipeline is studied.Sensitivity analysis is carried out to study the influence of the various parameters on the mode of the pressurizing pipeline.Genetic algorithm based on Pareto optimality is introduced for multi-objective optimization of pressurizing pipeline.The optimization results show that the natural frequency of the pressurizing pipeline increases by 2.4%and the displacement response is reduced by 17.7%.

Multi-objective steady-state optimization of two-chamber microbial fuel cells

A microbial fuel cell(MFC)is a novel promising technology for simultaneous renewable electricity generation and wastewater treatment.Three non-comparable objectives,i.e.power density,attainable current density and waste removal ratio,are often conflicting.A thorough understanding of the relationship among these three conflicting objectives can be greatly helpful to assist in optimal operation of MFC system.In this study,a multiobjective genetic algorithm is used to simultaneously maximizing power density,attainable current density and waste removal ratio based on a mathematical model for an acetate two-chamber MFC.Moreover,the level diagrams method is utilized to aid in graphical visualization of Pareto front and decision making.Three biobjective optimization problems and one three-objective optimization problem are thoroughly investigated.The obtained Pareto fronts illustrate the complex relationships among these three objectives,which is helpful for final decision support.Therefore,the integrated methodology of a multi-objective genetic algorithm and a graphical visualization technique provides a promising tool for the optimal operation of MFCs by simultaneously considering multiple conflicting objectives.

Method of Searching for Earthquake Disaster Evacuation Routes Using Multi-Objective GA and GIS

This study treats the determination of routes for evacuation on foot in earthquake disasters as a multi-objective optimization problem, and aims to propose a method for quantitatively searching for evacuation routes using a multi-objective genetic algorithm (multi-objective GA) and GIS. The conclusions can be summarized in the following three points. 1) A GA was used to design and create an evacuation route search algorithm which solves the problem of the optimization of earthquake disaster evacuation routes by treating it as an optimization problem with multiple objectives, such as evacuation distance and evacuation time. 2) In this method, goodness of fit is set by using a Pareto ranking method to determine the ranking of individuals based on their relative superiorities and inferiorities. 3) In this method, searching for evacuation routes based on the information on present conditions allows evacuation routes to be derived based on present building and road locations.?Further, this method is based on publicly available information;therefore, obtaining geographic information similar to that of this study enables this method to be effective regardless of what region it is applied to, or whether the data regards the past or the future. Therefore, this method has high degree of spatial and temporal reproducibility.

Maintaining an Optimal Flow of Forest Products under a Carbon Market: Approximating a Pareto Set of Optimal Silvicultural Regimes for Eucalyptus fastigata

A competitive co-evolutionary Multi-Objective Genetic Algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes for Eucalyptus fastigata. The three objectives to be maximised included, sawlog, pulpwood and carbon sequestration payment. Three carbon price scenarios (3CPS), i.e. NZ $25, NZ $50 and NZ $100 for a tonne of CO2 sequestered, were used to assess the impact on silvicultural regimes, against a fourth non-carbon Pareto set of efficient regimes (nonCPS), determined from a cc-MOGA with two objectives, i.e. competing sawlog and pulpwood productions. Carbon prices included in stand valuation were found to influence the silvicultural regimes by increasing the rotation length and lowering the final crop number before clearfell. However, there were no significant changes in the frequency, timing, and intensity of thinning operations amongst all the four Pareto sets of solutions. However, the 3CPS were not significantly different from each other, which meant that these silvicultural regimes were insensitive to the price of carbon. This was because maximising carbon sequestration was directly related to the biological growth rate. As such an optimal mix of frequency, intensity, and timing of thinning maintained maximum growth rate for as long as possible for any one rotation.

Parametric Optimization Design of Aircraft Based on Hybrid Parallel Multi-objective Tabu Search Algorithm

For dealing with the multi-objective optimization problems of parametric design for aircraft, a novel hybrid parallel multi-objective tabu search （HPMOTS） algorithm is used. First, a new multi-objective tabu search （MOTS） algorithm is proposed. Comparing with the traditional MOTS algorithm, this proposed algorithm adds some new methods such as the combination of MOTS algorithm and ＂Pareto solution＂, the strategy of ＂searching from many directions＂ and the reservation of good solutions. Second, this article also proposes the improved parallel multi-objective tabu search （PMOTS） algorithm. Finally, a new hybrid algorithm--HPMOTS algorithm which combines the PMOTS algorithm with the non-dominated sorting-based multi-objective genetic algorithm （NSGA） is presented. The computing results of these algorithms are compared with each other and it is shown that the optimal result can be obtained by the HPMOTS algorithm and the computing result of the PMOTS algorithm is better than that of MOTS algorithm.

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 Optimization of Continuous Drive Friction Welding Process Parameters Using Response Surface Methodology with Intelligent Optimization Algorithm

The optimum friction welding （FW） parameters of duplex stainless steel （DSS） UNS $32205 joint was determined. The experiment was carried out as the central composite array of 30 experiments. The selected input parameters were friction pressure （F）, upset pressure （U）, speed （S） and burn-off length （B）, and responses were hardness and ultimate tensile strength. To achieve the quality of the welded joint, the ultimate tensile strength and hardness were maximized, and response surface methodology （RSM） was applied to create separate regression equations of tensile strength and hardness. Intelligent optimization technique such as genetic algorithm was used to predict the Pareto optimal solutions. Depending upon the application, preferred suitable welding parameters were selected. It was inferred that the changing hardness and tensile strength of the friction welded joint influenced the upset pressure, friction Pressure and speed of rotation.

Best compromising crashworthiness design of automotive S-rail using TOPSIS and modified NSGAⅡ

In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II(NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy(E), peak crushing force(Fmax) and mass of the structure(W) as three conflicting objective functions. In the multi-objective optimization problem(MOP), E and Fmax are defined by polynomial models extracted using the software GEvo M based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point(NIP)method and technique for ordering preferences by similarity to ideal solution(TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.

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.

Finding middle ground:Flow regimes designed for salmon and energy value

In regulated rivers,shaping seasonal flows to recover species at risk depends on understanding when to expect conflicts with competing water users and when their interests are aligned.Multi-objective optimization can be used to reveal such conflicts and commonalities.When species are involved,multi-objective optimization is challenged by the need to simulate complex species responses to flow regimes.Previously,we addressed that challenge by developing a simplified salmon model(Quantus)that defines cohorts of salmon by the river section and time in which they were spawned.Salmon in these space-time cohorts are tracked from the time redds(nests)are constructed until the cohort exits the tributary en route to the ocean.In this study,we modeled seasonal patterns in energy value and developed a Pareto-optimal frontier of seasonal flow patterns to maximize in-river salmon survival and hydropower value.Candidate flow regimes were characterized by two pulse flows varying in magnitude,timing,and duration and constrained by a total annual flow near the historical median.Our analysis revealed times when economic and salmon objectives were aligned and times when they differed.Pulse flows that favored higher energy value were timed to meet demand during extreme temperatures.Both salmon and hydropower objectives produced optimal flow regimes with pulse flows in early summer,but only solutions favoring hydropower value included high flows in mid-winter.Solutions favoring higher age-0 salmon survival provided an extended pulse flow in late winter/early spring,which suggests that access to productive floodplain habitat allowed faster growth and earlier out-migration and reduced the need for higher temperature-moderating flows later in spring.Minimum flows were also higher among solutions favoring salmon over energy.The tools used to produce these results can help to design simplified seasonal flow regimes by revealing compromise solutions that satisfy both fish and energy producers and highlighting when potential conflicts are likely.