A multi-objective fuzzy optimization model for cropping structure and water resources and its method

Cropping structure has a close relationship with the optimal allocation of agricultural water resources. Based on the analysis of the relationship between agricultural water resources and sustainable development, this paper presents a multi objective fuzzy optimization model for cropping structure and water allocation, which overcomes the shortcoming of current models that only considered the economic objective,and ignored the social and environmental objectives. During the process, a new method named fuzzy deciding weight is developed to decide the objective weight. A case study shows that the model is reliable, the method is simple and objective, and the results are reasonable. This model is useful for agricultural management and sustainable development.

CEE-Gr:A Global Router with Performance Optimization Under Multi-Constraints

A global routing algorithm with performance optimization under multi constraints is proposed,which studies RLC coupling noise,timing performance,and routability simultaneously at global routing level.The algorithm is implemented and the global router is called CEE Gr.The CEE Gr is tested on MCNC benchmarks and the experimental results are promising.

Multi Objective Multireservoir Optimization in Fuzzy Environment for River Sub Basin Development and Management

In this paper, a multi objective, multireservoir operation model is proposed using Genetic algorithm (GA) under fuzzy environment. A monthly Multi Objective Genetic Algorithm Fuzzy Optimization (MOGAFU-OPT) model for the present study is developed in ‘C’ Language. The GA parameters i.e. population size, number of generations, crossover probability, and mutation probability are decided based on optimized val-ues of fitness function. The GA operators adopted are stochastic remainder selection, one point crossover and binary mutation. Initially the model is run for maximization of irrigation releases. Then the model is run for maximization of hydropower production. These objectives are fuzzified by assuming a linear membership function. These fuzzified objectives are simultaneously maximized by defining level of satisfaction (?) and then maximizing it. This approach is applied to a multireservoir system in Godavari river sub basin in Ma-harashtra State, India. Problem is formulated with 4 reservoirs and a barrage. The optimal operation policy for maximization of irrigation releases, maximization of hydropower production and maximization of level of satisfaction is presented for existing demand in command area. This optimal operation policy so deter-mined is compared with the actual average operation policy for Jayakwadi Stage-I reservoir.

Multidisciplinary Design Optimization of Vehicle Instrument Panel Based on Multi-objective Genetic Algorithm

Typical multidisciplinary design optimization（MDO） has gradually been proposed to balance performances of lightweight, noise, vibration and harshness（NVH） and safety for instrument panel（IP） structure in the automotive development. Nevertheless, plastic constitutive relation of Polypropylene（PP） under different strain rates, has not been taken into consideration in current reliability-based and collaborative IP MDO design. In this paper, based on tensile test under different strain rates, the constitutive relation of Polypropylene material is studied. Impact simulation tests for head and knee bolster are carried out to meet the regulation of FMVSS 201 and FMVSS 208, respectively. NVH analysis is performed to obtain mainly the natural frequencies and corresponding mode shapes, while the crashworthiness analysis is employed to examine the crash behavior of IP structure. With the consideration of lightweight, NVH, head and knee bolster impact performance, design of experiment（DOE）, response surface model（RSM）, and collaborative optimization（CO） are applied to realize the determined and reliability-based optimizations, respectively. Furthermore, based on multi-objective genetic algorithm（MOGA）, the optimal Pareto sets are completed to solve the multi-objective optimization（MOO） problem. The proposed research ensures the smoothness of Pareto set, enhances the ability of engineers to make a comprehensive decision about multi-objectives and choose the optimal design, and improves the quality and efficiency of MDO.

Multi-Objective Optimization and Analysis Model of Sintering Process Based on BP Neural Network

A multi-objective optimization and analysis model of the sintering process based on BP neural network is presented. Genetic algorithms are combined to simplify the BP neural network, which can reduce the learning time and increase the forecasting accuracy of the network model. This model has been experimented in the sintering process, and the production cost, the energy consumption, the quality （revolving intensity）, and the output are considered at the same time. Moreover, the relation between some factors and the multi-objectives has been analyzed, and the results are consistent with the process. Different objectives are emphasized at different practical periods, and this can provide a theoretical basis for the manager.

Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

Rotary unmanned aerial vehicles path planning in rough terrain based on multi-objective particle swarm optimization

This paper presents a path planning approach for rotary unmanned aerial vehicles(R-UAVs)in a known static rough terrain environment.This approach aims to find collision-free and feasible paths with minimum altitude,length and angle variable rate.First,a three-dimensional(3D)modeling method is proposed to reduce the computation burden of the dynamic models of R-UAVs.Considering the length,height and tuning angle of a path,the path planning of R-UAVs is described as a tri-objective optimization problem.Then,an improved multi-objective particle swarm optimization algorithm is developed.To render the algorithm more effective in dealing with this problem,a vibration function is introduced into the collided solutions to improve the algorithm efficiency.Meanwhile,the selection of the global best position is taken into account by the reference point method.Finally,the experimental environment is built with the help of the Google map and the 3D terrain generator World Machine.Experimental results under two different rough terrains from Guilin and Lanzhou of China demonstrate the capabilities of the proposed algorithm in finding Pareto optimal paths.

A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

Two-Phase Genetic Algorithm Applied in the Optimization of Multi-Modal Function

This paper presents a two-phase genetic algorithm (TPGA) based on the multi- parent genetic algorithm (MPGA). Through analysis we find MPGA will lead the population' s evol vement to diversity or convergence according to the population size and the crossover size, so we make it run in different forms during the global and local optimization phases and then forms TPGA. The experiment results show that TPGA is very efficient for the optimization of low-dimension multi-modal functions, usually we can obtain all the global optimal solutions.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

Interactive Multi-objective Optimization Design for the Pylon Structure of an Airplane

The pylon structure of an airplane is very complex, and its high-fidelity analysis is quite time-consuming. If posterior preference optimization algorithm is used to solve this problem, the huge time consumption will be unacceptable in engineering practice due to the large amount of evaluation needed for the algorithm. So, a new interactive optimization algorithm-interactive multi-objective particle swarm optimization （IMOPSO） is presented. IMOPSO is efficient, simple and operable. The decision-maker can expediently determine the accurate preference in IMOPSO. IMOPSO is used to perform the pylon structure optimization design of an airplane, and a satisfactory design is achieved after only 12 generations of IMOPSO evolutions. Compared with original design, the maximum displacement of the satisfactory design is reduced, and the mass of the satisfactory design is decreased for 22%.

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

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.

Multi-objective workflow scheduling in cloud system based on cooperative multi-swarm optimization algorithm

In order to improve the performance of multi-objective workflow scheduling in cloud system, a multi-swarm multiobjective optimization algorithm(MSMOOA) is proposed to satisfy multiple conflicting objectives. Inspired by division of the same species into multiple swarms for different objectives and information sharing among these swarms in nature, each physical machine in the data center is considered a swarm and employs improved multi-objective particle swarm optimization to find out non-dominated solutions with one objective in MSMOOA. The particles in each swarm are divided into two classes and adopt different strategies to evolve cooperatively. One class of particles can communicate with several swarms simultaneously to promote the information sharing among swarms and the other class of particles can only exchange information with the particles located in the same swarm. Furthermore, in order to avoid the influence by the elastic available resources, a manager server is adopted in the cloud data center to collect the available resources for scheduling. The quality of the proposed method with other related approaches is evaluated by using hybrid and parallel workflow applications. The experiment results highlight the better performance of the MSMOOA than that of compared algorithms.

Multi-objective Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Differential Evolution Algorithm

Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution（DE） algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.

System optimization-oriented spare parts dynamic configuration model for multi-echelon multi-indenture system

In order to optimize the spares configuration project at different stages during the life cycle, the factor of time is considered to relax the assumption of the spares steady demand in multi-echelon technique for recoverable item control (METRIC) theory. According to the method of systems analysis, the dynamic palm theorem is introduced to establish the prediction model of the spares demand rate, and its main influence factors are analyzed, based on which, the spares support effectiveness evaluation index system is studied, and the system optimization-oriented spares dynamic configuration method for multi-echelon multi-indenture system is proposed. Through the analysis of the optimization algorithm, the layered marginal algorithm is designed to improve the model calculation efficiency. In a given example, the multi-stage spares configuration project during its life cycle is gotten, the research result conforms to the actual status, and it can provide a new way for the spares dynamic optimization.

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

Integrated building design is inherently a multi-objective optimization problem where two or more conflicting objectives must be minimized and/or maximized concurrently.Many multi-objective optimization algorithms have been developed;however few of them are tested in solving building design problems.This paper compares performance of seven commonly-used multi-objective evolutionary optimization algorithms in solving the design problem of a nearly zero energy building(n ZEB) where more than 1.610 solutions would be possible.The compared algorithms include a controlled non-dominated sorting genetic algorithm witha passive archive(p NSGA-II),a multi-objective particle swarm optimization(MOPSO),a two-phase optimization using the genetic algorithm(PR_GA),an elitist non-dominated sorting evolution strategy(ENSES),a multi-objective evolutionary algorithm based on the concept of epsilon dominance(ev MOGA),a multi-objective differential evolution algorithm(sp MODE-II),and a multi-objective dragonfly algorithm(MODA).Several criteria was used to compare performance of these algorithms.In most cases,the quality of the obtained solutions was improved when the number of generations was increased.The optimization results of running each algorithm20 times with gradually increasing number of evaluations indicated that the PR_GA algorithm had a high repeatability to explore a large area of the solution-space and achieved close-to-optimal solutions with a good diversity,followed by the p NSGA-II,ev MOGA and sp MODE-II.Uncompetitive results were achieved by the ENSES,MOPSO and MODA in most running cases.The study also found that 1400-1800 were minimum required number of evaluations to stabilize optimization results of the building energy model.

Multi-objective Optimization Conceptual Design of Product Structure Based on Variable Length Gene Expression

It is a complicated problem for the bottom-to-top adaptive conceptual design of complicated products between structure and function. Reliable theories demand to be found in order to determine whether the structure accords with the requirement of design. For the requirement generally is dynamic variety as time passes, new requirements will come, and some initial requirements can no longer be used. The number of product requirements, the gene length expressing requirements, the structure of the product, and the correlation matrix are varied with individuation of customer requirements of the product. By researching on the calculation mechanisms of dynamic variety, the approaches of gene expression and variable length gene expression are proposed. According to the diversity of structure selection in conceptual design and mutual relations between structure and function as well as structure and structure, the correlation matrixes between structure and function as well as structure and structure are defined. By the approach of making the sum of the elements of correlation matrix maximum, the mathematical models of multi-object optimization for structure design are provided based on variable requirements. An improved genetic algorithm called segment genetic algorithm is proposed based on optimization preservation simple genetic algorithm. The models of multi-object optimization are calculated by the segment genetic algorithm and hybrid genetic algorithm. An example for the conceptual design of a washing machine is given to show that the proposed method is able to realize the optimization structure design fitting for variable requirements. In addition, the proposed approach can provide good Pareto optimization solutions, and the individuation customer requirements for structures of products are able to be resolved effectively.

Solving Multi-Area Environmental/Economic Dispatch by Pareto-Based Chemical-Reaction Optimization Algorithm

In this study, we present a Pareto-based chemicalreaction optimization(PCRO) algorithm for solving the multiarea environmental/economic dispatch optimization problems.Two objectives are minimized simultaneously, i.e., total fuel cost and emission. In the proposed algorithm, each solution is represented by a chemical molecule. A novel encoding mechanism for solving the multi-area environmental/economic dispatch optimization problems is designed to dynamically enhance the performance of the proposed algorithm. Then, an ensemble of effective neighborhood approaches is developed, and a selfadaptive neighborhood structure selection mechanism is also embedded in PCRO to increase the search ability while maintaining population diversity. In addition, a grid-based crowding distance strategy is introduced, which can obviously enable the algorithm to easily converge near the Pareto front. Furthermore,a kinetic-energy-based search procedure is developed to enhance the global search ability. Finally, the proposed algorithm is tested on sets of the instances that are generated based on realistic production. Through the analysis of experimental results, the highly effective performance of the proposed PCRO algorithm is favorably compared with several algorithms, with regards to both solution quality and diversity.

Multi-Strategy Dynamic Spectrum Access in Cognitive Radio Networks: Modeling, Analysis and Optimization

Dynamic spectrum access(DSA) based on cognitive radios(CR) technique is an effective approach to address the "spectrum scarcity" issue. However, traditional CR-enabled DSA system employs only single DSA strategy, which might not be suited to the dynamic network environment. In this paper, we propose a multi-strategy DSA(MS-DSA) system, where the primary and the secondary system share spectrum resources with multiple DSA strategies simultaneously. To analyze the performance of the proposed MS-DSA system, we model it as a continuous-time Markov chain(CTMC) and derive the expressions to compute the corresponding performance metrics. Based on this, we define a utility function involving the concerns of effective throughput, interference quantity on primary users, and spectrum leasing cost. Two optimization schemes, named as spectrum allocation and false alarm probability selection, are proposed to maximize the utility function. Finally, numerical simulations are provided to validate our analysis and demonstrate that the performance can be significantly improved caused by virtues of the proposed MS-DSA system.