scholarly journals A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Zhiming Song ◽  
Maocai Wang ◽  
Guangming Dai ◽  
Massimiliano Vasile
Keyword(s):  
Regression Analysis ◽  
Probability Distribution ◽  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Dimensional Manifold ◽  
Decision Space ◽  
Nsga Ii ◽  
Multiobjective Evolutionary Algorithm ◽  
Piecewise Continuous

As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m-1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m-1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

Multiobjective optimization of parallel kinematic mechanisms by the genetic algorithms

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 783-797 ◽  
Author(s):  
Ridha Kelaiaia ◽  
Olivier Company ◽  
Abdelouahab Zaatri
Keyword(s):  
Genetic Algorithms ◽  
Multiobjective Optimization ◽  
High Speed ◽  
Optimization Problem ◽  
Multiobjective Optimization Problem ◽  
Dimensional Synthesis ◽  
Nsga Ii ◽  
Parallel Kinematic ◽  
Parallel Kinematic Mechanisms ◽  
Kinematic Mechanisms

SUMMARYIt is well known that Parallel Kinematic Mechanisms (PKMs) have an intrinsic dynamic potential (very high speed and acceleration) with high precision and high stiffness. Nevertheless, the choice of optimal dimensions that provide the best performances remains a difficult task, since performances strongly depend on dimensions. On the other hand, there are many criteria of performance that must be taken into account for dimensional synthesis, and which are sometimes antagonist. This paper presents an approach of multiobjective optimization for PKMs that takes into account several criteria of performance simultaneously that have a direct impact on the dimensional synthesis of PKMs. We first present some criteria of performance such as the workspace, transmission speeds, stiffness, dexterity, precision, as well as dynamic dexterity. Secondly, we present the problem of dimensional synthesis, which will be defined as a multiobjective optimization problem. The method of genetic algorithms is used to solve this type of multiobjective optimization problem by means of NSGA-II and SPEA-II algorithms. Finally, based on a linear Delta architecture, we present an illustrative application of this methodology to a 3-axis machine tool in the context of manufacturing of automotive parts.

Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front

2017 ◽  
Vol 25 (2) ◽  
pp. 309-349 ◽  
Author(s):  
Rubén Saborido ◽  
Ana B. Ruiz ◽  
Mariano Luque
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Weight Vector ◽  
Reference Points ◽  
Pareto Optimal ◽  
Computational Results ◽  
Nsga Ii ◽  
Nondominated Solutions ◽  
Pareto Optimal Front

In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.

scholarly journals HYBRID NSGA-II OPTIMIZATION FOR IMPROVING THE THREE-TERM BP NETWORK FOR MULTICLASS CLASSIFICATION PROBLEMS

2015 ◽  
Author(s):  
Ashraf Osman Ibrahim ◽  
Siti Mariyam Shamsuddin ◽  
Sultan Noman Qasem
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithm ◽  
Hybrid Algorithm ◽  
Search Algorithm ◽  
Classification Performance ◽  
Classification Problems ◽  
Nsga Ii ◽  
Bp Network ◽  
Multiobjective Evolutionary Algorithm

Recently, hybrid algorithms have received considerable attention from a number of researchers. This paper presents a hybrid of the multiobjective evolutionary algorithm to gain a better accuracy of the fi nal solutions. The aim of using the hybrid algorithm is to improve the multiobjective evolutionary algorithm performance in terms of the enhancement of all the individuals in the population and increase the quality of the Pareto optimal solutions. The multiobjective evolutionary algorithm used in this study is a nondominated sorting genetic algorithm-II (NSGA-II) together with its hybrid, the backpropagation algorithm (BP), which is used as a local search algorithm to optimize the accuracy and complexity of the three-term backpropagation (TBP) network. The outcome positively demonstrates that the hybrid algorithm is able to improve the classification performance with a smaller number of hidden nodes and is effective in multiclass classifi cation problems. Furthermore, the results indicate that the proposed hybrid method is a potentially useful classifi er for enhancing the classification process ability when compared with the multiobjective genetic algorithm based on the TBP network (MOGATBP) and certain other methods found in the literature.  

Defining the Space of Feasible Transmission Designs for Retrofitting a Rear-Wheel-Drive Automobile With a Power Split CVT

2019 ◽  
Author(s):  
Sean D. Vermillion
Keyword(s):  
Multiobjective Optimization ◽  
Fuel Economy ◽  
Optimization Problem ◽  
Rear Wheel ◽  
Gear Ratio ◽  
Multiobjective Optimization Problem ◽  
Nsga Ii ◽  
Feasible Set ◽  
Wheel Drive ◽  
Power Split

Abstract In this paper, we describe a strategy for modeling the feasible set of power-split continuously variable transmission (CVT) system designs for retrofitting rear-wheel-drive consumer automobiles. A design is considered feasible if it produces a higher fuel economy than the stock vehicle’s fuel economy rating. Towards modeling the feasible set of designs, we first model a vehicle with a power-split CVT system taking into account the system’s mass and CVT efficiency. In this model, the effective design variables are the mass of the transmission system, the CVT functional efficiency, and effective gear ratio defining the allowable power split through and around the CVT. We formulate the set of feasible design solutions utilizing a multiobjective optimization problem to define the boundaries of the maximum allowable system mass, minimum allowable efficiency, and minimum allowable effective gear ratio. We solve this multiobjective optimization problem using NSGA-II and fit a quadratic model to the NSGA-II results to define a surrogate model of the feasible design set. We show that this surrogate modeling approach is sufficient for predicting the feasibility of a candidate transmission design.

Modeling the Multiobjective Optimization of Electricity Consumption for Residential Consumers

2013 ◽  
Vol 748 ◽  
pp. 493-497 ◽  
Author(s):  
José L. Bernal-Agustín ◽  
Tomás Cortés-Arcos ◽  
Rodolfo Dufo-López ◽  
Juan M. Lujano-Rojas ◽  
Cláudio Monteiro
Keyword(s):  
Mathematical Model ◽  
Multiobjective Optimization ◽  
Smart Grid ◽  
Evolutionary Algorithm ◽  
Pareto Optimality ◽  
Electricity Consumption ◽  
Cost Of Electricity ◽  
Multiobjective Evolutionary Algorithm ◽  
The Cost ◽  
The Mathematical Model

This paper presents a mathematical model to simultaneously optimize the cost of electricity and the satisfaction of a residential consumer using the communication infrastructure of a smart grid. For this task the concept of Pareto optimality has been used. It is possible to consider the satisfaction of the consumer as an independent objective to be maximized, and simultaneously, to minimize the cost of the electrical bill. In future works a multiobjective evolutionary algorithm will be applied along with the mathematical model presented in this paper.

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