scholarly journals Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

2012 ◽  
Vol 03 (07) ◽  
pp. 765-771
Author(s):  
Wei Xing ◽  
Boying Wu
Keyword(s):  
Multiobjective Optimization ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Continuous Method ◽  
Multiobjective Optimization Problem ◽  
Feasible Set ◽  
Weak Efficient Solution

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.

scholarly journals Approximate dual and approximate vector variational inequality for multiobjective optimization

1989 ◽  
Vol 47 (3) ◽  
pp. 418-423 ◽  
Author(s):  
G.–Y. Chen ◽  
B. D. Craven
Keyword(s):  
Variational Inequality ◽  
Multiobjective Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Strong Duality ◽  
Vector Variational Inequality ◽  
Weak Duality ◽  
Multiobjective Optimization Problem ◽  
Feasible Set

AbstractAn approximate dual is proposed for a multiobjective optimization problem. The approximate dual has a finite feasible set, and is constructed without using a perturbation. An approximate weak duality theorem and an approximate strong duality theorem are obtained, and also an approximate variational inequality condition for efficient multiobjective solutions.

Linear Complementarity Problem and Multiobjective Optimization

2011 ◽  
Vol 101-102 ◽  
pp. 236-239
Author(s):  
Long Quan Yong
Keyword(s):  
Multiobjective Optimization ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Linear Complementarity ◽  
New Method ◽  
Multiobjective Optimization Problem ◽  
Minimax Method

A new method is proposed for the linear complementarity problem (LCP). Firstly we formulate the LCP into a multiobjective optimization problem (MOP), and study the relations between the efficient solution of MOP and optimal solution of LCP. Based on the efficient solution of MOP, we define zero-efficient solution. Then we indicate that zero-efficient solution of the MOP is also the solution to the LCP. Finally some standard LCP examples are respectively transformed into MOP and solved by minimax method. Numerical results indicate that the proposed method is effective.

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