Approximating Pareto Optimal Set by An Incremental Learning Model

Abstract This article proposes a method for optimally approximating real values with rational numbers. Such requirements arise in the design of various types of gear sets, where integer numbers of gear teeth force individual stage ratios to assume rational values. The kinematic design of an 18-speed gearbox, taken from the literature, is analyzed and solved using the proposed method. The method, called sequential exhaustion, sequentially considers each stage of the gearbox design, exhaustively examining each stage. Examination of 94 solutions leads to a pareto-optimal set containing 11 solutions. Further, although the layout of the gearbox is predefined for the kinematic design problem, certain solutions of the problem exhibit “non-reducing” gear pairs, revealing previously unforeseen changes in the gearbox layout.

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Application of multi-criteria decision making methods for selection of ship internal layout design from a Pareto optimal set

Ocean Engineering ◽

10.1016/j.oceaneng.2020.107151 ◽

2020 ◽

Vol 202 ◽

pp. 107151 ◽

Cited By ~ 4

Author(s):

H. Jafaryeganeh ◽

M. Ventura ◽

C. Guedes Soares

Keyword(s):

Decision Making ◽

Layout Design ◽

Pareto Optimal ◽

Multi Criteria Decision Making ◽

Pareto Optimal Set ◽

Optimal Set ◽

Selection Of

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The Skewboid Method: A Simple and Effective Approach to Pareto Relaxation and Filtering

Volume 3: 38th Design Automation Conference, Parts A and B ◽

10.1115/detc2012-70323 ◽

2012 ◽

Author(s):

Matthew I. Campbell

Keyword(s):

Pareto Optimality ◽

Population Based ◽

Pareto Optimal ◽

Large Set ◽

Number Of Solutions ◽

Target Number ◽

Relaxation Methods ◽

Pareto Optimal Set ◽

Optimal Set ◽

Adjustment Parameter

The concept of Pareto optimality is the default method for pruning a large set of candidate solutions in a multi-objective problem to a manageable, balanced, and rational set of solutions. While the Pareto optimality approach is simple and sound, it may select too many or too few solutions for the decision-maker’s needs or the needs of optimization process (e.g. the number of survivors selected in a population-based optimization). This inability to achieve a target number of solutions to keep has caused a number of researchers to devise methods to either remove some of the non-dominated solutions via Pareto filtering or to retain some dominated solutions via Pareto relaxation. Both filtering and relaxation methods tend to introduce many new adjustment parameters that a decision-maker (DM) must specify. In the presented Skewboid method, only a single parameter is defined for both relaxing the Pareto optimality condition (values between −1 and 0) and filtering more solutions from the Pareto optimal set (values between 0 and 1). This parameter can be correlated with a desired number of solutions so that this number of solutions is input instead of an unintuitive adjustment parameter. A mathematically sound derivation of the Skewboid method is presented followed by illustrative examples of its use. The paper concludes with a discussion of the method in comparison to similar methods in the literature.

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