Interactive physical programming - Tradeoff analysis and decision making in multicriteria optimization

Tappeta, Ravindra V.; Renaud, John E.; Sundararaj, Glynn J.; Messac, Achille

doi:10.2514/6.1999-1209

Cited by 11 publications

(18 citation statements)

References 6 publications

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“…e limitation of the physical programming is that it requires a priori selection of range parameters for each of the objective functions and provides information for only one design scenario (i.e., a single Pareto solution). Tappeta et al [13] have twinned linear physical programming with an interactive algorithm [1]. eir algorithm �nds a Pareto solution and can generate other Pareto designs in the neighbourhood of the current Pareto solution.…”

Section: Multiobjective Problem Andmentioning

confidence: 99%

Collaborative Decision-Making in Product Design: An Interactive Multiobjective Approach

Baril

Yacout

Clément

2013

Journal of Industrial Engineering

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This paper presents a new procedure to solve multiobjective problems, where the objectives are distributed to various working groups and the decision process is centralized. The approach is interactive and considers the preferences of the working groups. It is based on two techniques: an interactive technique that solves multi-objective problems based on goal programming, and a technique called “linear physical programming” which considers the preferences of the working groups. The approach generates Pareto-optimal solutions. It guides the director in the determination of target values for the objective functions. The approach was tested on two problems that present its capacity to generate Pareto-optimal solutions and to show the convergence to compromise solutions for all the working groups.

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Section: Multiobjective Problem Andmentioning

confidence: 99%

Collaborative Decision-Making in Product Design: An Interactive Multiobjective Approach

Baril

Yacout

Clément

2013

Journal of Industrial Engineering

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“…An interactive physical programming framework was proposed by Tappeta et al [67] which considers decision maker's preferences during the optimization process and allows for the efficient design exploration around a given Pareto point. Pareto sensitivity information, a second-order Pareto surface representation, an iterative decision making strategy and a Pareto visualization tool assisting tradeoff analysis and decision making are the functionalities provided by this framework.…”

Section: Interactive Physical Programmingmentioning

confidence: 99%

Physical Programming: A Review of the State of the Art

Ilgın¹,

Gupta²

2012

SIC

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Most traditional multi-criteria optimization techniques require that the decision maker construct an aggregate objective function using the weights determined as a result of a trial and error process. Physical programming (PP) eliminates this tedious weight assignment process by providing decision makers with a flexible and more natural problem formulation. In PP, the decision maker specifies ranges of different degrees of desirability instead of defining weights. In this paper, we present a comprehensive review of PP studies by classifying them into four major categories (viz., methodological papers, industrial engineering applications, mechanical engineering applications and other applications). Insights from the review and future research directions conclude the paper.

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“…A recent study by Tappeta and Renaud on tradeoff analysis is closely related to approximating the Pareto frontier. 19 However, they use a different approach for generating the Pareto frontier. They use first and second order derivatives of the objectives; and they note that reducing computational error associated with the approximation requires accurate second order derivatives.…”

Section: B Survey Of Pareto Set Generatorsmentioning

confidence: 99%

“…To generate a set of evenly distributed points along the Pareto frontier, we reduce the design space using the NCSR process for each point p k obtained using Eqs. (19)(20)(21) where α j is evenly varied from 0 to 1. Importantly, the MO problem (Problem 1) is transformed to a single objective optimization problem as shown below in Problem 2.…”

Section: Sequential Reduction and Optimizationmentioning

confidence: 99%

Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier

Messac,

Mattson

2004

AIAA Journal

Self Cite

226

188

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Multiobjective optimization is rapidly becoming an invaluable tool in engineering design. A particular class of solutions to the multiobjective optimization problem is said to belong to the Pareto frontier. A Pareto solution, the set of which comprises the Pareto frontier, is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other. Accordingly, the Pareto frontier plays an important role in engineering design -it characterizes the tradeoffs between conflicting design objectives. Some optimization methods can be used to automatically generate a set of Pareto solutions from which a final design is subjectively chosen by the designer. For this approach to be successful, the generated Pareto set must be truly representative of the complete optimal design space (Pareto frontier). In other words, the set must not over represent one region of the design space, or neglect others. Some commonly used methods comply with this requirement, while others do not. This paper offers a new phase in the development of the Normal Constraint method, which is a simple approach for generating Pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives. The even distribution of the generated Pareto solutions can facilitate the process of developing an analytical expression for the Pareto frontier in n-dimension. An even distribution of Pareto solutions also facilitates the task of choosing the most desirable (final) design from among the set of Pareto solutions. The Normal Constraint method bears some similarities to the Normal Boundary Intersection and ε-Constraint methods. Importantly, the developments presented in this paper define its critical distinction: Namely, the ability to generate a set of evenly distributed Pareto solutions over the complete Pareto frontier. Examples are provided that show the Normal Constraint method to perform favorably under the new developments when compared with the Normal Boundary Intersection method, as well as with the original Normal Constraint method.

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Interactive physical programming - Tradeoff analysis and decision making in multicriteria optimization

Cited by 11 publications

References 6 publications

Collaborative Decision-Making in Product Design: An Interactive Multiobjective Approach

Collaborative Decision-Making in Product Design: An Interactive Multiobjective Approach

Physical Programming: A Review of the State of the Art

Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier

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