The ability of objective functions to generate non-convex Pareto frontiers

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

doi:10.2514/6.1999-1211

Cited by 29 publications

(31 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This parameter (weight) will determine the relative compromise of different responses and hence the decisionmaker's preference on multiple objectives. As Messac et al [22] proved, assigning priorities to responses through an exponent is an effective practice to manipulate the objective function curvature and capture compromise solutions at convex and non-convex response surfaces.…”

Section: Proposed Methodsmentioning

confidence: 99%

Multiple response optimization: a global criterion‐based method

Costa

Pereira

2010

Journal of Chemometrics

View full text Add to dashboard Cite

Processes and products have by nature many quality characteristics that must be in some sense optimized simultaneously. With this aim, a method which can be used easily and efficiently by practitioners for optimizing multi-response problems is proposed. Implementation steps and considerations, in addition to optimization measures to assess method's solutions and guide the analyst in finding an effective compromise solution, are also presented. Three classical examples from the literature are used to assess the performance of several prominent methods in the response surface methodology (RSM) framework and help practitioners make a better-informed choice among them.

show abstract

Section: Proposed Methodsmentioning

confidence: 99%

Multiple response optimization: a global criterion‐based method

Costa

Pereira

2010

Journal of Chemometrics

View full text Add to dashboard Cite

show abstract

“…In summary, weighted methods are very powerful, but have two inherent limitations: (1) not all pareto-optimal designs can be obtained via suitable weighting, and (2) finding suitable weights is non-trivial [10,11,25].…”

Section: Weighted Optimizationmentioning

confidence: 99%

“…By appropriately choosing the weights, a set of paretooptimal designs is obtained. This method has numerous deficiencies [10,11], but can be useful if implemented in conjunction with engineering insights [22].…”

Section: Weighted Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

Efficient generation of pareto‐optimal topologies for compliance optimization

Turevsky

Suresh

2011

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIn multi-objective optimization, a design is defined to be pareto-optimal if no other design exists that is better with respect to one objective, and as good with respect to other objectives. In this paper, we first show that if a topology is pareto-optimal, then it must satisfy certain properties associated with the topological sensitivity field, i.e. no further comparison is necessary. This, in turn, leads to a deterministic, i.e. non-stochastic, method for efficiently generating pareto-optimal topologies using the classic fixedpoint iteration scheme. The proposed method is illustrated, and compared against SIMP-based methods, through numerical examples. In this paper, the proposed method of generating pareto-optimal topologies is limited to bi-objective optimization, namely compliance-volume and compliance-compliance. The future work will focus on extending the method to non-compliance and higher dimensional pareto optimization.

show abstract

“…First, the generation of the Pareto set is a challenging problem [15][16]. Second, selecting a solution from among a Pareto set is a task made more challenging with the existence of distinct and dynamic preferences among designers [17].…”

Section: Multi-objective Design Problemsmentioning

confidence: 99%

Visualization of Multidimensional Design and Optimization Data Using Cloud Visualization

Eddy

Lewis

2002

Volume 2: 28th Design Automation Conference

View full text Add to dashboard Cite

Some of the first attempts at using visualization methods to aid decisions in design and optimization are found in [1]. More recent advances in computer visualization and Virtual Reality (VR) [2][3][4] are allowing designers and scientists to interact and manipulate vast amounts of data. Until these innovations, computers were solely relied on to interpret results and compute answers based on programs written. It is now possible to interact with these large datasets even while they are being used in running analyses [5][6][7][8][9][10][11]. Users have the ability to compress large amounts of data into a visual format, to investigate trends and relationships that could not be seen otherwise, and then make informed decisions regarding a product or process design.As our ability to generate more and more data for increasingly large engineering models improves, the need for methods for managing that data becomes greater. Information management from a decision-making perspective involves being able to capture and represent significant information to a designer so that they can make effective and efficient decisions. However, most visualization techniques used in engineering, such as graphs and charts, are limited to twodimensional representations and at most three-dimensional representations. In this paper, we present a new visualization technique to capture and represent engineering information in a multidimensional context. The new technique, Cloud Visualization, is based upon representing sets of points as clouds in both the design and performance spaces. The technique is applicable to both single and multiobjective optimization problems and the relevant issues with each type of problem are discussed. A multiobjective case study is presented to demonstrate the application and usefulness of the Cloud Visualization techniques.

show abstract

The ability of objective functions to generate non-convex Pareto frontiers

Cited by 29 publications

References 9 publications

Multiple response optimization: a global criterion‐based method

Multiple response optimization: a global criterion‐based method

Efficient generation of pareto‐optimal topologies for compliance optimization

Visualization of Multidimensional Design and Optimization Data Using Cloud Visualization

Contact Info

Product

Resources

About