Incorporating Engineering Knowledge Max Yi Ren, Panos Y. Papalambros - - PowerPoint PPT Presentation

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Adaptive Choice-Based Conjoint Analysis Incorporating Engineering Knowledge Max Yi Ren, Panos Y. Papalambros University of Michigan, Ann Arbor IDETC14 Buffalo, NY Aug 19 th , 2014 Motivation (1/2) partworth Engineering Survey or &

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Adaptive Choice-Based Conjoint Analysis Incorporating Engineering Knowledge

Max Yi Ren, Panos Y. Papalambros University of Michigan, Ann Arbor IDETC’14 Buffalo, NY Aug 19th, 2014

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Motivation (1/2)

Objective from marketing perspective: Improve the hit-rate of the preference model to help design optimization.

Preference model Survey or market data Engineering & cost model Conditional probabilities to be the most profitable 1 2 3

Optimal design: Design w/ the highest prob. to be the most profitable.

partworth

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Motivation (2/2)

Cost

8G 16G 32G 64G 128G 256G $5 $5 $6 $16 $40 $200 Consider optimizing the profit of a USB drive w.r.t. memory capacity

“8G” is never optimal if larger memory is more preferred.
No need to measure the partworth on the level “8G”.
Probability of “256G” to be the optimal is low due to high cost.

(Example modified from E. Feit Dissertation)

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Outline

Overview: Optimization by asking good questions
Intuition: Preference modeling vs. design optimization
Algorithm: Group Generalized Binary Search
Case study
Conclusion

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Overview

Objective: To find the optimal design w/ the least number of queries

Preference model Queries (pairwise choices) Deterministic engineering & cost model Conditional probabilities to be the most profitable

Partworth distribution

1 2 3

Optimal design: One w/ the highest prob. to be the most profitable, within a finite set.

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Intuition

User feedback to a query is a cut in the version space (the space of feasible partworth). The difference b/w preference modeling and design optimization:

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Group Generalized Binary Search (1/3)

A sequence of queries forms a path. Ideally, it

terminates when the optimal design is derived.

A query strategy determines which query to make

under user feedback to previous queries.

Internal node: Contains the constrained version space reaching the node, the current query and response. Leaf node: Contains the final constrained version space, and the design most probable to be the most profitable.

Originally proposed in: Bellala et al., 2012. “Group based active query selection for rapid diagnosis in time critical situations”. IEEE Transactions on Information Theory, 58(1), pp. 459–478.

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Group Generalized Binary Search (2/3)

The partworths of the user is a random vector

following an unknown distribution. A prior distribution is assumed.

Each query strategy leads to an expected path length,

which could be minimized by the best strategy.

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The GGBS algorithm finds the best question to ask, based on current and previous users’ responses The algorithm minimizes at each node : Most uncertain question

Probability mass from the same design into the same child node

D1 D2

Group Generalized Binary Search (3/3)

MCMC used for calculating conditional probabilities.

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Case Study: Dial-readout Scale Design

2455 feasible designs on 6 attributes w/ 5 levels.

Data and model from Michalek, Feinberg, Papalambros, 2005.

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Case Study: Settings & Assumptions

The true partworths are used to simulate responses.
Responses have no random error.
Engineering models are deterministic.
The best query is picked from four candidates w/ the

highest conditional probabilities to be the optimal.

GGBS is compared w/ uncertainty sampling (utility

balance).

20 independent simulations, each with 50 queries.

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Case Study: Convergence Result

Proposed GGBS Utility balance Most probable vs. current chosen

27 34 Average #query to find the correct best two designs derived from full knowledge

Variance from MCMC Sampling size = 1e5

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