Class
Article
College
College of Science
Department
Mathematics and Statistics Department
Faculty Mentor
Stephen J. Walsh
Presentation Type
Poster Presentation
Abstract
The modern dominant approach to planning experiments in industrial engineering and manufacturing is optimal design. This is a popular design paradigm because it 1) requires specification of an optimality criterion which incorporates practical objectives as definition of a design with high quality and 2) yields a design via high-dimensional optimization that gives the researcher ‘the most bang for the buck’ for a fixed sample/experimental run size. We aim to adapt the state-of-the-art meta-heuristic optimization algorithm, the Particle Swarm Optimization (PSO), to generating optimal designs with user-specified replication structure. Recently, PSO has been demonstrated to be highly effective at generating candidate optimal designs with high optimality scores. Walsh (2021) provided an initial formulation of a design criteria to encode user-specified replication structure. Problems studied by Gilmour and Trinca (2012) appealed to several subset optimality criteria which used a fairly esoteric construction, the Kronecker product. Thus, the first phase of our research is to provide a solution, via Julia programming, to meld the objective definitions of Walsh (2021) and Gilmour and Trinca (2012). This will enable a domain first application of PSO to this problem. We have currently implemented PSO on 68 number of Design scenarios and several criteria as described in Gilmour and Trinca. Nearly all of the designs computed thus far from Gilmour and Trinca’s replication structures have increased in efficiency, some have even seen over a 10% increase in efficiency. In addition to that, our new designs have also shown that they have more desirable relative prediction variance over the design space in contrast with the previously stated ”optimal” designs.
Location
Logan, UT
Start Date
4-12-2023 11:30 AM
End Date
4-12-2023 12:30 PM
Included in
Using Particle Swarm Optimization to Generate Optimal Experimental Designs With Replication Structures
Logan, UT
The modern dominant approach to planning experiments in industrial engineering and manufacturing is optimal design. This is a popular design paradigm because it 1) requires specification of an optimality criterion which incorporates practical objectives as definition of a design with high quality and 2) yields a design via high-dimensional optimization that gives the researcher ‘the most bang for the buck’ for a fixed sample/experimental run size. We aim to adapt the state-of-the-art meta-heuristic optimization algorithm, the Particle Swarm Optimization (PSO), to generating optimal designs with user-specified replication structure. Recently, PSO has been demonstrated to be highly effective at generating candidate optimal designs with high optimality scores. Walsh (2021) provided an initial formulation of a design criteria to encode user-specified replication structure. Problems studied by Gilmour and Trinca (2012) appealed to several subset optimality criteria which used a fairly esoteric construction, the Kronecker product. Thus, the first phase of our research is to provide a solution, via Julia programming, to meld the objective definitions of Walsh (2021) and Gilmour and Trinca (2012). This will enable a domain first application of PSO to this problem. We have currently implemented PSO on 68 number of Design scenarios and several criteria as described in Gilmour and Trinca. Nearly all of the designs computed thus far from Gilmour and Trinca’s replication structures have increased in efficiency, some have even seen over a 10% increase in efficiency. In addition to that, our new designs have also shown that they have more desirable relative prediction variance over the design space in contrast with the previously stated ”optimal” designs.