Numerical investigation of non-hierarchical coordination for distributed multidisciplinary design optimization with fixed computational budget
Bibliographic record
Abstract
This paper presents a numerical investigation of the non-hierarchical formulation of Analytical Target Cascading (ATC) for coordinating distributed multidisciplinary design optimization (MDO) problems. Since the computational cost of the analyses can be high and/or asymmetric, it is beneficial to understand the impact of the number of ATC iterations required for coordination and the number of iterations required for disciplinary feasibility on the quality of the obtained MDO solution. At each ATC iteration, the disciplinary optimization subproblems are solved for a predefined maximum number of loop iterations. The numerical experiments consider different numbers of maximum outer iterations while keeping the total computational budget of analyses constant. Solution quality is quantified by optimality (objective function value) and consistency (violation of coordination-related consistency constraints). Since MDO problems are typically simulation-based (and often blackbox) problems, we compare implementations of the mesh-adaptive direct search optimization algorithm (a derivative-free method with convergence properties) to the gradient-based interior-point algorithm implementation of the popular Matlab optimization toolbox. The impact of the values of two parameters involved in the alternating directions updating scheme of the augmented Lagrangian penalty functions (aka method of multipliers) on solution quality is also investigated. Numerical results are provided for a variety of MDO test problems. The results indicate consistently that a balanced modest number of outer and inner iterations is more effective; moreover, there seems to be a specific combination of parameter value ranges that yield better results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".