5.10 Hybrid CCD Solution Workflows

Hybridize solvers without changing the formulation¶

A hybrid workflow combines numerical strengths while retaining one joint CCD objective and constraint set. Examples include:

use nested CCD to generate a physically meaningful warm start, then finish with simultaneous CCD;
solve a reduced-order simultaneous problem, then validate and refine with a high-fidelity nested model;
alternate variable blocks using the same $J_{sys}$ and all coupled constraints, then perform a full KKT solve.

These are CCD solution workflows because every stage targets or approximates the same joint problem. In contrast, alternating independent plant and control objectives remains an iterated sequential baseline.

Transfer checks¶

Whenever the formulation, model fidelity, or variable representation changes between stages, evaluate

ΔJ_{transfer}=(J_{target}-J_{source})/|J_{source}|.

and recheck every coupled constraint. A warm start is useful only if it reduces total verified work.

Activity 5.10: evaluate a hybrid CCD workflow¶

Activity 5.10: evaluate a hybrid CCD workflow

A direct simultaneous solve from a generic initial guess requires 520 iterations at 1.8 s/iteration and succeeds in 70% of runs. A hybrid workflow first performs a 210 s nested reduced-order solve, then a warm-started simultaneous solve requiring 260 iterations. High-fidelity validation takes 90 s for either workflow.

Compute total time for the direct and hybrid workflows.
Compute the hybrid percentage time reduction.
The reduced-order solution has $J=0.690$ ; after transfer, the high-fidelity objective is 0.724. Compute $ΔJ_{transfer}$ .
If the hybrid succeeds in 92% of runs, compute expected time per successful result as $T/P_{success}$ for both workflows.
State the evidence needed to call this a hybrid CCD solver rather than an iterated sequential design.

Chapter summary¶

One-pass and conventional iterated sequential design are non-CCD baselines. Nested and simultaneous formulations are CCD because physical and control decisions are optimized under one system objective and one coupled feasible set. Hybrid workflows remain CCD only when their stages preserve that joint formulation.

Common mistakes¶

calling any repeated plant–control exchange “CCD”;
comparing a sequential baseline and CCD with different objectives or constraints;
accepting loose inner solves in nested CCD;
reporting simultaneous NLP convergence without mesh verification;
confusing numerical equivalence with global optimality; and
omitting failed starts, derivative cost, or validation effort.

Exercises¶

Write the sequential baseline and joint CCD formulations for a two-mass suspension.
Identify exactly which variables and constraints are frozen at each sequential handoff.
Derive the nested value function and the simultaneous decision vector.
Construct a fair comparison table containing performance, feasibility, cost, and validation.
Propose a hybrid CCD workflow and state how you would verify formulation consistency.

Principal sources¶

Herber and Allison on nested and simultaneous CCD; Sundarrajan and Herber on fair comparisons; and Allison, Guo, and Han on simultaneous suspension CCD.

Open research question¶

Can coupling strength, derivative structure, and solver reliability predict whether nested, simultaneous, or a hybrid CCD workflow will be most efficient before all alternatives are solved?