Simulation & Design Solutions
Structural, thermal, CFD, modal, impact and multi-physics analysis with optimisation.
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Multi-objective and many-objective optimisation with Pareto fronts and reference points.
Almost every real design problem has more than one objective, and the objectives disagree. Lighter is usually weaker. Faster is usually costlier. Optimisation done properly does not resolve that conflict — it shows you the whole shape of it.
NSGA-II is the workhorse. It sorts a population into non-dominated fronts, keeps the best, and uses crowding distance to hold the solutions apart so the Pareto front comes out evenly spread rather than bunched. For two or three objectives it is fast, well understood and accepted everywhere.
NSGA-III exists because that approach stops working as objectives multiply. With four or more objectives almost every solution becomes non-dominated, crowding distance loses its meaning, and the algorithm has no way to tell a well-spread population from a clustered one. NSGA-III replaces crowding distance with a set of evenly distributed reference points and associates solutions with them, which keeps the spread under control in high dimensions.
The practical rule follows from that: two or three objectives, use NSGA-II; four or more, use NSGA-III and say why. Reviewers ask this question, and 'because it is newer' is not an answer.
From formulating the problem to defending the front you found.
Evolutionary algorithms are stochastic. Run NSGA-II twice with different random seeds and you get two different fronts. A paper that reports one run has reported one sample from a distribution, and a reviewer who works in this area will ask for more.
The accepted practice is between twenty and thirty independent runs, with performance metrics reported as a median and an interquartile range, and a non-parametric test — Wilcoxon rank-sum or Friedman with a post-hoc correction — when comparing algorithms. Hypervolume is the metric most reviewers expect, because it captures convergence and spread together, and it needs a stated reference point to be reproducible.
We set this up as standard: the runs, the metrics, the statistical comparison and the parameter settings all reported in a table that a reader could use to reproduce the study. It is more work than a single run and it is the difference between a result and an anecdote.
Variables, objectives, constraints and bounds written down precisely. Most optimisation problems are solved or lost at this step.
NSGA-II, NSGA-III or another approach, chosen on the number of objectives and the structure of the problem, with the reason recorded.
The model that turns a design vector into objective values — analytical, simulation-coupled or surrogate.
Population, generations, operators and reference points set, then run repeatedly with independent seeds.
Hypervolume and spread metrics across runs, with statistical comparison against a baseline algorithm.
A defensible choice from the front, the trade-off explained, and every parameter tabulated for reproducibility.
A Pareto front is not an answer, it is a menu. At some point somebody has to pick one design, and how that choice is made belongs in the thesis rather than in a footnote. The three honest routes are a stated preference weighting, a formal multi-criteria method such as TOPSIS or VIKOR with the weights justified, and the knee point where further gain in one objective costs disproportionately in another.
What is not acceptable is picking the solution that happens to look best and presenting it as the optimum. If weights were used they must be stated and their source explained, and a sensitivity check showing how the selection changes as the weights move makes the argument much stronger.
Where the objectives are on very different scales, normalisation matters as much as weighting. We report the normalisation used, because a different choice there can move the selected design entirely.
| What you receive |
|---|
| Formal problem formulation with variables, objectives and constraints |
| Working, documented optimisation code you keep |
| Parameter settings table for reproducibility |
| Pareto fronts from multiple independent runs |
| Hypervolume and spread metrics with statistical comparison |
| Front visualisations in two, three and many dimensions |
| Decision analysis with weights and sensitivity |
| Written methodology and results sections |
Four is the usual threshold. At two or three, NSGA-II with crowding distance works well and is easier to defend. From four upwards the fraction of non-dominated solutions rises sharply and reference-point methods such as NSGA-III keep the spread under control where crowding distance cannot.
Yes, through a surrogate. You run a designed set of expensive simulations, fit a response surface or Kriging model, optimise on the surrogate, and verify the promising designs with the real model. We build the design of experiments and the verification step, because a surrogate optimum that was never checked against the true model is not a result.
Twenty to thirty independent runs for the statistics. Generations are decided by watching the hypervolume flatten — we plot it and stop where it stops improving, then report that plot so the choice is visible rather than asserted.
Yes. That coupling — writing the design variables in, running the solve, reading the objectives out — is a routine part of the work, and we hand over the scripts so you can rerun or extend the study yourself.
Structural, thermal, CFD, modal, impact and multi-physics analysis with optimisation.
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Conceptual design, CAD, FEA, thermal and fluid analysis, optimisation and validation.
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