r/optimization

I'm working on optimizing an oil decolorization step using a column with three layers of different adsorbents/decolorizing materials.

My optimization problem has two types of variables:

- Mixture variables: the proportions of the three materials/layers.

- Process variables: contact time, agitation speed, contact surface/area, etc.

I also have two constraints:

- Cost ≤ a maximum acceptable value

- Quality ≥ a minimum acceptable value

My initial idea was to split the optimization into two stages:

1. Use a mixture design to determine the optimal proportions of the three layers.

2. Then use Response Surface Methodology (RSM) to optimize the process parameters using those proportions.

However, I'm concerned that optimizing the two stages independently could miss the global optimum, because the optimal process parameters may depend on the mixture proportions, and vice versa.

So my question is: What would be the correct experimental design/statistical approach to optimize both the mixture proportions and the process parameters simultaneously, while applying the cost and quality constraints to the final solution?

Would a combined mixture-process design be appropriate here, or is there a better approach?

Title. I would like to get more on the multiobjective side of things with mathematical optimization, what are the techniques that work the best for this area? And using which tools? Do we always have to move to single objective by the means of penalties, weighted sums, and what not?

I spent six months in 2021 building a TSP solver from geometric first principles, with no prior reading of the literature. Recently turned it into an interactive web app with step-by-step animation of every algorithmic move.

Interesting result: the algorithm independently rediscovered convex hull seeding and 2-opt uncrossing. It also produced a farthest-neighbour strategy.

On Berlin52: 7783 vs world optimal 7542 (3.2% above). 14ms on a single CPU core.

Demo: tsp.uncledroid.app
Paper: tsp.uncledroid.app/paper.pdf

Happy to discuss the algorithm — especially if anyone can point me to prior work on farthest-neighbour as a TSP construction heuristic.

video: youtu.be/-gAhARI2ZFI