CASCADE v3.1pymoo NSGA-II

CASCADE v3.1

Calculus-Adaptive Scale-Calibrated Derivative Engine

A 5-step optimization recipe that picks a calculus parameter k, transforms the search bounds, and runs pymoo NSGA-II. In this repository it has been exercised only on synthetic toy problems.

The 5-Step CASCADE Pipeline

CASCADE reframes a search near a singular point as a multi-objective optimization in transformed bounds. It has not been shown to reach anything a classical optimizer cannot; the only stored evaluation is a synthetic toy benchmark.

1. Find k
2. Transform
3. Find Edges
4. Search
5. Convert

Pipeline Steps

Implementation: simulations/utils/cascade.py,meta_calculus/moo_integration.py

1

Choose k (MOO)

Use a MOO backend to discover which calculus variant (k-value) is useful for your problem's singularity structure. The stored runs use pymoo NSGA-II.

Method: pymoo NSGA-II
Output: Candidate k, w, p
Example: project default k=-1 for 1/r
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2

Convert Problem to NNC Format

Transform the problem bounds into NNC space using k from Step 1. Frame finding the solution as a multi-objective optimization.

x_nnc = alpha_k(x_physics)// Forward transform
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3

Find Edges (MOO)

Use MOO to discover the edges of the simulation space - the boundaries of what's achievable before running the focused interior search.

Objectives: Distance to singularity, scheme disagreement
Output: [lower_bound, upper_bound] edges
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4

Interior Search (pymoo NSGA-II)

Use the defined edges to help a specialized model search for the particular MOO answer within the bounded region.

Bounds: Constrained by Step 3 edges
Output: Pareto front in NNC space
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5

Convert Back to Regular Math

Transform the NNC solutions back to classical physics coordinates for interpretation.

x_physics = alpha_k^(-1)(y_nnc)// Inverse transform

Interactive Visualization

Implementation Files

Core CASCADE

simulations/utils/cascade.pymeta_calculus/moo_integration.py

Documentation and Archived Notes

docs/THREE-MOO-CASCADE-METHODOLOGY.mddocs/archive/status-planning/simulations/CASCADE_QUICK_REFERENCE.md