Multi-Objective Keyboard Layout Optimizer

A streamlined framework for finding Pareto-optimal layouts using weighted multi-objective optimization.

Repository: https://github.com/binarybottle/optimize_layouts.git
Author: Arno Klein (arnoklein.info)
License: MIT License (see LICENSE)

This framework discovers Pareto-optimal layouts by optimizing multiple objectives simultaneously. It combines direct key-pair score lookup with multi-objective search to find layouts that represent the best trade-offs across an arbitrary number of competing criteria.

Multi-Objective Optimization (MOO) with exhaustive search

  # Basic MOO with default settings in config.yaml
  python optimize_layouts.py --config config.yaml

  # MOO with specific objectives
  python optimize_layouts.py --config config.yaml \
      --objectives engram_keys,engram_rows,engram_columns,engram_order

  # MOO with custom weights and directions
  python optimize_layouts.py --config config.yaml \
      --objectives engram_keys,engram_rows,engram_columns,engram_order \
      --weights 1.0,2.0,0.5,0.75 --maximize true,true,false,true \
      --max-solutions 100 --time-limit 3600 --verbose

  # Validation run
  python optimize_layouts.py --config config.yaml --validate --dry-run

Analysis and (keyboard layout) visualization

  # Analyze optimization results
  python analyze_results.py --results-dir output/layouts

  # Compare input data (raw vs normalized)
  python analyze_input.py --config config.yaml

  # Visualize keyboard layout as ASCII
  python display_layout.py --letters "etaoinsrhl" --positions "FDESVRJKIL"

  # Generate rich HTML keyboard layout
  python display_layout.py --letters "zplr  diwychts  aeomxvbn  ugkfqj" \
    --positions "QWERTYUIOPASDFGHJKL;ZXCVBNM,./['" \
    --html

Architecture

optimize_layouts/ ├── README.md # This file │ │ # Configuration ├── config.yaml # Main configuration file │ │ # Core MOO system ├── optimize_layouts.py # Main entry point for optimization ├── moo_scoring.py # Item-pair-weighted MOO scoring ├── moo_search.py # Pareto-optimal search algorithms ├── config.py # Configuration management │ │ # MOO results analysis ├── layouts_consolidate.py # Select global Pareto solutions from separate files ├── layouts_filter.py # Filter MOO results ├── layouts_plot.py # Analyze and plot MOO results │ │ # I/O (inputs are for a keyboard optimization study) ├── input/ │ ├── engram_2key_scores.csv # Position-pair scoring (bigram) │ ├── engram_3key_order_scores.csv # Position-triple scoring (trigram) │ └── frequency/ │ ├── english-letter-pair-counts-google-ngrams_normalized.csv │ └── english-letter-triple-counts-google-ngrams_normalized.csv ├── run_jobs.py # Run multiple jobs ├── output/
│ └── layouts/ # MOO optimization results │ │ # Optional utilities ├── utilities/ │ ├── calc_positions_items.py # Calculate permutations │ ├── count_files.py # Count files in a folder (with find command) │ ├── generate_command.py # Generate command to score and visualize layouts │ ├── normalize_and_analyze.py # Normalize data and compare raw vs normalized data │ └── run_jobs_slurm.sh # SLURM cluster job submission │ │ # Keyboard study └── keyboard_study/ ├── README_keyboards.md # README for keyboard layout optimization study ├── analyze_frequencies.py # Analyze item-pair (bigram) frequencies ├── compare_layouts.py # Keyboard comparisons with filtering and plotting ├── display_layout.py # Keyboard visualization from single layout ├── display_layouts.py # Keyboard visualization from table of layouts ├── generate_configs1.py # Generate config files for parallel optimization phase 1 └── generate_configs2.py # Generate config files for parallel optimization phase 2

Inputs

The system accepts normalized score files in CSV format. The code will accept any set of letters (or special characters) to represent item-pairs and position-pairs, so long as each item-pair is represented by two item characters and each position-pair is represented by two position characters.

Normalized scores

Item-pair (normalized) scores file:
csv item_pair, score ab, 0.1 ba, 0.3 ac, 0.2 ca, 0.1 bc, 0.4 cb, 0.2 Position-pair (normalized multi-objective) scores file:
csv position_pair,engram_keys,engram_rows,engram_columns,engram_order FD,0.85,0.72,0.91,0.78,0.65,0.88 DE,0.72,0.68,0.88,0.82,0.71,0.85 ES,0.68,0.71,0.85,0.75,0.69,0.82

Multi-objective search algorithms

The system provides two Pareto-optimal search algorithms with different performance characteristics: Exhaustive Search (Default)

Guaranteed complete: Finds ALL Pareto-optimal solutions Simple and reliable: No complex pruning logic or upper bound calculations Optimal for ≤10 items: Faster than branch-and-bound for smaller problems Direct evaluation: Tests every possible permutation with minimal overhead

Branch-and-Bound Search

Intelligent pruning: Uses upper bounds to eliminate dominated solution branches Optimal for ≥12 items: Essential when factorial growth becomes prohibitive Complex but scalable: More overhead per node but massive savings on large problems Preserves optimality: Mathematically sound pruning ensures no optimal solutions are lost

Bigram and Trigram Scoring

The system supports both bigram (2-key) and trigram (3-key) objective scoring; it automatically detects which objectives are bigram vs trigram based on input scoring tables.

• Bigram objectives: Scored using position-pair table (e.g., engram_keys,engram_rows,engram_columns,engram_order,...)
• Trigram objectives: Scored using position-triple table (e.g., engram_3key_order)
• Weighting: Bigram and trigram scores are weighted by item-pair/triple scores

Output

Console output

• Configuration summary and search space analysis
• Pareto front analysis with objective ranges
• Top solutions with detailed score breakdowns
• Performance metrics and timing statistics
• Optional ASCII art visualization of keyboard layouts

CSV results

• Complete Pareto front with all objectives: moo_results_config_YYYYMMDD_HHMMSS.csv

Analysis outputs

• Objective correlation plots and scatter visualizations
• Input data distribution comparisons
• Global Pareto front analysis across multiple runs

Running many configurations

You can generate configuration files by creating your own generate_configs.py script, following the example in keyboards/generate_configs1.py, then modify the run_jobs_local.py script for your needs (see run_jobs_slurm.sh for running jobs on a linux cluster):

  python generate_configs.py
  python run_jobs.py