BOPS — Batch Bayesian Optimisation with Pareto-Based Selection

Supplementary code repository for peer-review reproducibility verification:

"Pareto-Based Selection Strategies for Batch Bayesian Optimization of Expensive Black-Box Functions"

This self-contained repository provides a functional demonstration of the complete optimization pipeline proposed in the paper. It executes all 5 batch selection methods across independent trials on standard benchmark functions to facilitate rapid verification by reviewers without requiring any project-specific data paths or heavy infrastructure. The settings are intentionally small and are meant as a reproducibility/demo run, not as a replacement for the full experimental study in the paper.

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Folder Structure

BOPS/
├── methods.py          # All 5 method definitions (self-contained)
├── run_demo.py         # Optimisation pipeline + demo runner
└── README.md           # This file

After running the demo, the following folders are created automatically:

BOPS/
├── demo_training_data/ # LHD initial designs (auto-generated)
├── demo_results/       # .npz result files (one per run)
└── demo_summary.txt    # Plain-text results table

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Requirements

Python 3.8 or later is required. Install all dependencies with:

pip install numpy scipy GPy scikit-learn pymoo cma pyDOE2

Package	Purpose
numpy, scipy	Numerical computations
GPy	Gaussian Process surrogate model
scikit-learn	DBSCAN and KMeans clustering (CSAW, ClusterHC)
pymoo	Non-dominated sorting for Pareto front
cma	CMA-ES optimiser (eShotgun exploit step, D≥2)
pyDOE2	Latin Hypercube sampling (acquisition optimiser multi-start)

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Quick Start

Step 1 — Download or copy the two files into a folder:

BOPS/
├── methods.py
└── run_demo.py

Step 2 — Open a terminal in that folder and run:

python run_demo.py

That is all. No path configuration is needed. The script locates itself automatically.

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What the Demo Does

The script runs all 5 methods on two test functions:

Problem	D	Description	Known optimum
SixHumpCamel	2	Six-Hump Camel function	f* ≈ −1.032
Branin	2	Classic 2-D benchmark	f* ≈ 0.398

Settings (small for quick verification):

Parameter	Value
Batch size q	4
Budget	20 function evaluations (excluding initial design)
Initial design	LHD with 5×D points, fixed per problem/run and shared by all methods
Independent runs	2 per method
Pareto scenario	Sobol

Initial Observations and Fairness

For each (problem, run) pair, the script creates one Latin Hypercube Design (LHD) initial data file with 5×D observations. All methods then reuse exactly the same initial observations for that (problem, run), so differences in the summary table are due to the batch selection methods rather than different starting data.

The default 5×D initial design is deliberately small to keep the demo fast. For a stronger but slower verification run, increase N_INIT_FACTOR in run_demo.py from 5 to 10 and optionally increase N_RUNS from 2 to 5 or more.

Methods evaluated:

Method	Type	Description
eShotgun	Pareto-based	ε-greedy + Gaussian shotgun batch
eCSAW_Batch	Pareto-based	ε-greedy first point via CSAW selection
eClusterHC_Batch	Pareto-based	ε-greedy first point via ClusterHC selection
ClusterHC_PF_Batch	Pareto-based	DBSCAN clustering + hypervolume contribution
CSAW_PF_Batch	Pareto-based	DBSCAN clustering + entropy-weighted SAW score

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Expected Output

The terminal will print a results table like:

=================================================================
  RESULTS SUMMARY
=================================================================
  Problem        Method                 Mean best    Run 1    Run 2
  -------------- ---------------------- ----------  -------  -------
  SixHumpCamel   eShotgun               -1.0232  -1.0149  -1.0316
  SixHumpCamel   eCSAW_Batch            -1.0254  -1.0281  -1.0228 
  ...
  Branin         eShotgun                0.4791   0.5409   0.4173
  ...

  Total time : ~ 20s
  Results in : demo_results/
  Summary    : demo_summary.txt
=================================================================

The full table is also saved to demo_summary.txt.

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File Descriptions

methods.py

Self-contained module containing all method definitions. No external package (other than those listed above) is required. All helper functions from the original project files are consolidated here.

Exports the BATCH_METHODS dictionary which maps method names to callables:

from methods import BATCH_METHODS
func = BATCH_METHODS['eShotgun']
Xnew = func(model, lb, ub, feval_budget, q, cf, epsilon=0.1, pf=True)

run_demo.py

Standalone demo script. Contains:

• SixHumpCamel and Branin test problem definitions (inline — no external data needed)
• GP fitting with GPy (Matérn-5/2 kernel)
• LHD initial design generation
• Optimisation loop (identical to the main BOPS pipeline)
• Results saving and summary table

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