Chapter 3: AI Optimization Algorithms

Learning Objectives

Understand the principles of Bayesian Optimization (PHYSBO)
Learn when to use each of NIMO's 11 algorithms
Configure algorithm-specific parameters
Choose the right algorithm for your optimization problem

3.1 The Exploration-Exploitation Trade-off

Before diving into specific algorithms, let's understand the fundamental challenge in optimization:

graph LR subgraph Exploration[Exploration] E1[Try new regions] E2[Discover unknowns] E3[Avoid local optima] end subgraph Exploitation[Exploitation] X1[Focus on known good areas] X2[Refine best solutions] X3[Maximize current knowledge] end Exploration <-->|Balance| Exploitation style Exploration fill:#667eea,color:#fff style Exploitation fill:#11998e,color:#fff

Exploration vs Exploitation

Exploration: Testing regions where we have little information, potentially finding better solutions in unexplored areas.

Exploitation: Focusing on regions where we've already found good results, refining our best solutions.

Good optimization algorithms balance both strategies automatically.

3.2 Bayesian Optimization (PHYSBO)

PHYSBO is NIMO's flagship algorithm, based on Bayesian Optimization principles. It's the recommended choice for most materials optimization problems.

How Bayesian Optimization Works

The algorithm follows a three-step process:

Build a surrogate model: Use a Gaussian Process (GP) to model the objective function based on existing data
Compute acquisition function: Calculate where the next experiment is most likely to improve results
Select next candidate: Choose the point that maximizes the acquisition function

graph TB A[Existing Data] --> B[Gaussian Process Model] B --> C[Predict Mean & Variance] C --> D[Acquisition Function] D --> E[Select Next Candidate] E --> F[Run Experiment] F --> A style B fill:#667eea,color:#fff style D fill:#f093fb,color:#fff style E fill:#28a745,color:#fff

PHYSBO in NIMO

Code Example 1: Basic PHYSBO Usage

import nimo

# Basic Bayesian Optimization
nimo.selection(
    method="PHYSBO",
    input_file="candidates.csv",
    output_file="proposals.csv",
    num_objectives=1,
    num_proposals=1
)

Code Example 2: PHYSBO with Advanced Options

import nimo

# Bayesian Optimization with configuration
nimo.selection(
    method="PHYSBO",
    input_file="candidates.csv",
    output_file="proposals.csv",
    num_objectives=1,
    num_proposals=3,
    physbo_score="EI",     # Acquisition function: EI, PI, or TS
    physbo_seed=42         # Random seed for reproducibility
)

Acquisition Functions

PHYSBO supports three acquisition functions:

Function	Full Name	Strategy	When to Use
EI	Expected Improvement	Balanced	Default choice, most situations
PI	Probability of Improvement	Exploitation-heavy	When close to optimal, need refinement
TS	Thompson Sampling	Exploration-heavy	Multi-modal functions, parallel experiments

Recommended: Expected Improvement (EI)

For most materials science problems, EI provides the best balance between exploration and exploitation. It naturally adapts to the optimization landscape.

3.3 Random Exploration (RE)

RE is a simple but essential algorithm: it randomly selects from untested candidates.

Code Example 3: Random Exploration

import nimo

# Random selection for initial data collection
nimo.selection(
    method="RE",
    input_file="candidates.csv",
    output_file="proposals.csv",
    num_objectives=1,
    num_proposals=5,
    re_seed=42  # For reproducibility
)

When to Use RE

First cycle: Collect initial data before other algorithms can work
Baseline comparison: Compare against random to validate AI improvement
High uncertainty: When you have no prior knowledge about the search space

Typical Workflow

Cycle 1: RE (collect 5-10 random samples)
Cycles 2+: PHYSBO (intelligent selection based on data)

3.4 BLOX: Random Forest Approach

BLOX uses Random Forest models instead of Gaussian Processes. This makes it faster for high-dimensional problems.

Code Example 4: BLOX Usage

import nimo

# Random Forest-based optimization
nimo.selection(
    method="BLOX",
    input_file="candidates.csv",
    output_file="proposals.csv",
    num_objectives=1,
    num_proposals=3
)

BLOX vs PHYSBO Comparison

Aspect	PHYSBO	BLOX
Model	Gaussian Process	Random Forest
Uncertainty	Well-calibrated	Approximate
Speed (low-dim)	Fast	Fast
Speed (high-dim)	Slow	Fast
Best for	≤20 descriptors	>20 descriptors

3.5 Phase Diagram Construction (PDC)

PDC is designed specifically for materials science problems where you need to map out different phases or regions.

Code Example 5: PDC Usage

import nimo

# Phase diagram construction
nimo.selection(
    method="PDC",
    input_file="candidates.csv",
    output_file="proposals.csv",
    num_objectives=1,
    num_proposals=3
)

When to Use PDC

Mapping phase boundaries in alloy systems
Identifying regions of different material properties
Exploring multi-component composition spaces

3.6 Multi-Objective Algorithms

When optimizing multiple objectives simultaneously (e.g., maximize strength AND minimize cost), use these algorithms:

PTR: Pareto-based Thompson Ranking

Code Example 6: Multi-Objective Optimization with PTR

import nimo

# Multi-objective optimization (2 objectives)
nimo.selection(
    method="PTR",
    input_file="candidates.csv",
    output_file="proposals.csv",
    num_objectives=2,  # Optimize 2 properties
    num_proposals=3
)

Pareto Optimality

A solution is Pareto optimal if no objective can be improved without worsening another. Multi-objective algorithms find the set of all Pareto optimal solutions (the Pareto front).

3.7 Algorithm Selection Guide

Use this decision tree to choose the right algorithm:

graph TD A[Start] --> B{First cycle?} B -->|Yes| C[Use RE] B -->|No| D{Multi-objective?} D -->|Yes| E{>2 objectives?} D -->|No| F{>20 descriptors?} E -->|Yes| G[Use PTR or BOMP] E -->|No| H[Use PTR] F -->|Yes| I[Use BLOX] F -->|No| J{Phase mapping?} J -->|Yes| K[Use PDC] J -->|No| L[Use PHYSBO] style C fill:#667eea,color:#fff style G fill:#11998e,color:#fff style H fill:#11998e,color:#fff style I fill:#f093fb,color:#fff style K fill:#28a745,color:#fff style L fill:#667eea,color:#fff

Quick Reference Table

Scenario	Recommended Algorithm	Reason
First experiments	RE	Need initial random data
General optimization	PHYSBO	Best overall performance
High dimensions (>20)	BLOX	Faster with many features
Phase mapping	PDC	Designed for phase diagrams
Multi-objective	PTR	Pareto optimization
Fast exploration	SLESA	Quick candidate selection

3.8 Algorithm-Specific Parameters

Each algorithm has specific parameters you can tune:

PHYSBO Parameters

physbo_score: "EI", "PI", or "TS"
physbo_seed: Random seed for reproducibility

RE Parameters

re_seed: Random seed for reproducibility

BLOX Parameters

blox_num_rand_basis: Number of random basis functions
blox_seed: Random seed for reproducibility

Exercises

Exercise 1: Algorithm Selection

For each scenario, choose the most appropriate algorithm:

You're starting a new optimization with no prior data (10 descriptors)
You want to optimize hardness and ductility simultaneously
You're mapping the phase diagram of a ternary alloy system
You have 50 descriptors and need fast optimization

Exercise 2: PHYSBO Configuration

Write NIMO code to:

Use PHYSBO with Thompson Sampling acquisition
Select 5 proposals per cycle
Set a random seed of 123 for reproducibility

Summary

Bayesian Optimization (PHYSBO) is the default choice for most problems
Random Exploration (RE) is essential for collecting initial data
BLOX scales better for high-dimensional problems
PDC is specialized for phase diagram construction
PTR handles multi-objective optimization
Always start with RE for the first cycle, then switch to intelligent algorithms

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