Understand the fitness landscape of your optimization problem.

A fitness landscape maps the candidates in a design space, such as protein variants or reaction conditions, to their measured performance. GraphFLA builds this landscape from your data and characterizes its topography, revealing what makes a problem easy or hard to model and to optimize. These insights help you develop better predictive models and search algorithms.

Quick start Tutorials

$ pip install graphfla

An illustrative fitness landscape with improving paths, one reaching the global optimum and two ending at local optima. — improving path to the global optimum

improving paths ending at local optima

20+

measures of landscape structure

7

landscape types for sequences, categorical, ordinal and mixed data

8

model landscapes and benchmark problems

12

step-by-step tutorials on published data

179

curated datasets across diverse domains

How it works

Build, analyze, and manipulate fitness landscapes as graphs.

Protein function and stability

Explore how amino acid variation affects protein function and stability.

1Provide your data

Protein variant screening data, pairing amino acid sequences with measurements such as catalytic activity, binding affinity or thermostability.

Your data

Protein sequence	Activity
MKTAYIAKQRQISFVKSHFS	23%
MKTAFIAKQRQISFVKSHFS	41%
MKTAYIGKQRQISFVKSHFS	36%
MKTAYIAKQKQISFVKSHFS	57%
MKTAFIGKQRQISFVKSHFS	42%
MKTAFIAKQKQISFVKSHFS	64%
MKTAYIGKQKQISFVKSHFS	73%
MKTAFIGKQKQISFVKSHFS	91%

2Build the landscape

GraphFLA connects variants that differ by a single amino acid substitution, mapping the measured property across sequence space.

Illustrative protein function and stability landscape with 4 peaks, drawn above its neighbor graph of 32 candidates.

Landscape Neighbor graph

3Analyze its topography

Characterize epistasis, mutational robustness and the accessibility of optimal sequences.

Landscape profile

Local optima4 / 32

Roughness0.68

Neutrality19%

Fitness-distance correlation−0.25

Variable interactions

Magnitude 52%
Sign 31%
Reciprocal sign 17%

Reaction conditions

Explore how reagents and reaction conditions affect chemical reactivity and selectivity.

1Provide your data

Reaction screening data, with columns describing reagents and reaction conditions alongside an outcome such as yield, conversion or selectivity.

Your data

Catalyst	Solvent	Temp.	Yield
Nickel	Water	40 °C	32%
Nickel	Ethanol	60 °C	48%
Copper	Water	60 °C	54%
Copper	Ethanol	80 °C	81%
Palladium	Water	40 °C	65%
Palladium	Ethanol	60 °C	72%
Nickel	Acetone	80 °C	51%
Copper	Acetone	40 °C	74%

2Build the landscape

GraphFLA connects experiments that differ in a single reagent choice or a step in one reaction condition.

Illustrative reaction conditions landscape with 3 peaks, drawn above its neighbor graph of 36 candidates.

Landscape Neighbor graph

3Analyze its topography

Characterize interactions between reaction factors, sensitivity to local changes and the accessibility of optimal conditions.

Landscape profile

Local optima3 / 36

Autocorrelation0.61

Neutrality12%

Fitness-distance correlation−0.70

Variable interactions

Magnitude 46%
Sign 35%
Reciprocal sign 19%

Alloy composition

Explore how alloy composition affects material properties.

1Provide your data

Composition–property data, pairing elemental proportions with measurements such as hardness, strength or conductivity.

Your data

Copper	Zinc	Nickel	Hardness
60%	25%	15%	145 HV
60%	20%	20%	170 HV
65%	20%	15%	158 HV
65%	15%	20%	185 HV
70%	20%	10%	135 HV
70%	15%	15%	162 HV
55%	25%	20%	176 HV
55%	20%	25%	198 HV

2Build the landscape

GraphFLA connects neighboring compositions through small adjustments in elemental proportions, mapping the chosen property across composition space.

Illustrative alloy composition landscape with 2 peaks, drawn above its neighbor graph of 28 candidates.

Landscape Neighbor graph

3Analyze its topography

Identify composition–property trends, interactions between alloying elements and regions with stable material performance.

Landscape profile

Local optima2 / 28

Autocorrelation0.83

Neutrality24%

Fitness-distance correlation−0.46

Variable interactions

Magnitude 63%
Sign 25%
Reciprocal sign 12%

Software configurations

Explore how software configuration options affect system performance.

1Provide your data

Configuration benchmark data, pairing software settings with performance measurements such as execution time, throughput or memory usage.

Your data

Cache	Parallel	Debug	Time
Off	Off	On	92 s
On	Off	On	61 s
Off	On	On	55 s
Off	Off	Off	78 s
On	On	On	32 s
On	Off	Off	49 s
Off	On	Off	43 s
On	On	Off	24 s

2Build the landscape

GraphFLA connects configurations that differ in a single option, mapping performance across configuration space.

Illustrative software configurations landscape with 3 peaks, drawn above its neighbor graph of 48 candidates.

Landscape Neighbor graph

3Analyze its topography

Characterize interactions between configuration options, performance sensitivity and the accessibility of optimal configurations.

Landscape profile

Local optima3 / 48

Autocorrelation0.72

Neutrality16%

Fitness-distance correlation−0.62

Variable interactions

Magnitude 57%
Sign 29%
Reciprocal sign 14%

Model hyperparameters

Explore how model hyperparameters affect predictive performance.

1Provide your data

Hyperparameter evaluation data, pairing model and training settings with validation metrics such as accuracy or prediction error.

Your data

Depth	Trees	Leaf	Error
4	50	1	25.4
4	100	4	23.8
8	50	1	18.2
8	100	2	15.6
12	50	2	17.4
12	100	4	16.1
16	50	1	16.7
16	100	4	16.2

2Build the landscape

GraphFLA connects neighboring configurations through a change in one hyperparameter, mapping predictive performance across the search space.

Illustrative model hyperparameters landscape with 2 peaks, drawn above its neighbor graph of 36 candidates.

Landscape Neighbor graph

3Analyze its topography

Characterize hyperparameter interactions, sensitivity to tuning and the accessibility of high-performing configurations.

Landscape profile

Local optima2 / 36

Autocorrelation0.56

Neutrality21%

Fitness-distance correlation−0.39

Variable interactions

Magnitude 49%
Sign 34%
Reciprocal sign 17%

Browse the datasets

Quick start

From raw data to landscape analysis in a few lines.

Simply load your dataset, specify the variables and the objective, and build the landscape. The same steps apply to laboratory measurements, simulations and model evaluations.

$ pip install graphfla

Run the quick start Try a worked tutorial Read the API reference

quickstart.pyPython

import pandas as pdfrom graphfla import analysisfrom graphfla.landscape import ProteinLandscape df = pd.read_csv("variants.csv")X = df["sequence"]  # Amino-acid sequence of each variantf = df["activity"]  # Measured activity, to maximize landscape = ProteinLandscape(maximize=True)landscape.build_from_data(X, f)analysis.profile(landscape, seed=42)

quickstart.pyPython

import pandas as pdfrom graphfla import analysisfrom graphfla.landscape import Landscape df = pd.read_csv("reactions.csv")X = df[["catalyst", "solvent"]]  # Reaction conditionsf = df["yield"]  # Product yield, to maximize landscape = Landscape(maximize=True)landscape.build_from_data(    X, f, data_types={c: "categorical" for c in X})analysis.profile(landscape, seed=42)

quickstart.pyPython

import pandas as pdfrom graphfla import analysisfrom graphfla.landscape import OrdinalLandscape df = pd.read_csv("alloys.csv")  # columns: W, Re, Os, hardnessX = df[["W", "Re"]]  # Os = 100 - W - Re, so it is impliedf = df["hardness"]  # Hardness at 1,000 °C, to maximize landscape = OrdinalLandscape(maximize=True)landscape.build_from_data(X, f)analysis.profile(landscape, seed=42)

quickstart.pyPython

import pandas as pdfrom graphfla import analysisfrom graphfla.landscape import BooleanLandscape df = pd.read_csv("builds.csv")flags = ["gvn", "inline", "instcombine",         "jump_threading", "sccp", "simplifycfg"]X = df[flags]  # One on/off column per compiler flagf = df["time"]  # Compilation time, to minimize landscape = BooleanLandscape(maximize=False)landscape.build_from_data(X, f)analysis.profile(landscape, seed=42)

quickstart.pyPython

import pandas as pdfrom graphfla import analysisfrom graphfla.landscape import Landscape df = pd.read_csv("grid_search.csv")X = df[["depth", "leaf", "features"]]  # Hyperparametersf = df["rmse"]  # Validation error, to minimize landscape = Landscape(maximize=False)landscape.build_from_data(    X, f, data_types={c: "ordinal" for c in X})analysis.profile(landscape, seed=42)

Seven landscape classes

Choose the class that matches your data.

What you can measure

A holistic picture of your landscape, with 20+ features across four aspects.

Each feature is implemented from established studies in evolutionary biology and optimization. Together they let you explore your problem from complementary angles and understand it fully.

Two landscapes side by side: a smooth one with a single peak and a rugged one with many local peaks.

smooth: one peak rugged: many local peaks

Ruggedness

A rugged landscape has many local peaks and abrupt changes in fitness between neighbors. Ruggedness makes it more likely that stepwise improvement stops short of the best candidate.

Explore ruggedness

a change that increases fitness here
the same change decreases it there

The same change increases fitness in one part of the landscape and decreases it in another.

Interactions

Variables interact when the effect of changing one depends on the values of others, known as epistasis in biology. Interactions that reverse the direction of an effect can block improving paths and create multiple peaks.

Explore interactions

reaches the global optimum
stops at a local optimum

Improving paths on a landscape with three peaks: two reach the global optimum, three stop at local optima.

Navigability

Navigability describes how easily a search can find the global optimum. The landscape may provide useful guidance or misleading signals that steer the search elsewhere.

Explore navigability

neutral neighbors
a step to higher fitness

Neutrality

Neutral changes leave fitness essentially unchanged. Large flat regions can stall a search, but they also connect distant candidates of equal quality.

Explore neutrality

Why landscape topography matters

Landscape features help interpret model performance and optimization outcomes.

Landscape features help explain why predictive models and search algorithms perform differently across problems. They reveal interactions that complicate prediction, local optima that can trap search, and broad trends that can guide optimization.

Zero-shot prediction

ProteinGym · Prediction performance across protein assays

Landscape feature Model

Directed evolution

18 near-complete combinatorial DMS assays

Landscape feature Search strategy

Performance

Scales to millions of candidates on a single machine.

Landscape construction in GraphFLA is heavily optimized for speed and memory efficiency, enabling analysis of large combinatorial spaces on a single machine.

59,161×

faster construction at 1,048,576 candidates

2,384×

lower peak memory on the same build

GraphFLA
Naive all-pairs

Construction time · log scale

Peak memory · log scale

Complete binary landscapes with 8 to 20 variables. Apple M4 Pro, Python 3.9, single thread. Peak memory includes Python and its dependencies. The baseline is a nested Python loop with a dense distance matrix.

Case studies

Applicable to any combinatorial optimization problem.

GraphFLA provides a unified framework for analyzing combinatorial optimization problems across domains, with flexible representations of variables, objectives and neighborhood relationships.