# Biogeography-Based Optimization (BBO) in MATLAB

URL: https://yarpiz.com/biogeography-based-optimization-ypea113
Author: Mostapha Kalami Heris
Published: 2015-09-06
Updated: 2026-10-30
Topics: Metaheuristics

> Implement biogeography-based optimization in MATLAB with blended migration, mutation, elitism, and a bounded Sphere test problem.

Biogeography-Based Optimization (BBO) is an evolutionary algorithm and metaheuristic inspired by biogeography: speciation (the evolution of new species), the migration of species between islands, and the extinction of species. Dan Simon proposed it in 2008 in [this paper](http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4475427).

The algorithm is based on a mathematical model of species migration between habitats. The optimizer turns the migration analogy into rates for exchanging the variables of candidate solutions. The suitability of a habitat is stored as the Habitat Suitability Index, which is defined from the objective function of the problem being solved. A more detailed description is in the [Wikipedia article on biogeography-based optimization](https://en.wikipedia.org/wiki/Biogeography-based_optimization).

## How BBO works

Each habitat is a candidate solution, and each decision variable is one feature of the habitat. A good habitat (low cost) has many species. It shares its features with others easily and accepts few new ones. A poor habitat has few species. It accepts new features easily and shares few.

BBO turns this into two rates for each habitat $i$:

- the emigration rate $\mu_i$, the chance that habitat $i$ shares a feature with another habitat,
- the immigration rate $\lambda_i$, the chance that a feature of habitat $i$ is replaced with information from another habitat.

With the population sorted from best to worst, the simplest choice is a linear model, in which $\mu_i$ falls from 1 for the best habitat to 0 for the worst, and

$$
\lambda_i = 1 - \mu_i
$$

### Migration

For each habitat $i$ and each variable $k$, migration happens with probability $\lambda_i$. A source habitat $j \neq i$ is then chosen with a probability proportional to its emigration rate $\mu_j$, so good habitats are chosen more often. In the original BBO, the feature is copied from $j$ to $i$. The code in this post uses a blended migration, which moves the feature only part of the way:

$$
x_{i,k}^{\text{new}} = x_{i,k} + \alpha\,\left(x_{j,k} - x_{i,k}\right)
$$

With $\alpha = 1$ this is the original copy. The code uses $\alpha = 0.9$.

### Mutation and elitism

After migration, each variable is mutated with a small probability by adding Gaussian noise. Then the best habitats of the old population are kept, and the rest of the new population is filled with the best new habitats. This elitism keeps the best solutions found so far.

## Implementation in MATLAB

This post shares a structured, open-source MATLAB implementation of BBO. If you know MATLAB, you will find it easy to use the source code in your research and projects.

### What is in the download

The `BBO` folder holds four files:

- `bbo.m`: the BBO script, with the problem definition, the parameters, the main loop and the results.
- `RouletteWheelSelection.m`: picks the source habitat in proportion to the emigration rates.
- `Sphere.m`: the sample cost function, $f(x) = \sum_{i=1}^{n} x_i^2$.
- `main.m`: a one line entry point that runs `bbo.m`.

To run the code, open the `BBO` folder in MATLAB and run `main.m`. The program prints the best cost of every iteration and then plots the best cost against the iteration number on a logarithmic scale.

The script creates the first habitats with `unifrnd`, a function of the Statistics and Machine Learning Toolbox, so it probably needs that toolbox.

### Parameters in the code

| Parameter | Meaning | Value |
| --- | --- | ---: |
| `nVar` | Number of decision variables | 5 |
| `VarMin`, `VarMax` | Lower and upper bounds of the variables | $-10$, $10$ |
| `MaxIt` | Maximum number of iterations | 1000 |
| `nPop` | Number of habitats (population size) | 50 |
| `KeepRate` | Share of the best habitats kept in each iteration | 0.2 |
| `mu`, `lambda` | Emigration and immigration rates | `linspace(1, 0, nPop)` and `1 - mu` |
| `alpha` | Migration coefficient | 0.9 |
| `pMutation` | Mutation probability of each variable | 0.1 |
| `sigma` | Standard deviation of the mutation | $0.02\,(\text{VarMax} - \text{VarMin})$ |

With these values, the 10 best habitats of the old population and the 40 best new habitats form the next population. Positions outside the bounds are set back to the nearest bound.

To solve your own problem, write a cost function that takes a row vector and returns a number, and set `CostFunction`, `nVar`, `VarMin` and `VarMax` in the problem definition section of `bbo.m`.

## Check the result

For the Sphere example, a low cost should correspond to coordinates near the origin and within the bounds. Keep the retained-elite count and new-population count consistent when changing `nPop` or `KeepRate`. The linear migration rates need a population with multiple members. Compare several runs to assess whether changing migration or mutation gives a consistent improvement.

## Related posts

- [YPEA](https://yarpiz.com/yarpiz-evolutionary-algorithms-ypea) is a MATLAB toolbox that includes BBO and 14 other algorithms that share one problem definition.
- [Particle Swarm Optimization in MATLAB](https://yarpiz.com/particle-swarm-optimization-ypea102) is another population based method with the same code structure.

## How to cite

Mostapha Kalami Heris, Biogeography-Based Optimization (BBO) in MATLAB (YPEA113), Yarpiz, 2015. https://yarpiz.com/biogeography-based-optimization-ypea113