# Combining local search with co-evolution in a remarkably simple way

## Abstract

The authors explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problem. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire gene-pool of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single sub-optimal solution with new, random ones. Large fluctuations, or avalanches, ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been conjectured to occur in the region of parameter space containing the hardest instances. We demonstrate how extremal optimization can be implemented for a variety of hard optimization problems. We believe that this will be a useful tool in the investigation of phase transitions in combinatorial optimization, thereby helping to elucidate the origin of computational complexity.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 768990

- Report Number(s):
- LA-UR-00-2318

TRN: AH200105%%106

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: Proceedings of the Congress on Evolutionary Computation, La Jolla, CA (US), 07/16/2000--07/19/2000; Other Information: PBD: 1 May 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; ALGORITHMS; ANNEALING; CRITICALITY; FLUCTUATIONS; GENETICS; OPTIMIZATION; ORIGIN; PERFORMANCE; PHYSICS

### Citation Formats

```
Boettcher, S., and Percus, A.
```*Combining local search with co-evolution in a remarkably simple way*. United States: N. p., 2000.
Web.

```
Boettcher, S., & Percus, A.
```*Combining local search with co-evolution in a remarkably simple way*. United States.

```
Boettcher, S., and Percus, A. Mon .
"Combining local search with co-evolution in a remarkably simple way". United States. https://www.osti.gov/servlets/purl/768990.
```

```
@article{osti_768990,
```

title = {Combining local search with co-evolution in a remarkably simple way},

author = {Boettcher, S. and Percus, A.},

abstractNote = {The authors explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problem. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire gene-pool of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single sub-optimal solution with new, random ones. Large fluctuations, or avalanches, ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been conjectured to occur in the region of parameter space containing the hardest instances. We demonstrate how extremal optimization can be implemented for a variety of hard optimization problems. We believe that this will be a useful tool in the investigation of phase transitions in combinatorial optimization, thereby helping to elucidate the origin of computational complexity.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {5}

}