# Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation

## Abstract

The 0-1 multiple knapsack problem appears in many domains from financial portfolio management to cargo ship stowing. Methods for solving it range from approximate algorithms, such as greedy algorithms, to exact algorithms, such as branch and bound. Approximate algorithms have no bounds on how poorly they perform and exact algorithms can suffer from exponential time and space complexities with large data sets. This paper introduces a market model based on agent decomposition and market auctions for approximating the 0-1 multiple knapsack problem, and an algorithm that implements the model (M(x)). M(x) traverses the solution space rather than getting caught in a local maximum, overcoming an inherent problem of many greedy algorithms. The use of agents ensures that infeasible solutions are not considered while traversing the solution space and that traversal of the solution space is not just random, but is also directed. M(x) is compared to a bound and bound algorithm (BB) and a simple greedy algorithm with a random shuffle (G(x)). The results suggest that M(x) is a good algorithm for approximating the 0-1 Multiple Knapsack problem. M(x) almost always found solutions that were close to optimal in a fraction of the time it took BB to run andmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., Livermore, CA (US)

- Sponsoring Org.:
- USDOE Office of Defense Programs (DP) (US)

- OSTI Identifier:
- 791413

- Report Number(s):
- UCRL-JC-135996

Journal ID: ISSN 0302--9743; TRN: US200511%%8

- DOE Contract Number:
- W-7405-Eng-48

- Resource Type:
- Conference

- Resource Relation:
- Journal Volume: 1821; Conference: Thirteenth International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, New Orleans, LA (US), 06/19/2000--06/22/2000; Other Information: PBD: 3 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; ARTIFICIAL INTELLIGENCE; CARGO; EXPERT SYSTEMS; MANAGEMENT; MARKET; NEGOTIATION

### Citation Formats

```
Smolinski, B.
```*Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation*. United States: N. p., 1999.
Web. doi:10.1007/3-540-45049-1_36.

```
Smolinski, B.
```*Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation*. United States. doi:10.1007/3-540-45049-1_36.

```
Smolinski, B. Fri .
"Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation". United States. doi:10.1007/3-540-45049-1_36. https://www.osti.gov/servlets/purl/791413.
```

```
@article{osti_791413,
```

title = {Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation},

author = {Smolinski, B},

abstractNote = {The 0-1 multiple knapsack problem appears in many domains from financial portfolio management to cargo ship stowing. Methods for solving it range from approximate algorithms, such as greedy algorithms, to exact algorithms, such as branch and bound. Approximate algorithms have no bounds on how poorly they perform and exact algorithms can suffer from exponential time and space complexities with large data sets. This paper introduces a market model based on agent decomposition and market auctions for approximating the 0-1 multiple knapsack problem, and an algorithm that implements the model (M(x)). M(x) traverses the solution space rather than getting caught in a local maximum, overcoming an inherent problem of many greedy algorithms. The use of agents ensures that infeasible solutions are not considered while traversing the solution space and that traversal of the solution space is not just random, but is also directed. M(x) is compared to a bound and bound algorithm (BB) and a simple greedy algorithm with a random shuffle (G(x)). The results suggest that M(x) is a good algorithm for approximating the 0-1 Multiple Knapsack problem. M(x) almost always found solutions that were close to optimal in a fraction of the time it took BB to run and with much less memory on large test data sets. M(x) usually performed better than G(x) on hard problems with correlated data.},

doi = {10.1007/3-540-45049-1_36},

journal = {},

issn = {0302--9743},

number = ,

volume = 1821,

place = {United States},

year = {1999},

month = {9}

}