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 and with much less memory on large test data sets. M(x) usually performed better than G(x) on hard problems with correlated data.

Design methodologies for resource management of many-core embedded systems

“…Market oriented approaches have been used for distributed resource allocation problems and can be classified into three models: 1) price-based, 2) auctionbased, and 3) trade-based [210]. Mechanisms that are based on price and auction usually require a centralized entity with a full picture of network conditions (e.g.…”

“…Mechanisms that are based on price and auction usually require a centralized entity with a full picture of network conditions (e.g. an auctioneer to run the auction or a decision-maker to calculate the price) [210,128,150]. Due to the nature of the system and problem, a trade-based distributed solution seems more effective.…”