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. Algorithms for solving it range from approximate, with no lower bounds on performance, to exact, which suffer from worst case exponential time and space complexities. 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, much like simulated annealing, overcoming an inherent problem of many greedy algorithms. The use of agents ensures infeasible solutions are not considered while traversing the solution space and traversal of the solution space is both random and directed. M(x) is compared to a bound and bound algorithm and a simple greedy algorithm with a random shuffle. The results suggest M(x) is a good algorithm for approximating the 0-1 Multiple Knapsack problem.