Distributed Lagrangean relaxation protocol for the generalized mutual assignment problem

Abstract. The generalized assignment problem (GAP) is a typical NP-hard problem and has been studied for many years mainly in the operations research community. The goal of the GAP is to find an optimal assignment of jobs to agents such that the assignment satisfies all of the resource constraints imposed on individual agents. This work provides a distributed formulation of GAP, the generalized mutual assignment problem (GMAP), to deal with the problems of job assignment in multi-agent systems. We present a distributed lagrangean relaxation protocol that enables agents to simultaneously solve a GMAP instance on peer-to-peer message exchange mechanisms. In the protocol we introduce a parameter that controls the range of "noise" mixed with increment/decrement in a lagrangean multiplier. This parameter can be used to produce quick agreement between the agents on a feasible solution with reasonably good quality. Our experimental results imply that the parameter may also allow us ...

• Type: Conference
• Year: 2006
• Where: ATAL
• Authors: Katsutoshi Hirayama
• Keywords: Assignment Problem, ATAL 2006, Generalized Assignment Problem, Intelligent Agents, Mutual Assignment Problem