Approximate Analysis of Distributed Dual Decomposition Algorithm for Mixed Integer Linear Programming

Abstract

This paper proposes a distributed dual decomposition algorithm for solving mixed-integer linear programming (MILP) problems in multi-agent systems. In the proposed approach, a MILP problem is transformed into an approximated problem by linear programming relaxation, which enables each agent to independently solve their local subproblems. The theoretical analysis provides guarantees on both the feasibility error bounds and the optimality gap of the solutions obtained by the proposed method. The effectiveness of the proposed method is shown through a numerical example of a fairness-aware multiple traveling salesman problem.