Distributed Pareto Local Search for Multi-Objective DCOPs

Many real world optimization problems involving sets of agents can be modeled as Distributed Constraint Optimization Problems (DCOPs). A DCOP is defined as a set of variables taking values from finite domains, and a set of constraints that yield costs based on the variables' values. Agents are in charge of the variables and must communicate to find a solution minimizing the sum of costs over all constraints. Many applications of DCOPs include multiple criteria. For example, mobile sensor networks must optimize the quality of the measurements and the quality of communication between the agents. This introduces trade-offs between solutions that are compared using the concept of Pareto dominance. Multi-Objective Distributed Constraint Optimization Problems (MO-DCOPs) are used to model such problems where the goal is to find the set of Pareto optimal solutions. This set being exponential in the number of variables, it is important to consider fast approximation algorithms for MO-DCOPs. The bounded multi-objective max-sum (B-MOMS) algorithm is the first and only existing approximation algorithm for MO-DCOPs and is suited for solving a less-constrained problem. In this paper, we propose a novel approximation MO-DCOP algorithm called Distributed Pareto Local Search (DPLS) that uses a local search approach to find an approximation of the set of Pareto optimal solutions. DPLS provides a distributed version of an existing centralized algorithm by complying with the communication limitations and the privacy concerns of multi-agent systems. Experiments on a multi-objective extension of the graph-coloring problem show that DPLS finds significantly better solutions than B-MOMS for problems with medium to high constraint density while requiring a similar runtime.