Getting What You Pay For: Is Exploration in Distributed Hill Climbing Really Worth it?

The Distributed Stochastic Algorithm (DSA), Distributed Breakout Algorithm (DBA), and variations such as Distributed Simulated Annealing (DSAN), MGM-1, and DisPeL, are distributed hill-climbing techniques for solving large Distributed Constraint Optimization Problems (DCOPs) such as distributed scheduling, resource allocation, and distributed route planning. Like their centralized counterparts, these algorithms employ escape techniques to avoid getting trapped in local minima during the search process. For example, the best known version of DSA, DSA-B, makes hill-climbing and lateral escape moves, moves that do not impact the solution quality, with a single probability $p$. DSAN uses a similar scheme, but also occasionally makes a move that leads to a worse solution in an effort to find a better overall solution. Although these escape moves tend to lead to a better solutions in the end, the cost of employing the various strategies is often not well understood. In this work, we investigate the costs and benefits of the various escape strategies by empirically evaluating each of these protocols in distributed graph coloring and sensor tracking domains. Through our testing, we discovered that by reducing or eliminating escape moves, the cost of using these algorithms decreases dramatically without significantly affecting solution quality.