Adaptive and Non-adaptive Distribution Functions for DSA

Distributed hill-climbing algorithms are a powerful, practical technique for solving large Distributed Constraint Satisfaction Problems (DSCPs) such as distributed scheduling, resource allocation, and distributed optimization. Although incomplete, an ideal hill-climbing algorithm finds a solution that is very close to optimal while also minimizing the cost (i.e. the required bandwidth, processing cycles, etc.) of finding the solution. The Distributed Stochastic Algorithm (DSA) is a hill-climbing technique that works by having agents change their value with probability p when making that change will reduce the number of constraint violations. Traditionally, the value of p is constant, chosen by a developer at design time to be a value that works for the general case, meaning the algorithm does not change or learn over the time taken to find a solution. In this paper, we replace the constant value of p with different probability distribution functions in the context of solving graph-coloring problems to determine if DSA can be optimized when the probability values are agent-specific. We experiment with non-adaptive and adaptive distribution functions and evaluate our results based on the number of violations remaining in a solution and the total number of messages that were exchanged.