Solving generalized open constraint optimization problem using two-level multi-agent framework

The open constraint optimization problem (OCOP) refers to the COP where constraints and variable domains can change over time and agents´ opinions have to be sought over a distributed network to form a solution. The openness of the problem has caused conventional approaches to COP such as branch-and-bound to fail to find optimal solutions. OCOP is a new problem and the approach to find an optimal solution (minimum total cost) introduced in [B. Faltings et al., (2003)] is based on an unrealistic assumption that agents are willing to report their options in non-decreasing order of cost. In this paper, we study a generalized OCOP where agents are self-interested and not obliged to reveal their private information such as the order of their options with respect to cost. The objective of the generalized OCOP is to find a solution with low total cost and high overall satisfaction level of agents. A two-level structured multi-agent framework has been proposed in the upper level, a neutral central solver allows agents report their preferred options in tiers and find a feasible initial solution from top tiers of options by constraint propagation and guided tiers expansion; in the lower level, agents form coalitions and negotiate among themselves on the initial solution by an argument of persuasive points. Experimental results have shown that this two-level structure yields very promising results that seek a good balance between the total cost of solution and the agents´ overall satisfaction level in the long run.