Algorithm Selection for Constraint Optimization Domains Avi Rosenfeld Department of Industrial Engineering Jerusalem College of Technology, Jerusalem, Israel 9116001 Email: rosenfa@jct.ac.il Abstract—In this paper we investigate methods for selecting the best algorithms in classic distributed constraint optimization problems. While these are NP-complete problems, many heuris- tics have nonetheless been proposed. We found that the best method to use can change radically based on the specifics of a given problem instance. Thus, dynamic methods are needed that can choose the best approach for a given problem. We found that large differences typically exist in the expected utility between algorithms, allowing for a clear policy. We present a dynamic algorithm selection approach based on this realization. As support for this approach, we describe the results from thousands of trials from Distributed Constraint Optimization problems that demonstrates the strong statistical improvement of this dynamic approach over the static methods they are based on. I. I NTRODUCTION When multiple agents operate within a joint envi- ronment, inter-agent constraints typically exist be- tween group members. Assuming these agents oper- ate within a cooperative environment, the team must decide how to coordinate satisfying as many of these constraints as possible [21]. Instances of such prob- lems are classic distributed planning and schedul- ing domains including specific applications such as supply chain management, disaster rescue manage- ment, Personal Data Assistant (PDA) scheduling, and military conflict planning [9], [19]. However, solving these real-world problems are challenging as they are known to be of NP-complete, or worse, complexities [10], [12], [19]. Despite the computational complexity inherent in these problems, a variety of algorithms have been suggested [4], [10], [11], [12], [15], [17], [21]. These algorithms differ in what and how agents communicate to attempt to find an optimal assignment. Each of these approaches have different resource cost requirements (e.g., time, number of messages), and are often useful in different problem classes. Thus, an important task for designers of these planning and scheduling systems is to find the algorithm that will work best for a given problem instance. In this paper we claim that an algorithm selection approach is helpful in dictating which type of ap- proach to use. The key to this approach is that differ- ences between algorithms are typically quite large, and can be locally measured. This allows agents to locally control what information to transfer to group members. To demonstrate the effectiveness of this approach we study a general Distributed Constraint Optimization Problem (DCOP) domain [10], [11], [21]. We performed thousands of trials involving a variety team sizes and problem parameters and found that the described algorithm selection ap- proach was effective in significantly outperforming the static methods they were based on. II. DOMAIN FORMALIZATION AND ALGORITHMS DESCRIPTION In this section, we formally present a general Dis- tributed Constraint Satisfaction and Optimization Problem domain (DCSP and DCOP respectively). The goal within a DCSP or DCOP problem is for distributed agents, each with control of some variables, to either satisfy (in DCSP) or to optimize (in DCOP) a global utility function. DCOP is a generalization of the DCSP problem as the goal is to minimize the number of non-fulfilled constraints, and is thus more suitable for most real-world prob- lems [9]. The DCOP problem has been previously defined as follows [4], [10]: • A set of N agents A = A 1 , A 2 ... , A N • A set of n variables V = x 1 , x 2 ... , x n • A set of domains D = D 1 , D 2 ... , D n where the value of x i is taken from D i . Each D i is assumed finite and discrete. • A set of cost function f = f 1 , f 2 ... , f m where each f i is a function f i : D i,1 × ... × D i,j → N ∪∞. Cost functions represent what must be optimized and are typically referred to as constraints. (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 4, No. 2, 2013 26 | Page www.ijacsa.thesai.org