Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks

This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the NP-complete multicast routing problem (MRP). The main contribution is the extension of PSO from continuous domain to the binary or discrete domain. Firstly, a novel bi-velocity strategy is developed to represent possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP where 1 stands for a node being selected to construct the multicast tree while 0 stands for being otherwise. Secondly, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the OR-library (Operation Research Library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly as it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on GA, ACO, and PSO

Using synchronous Boolean networks to model several phenomena of collective behavior

In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior of a member of a collective (agent) is called conforming if the opinion of this agent at current time moment conforms to the opinion of some other agents at the previous time moment. We presume that at each moment of time every agent makes a decision by choosing from the set {0,1} (where 1-decision corresponds to action and 0-decision corresponds to inaction). In our approach we model collective behavior with synchronous Boolean networks. We presume that in a network there can be agents that act at every moment of time. Such agents are called instigators. Also there can be agents that never act. Such agents are called loyalists. Agents that are neither instigators nor loyalists are called simple agents. We study two combinatorial problems. The first problem is to find a disposition of instigators that in several time moments transforms a network from a state where a majority of simple agents are inactive to a state with a majority of active agents. The second problem is to find a disposition of loyalists that returns the network to a state with a majority of inactive agents. Similar problems are studied for networks in which simple agents demonstrate the contrary to conforming behavior that we call anticonforming. We obtained several theoretical results regarding the behavior of collectives of agents with conforming or anticonforming behavior. In computational experiments we solved the described problems for randomly generated networks with several hundred vertices. We reduced corresponding combinatorial problems to the Boolean satisfiability problem (SAT) and used modern SAT solvers to solve the instances obtained