Ants-based Routing Marc Heissenbüttel University of Berne It’s based on the principle of “stigmergy”[Grasse 59], or “communication through the environment”. While foraging, ants lay down a trail of some chemical substance, pheromones. Any subsequent ant follows this trail with a certain probability, depending on how strong the concentration of the pheromons is on this trail. This causes a somehow autocatalytic reaction, i.e. one that is accelerated by itself. Ants attracted by the pheromone will lay more of the same on the same trail, causing even more ants to be attracted. This is one of two important ascpects. The other is called implicit evaluation. We mean the fact that shorter paths (which correspond to lower cost solution in artifical ants) will be completed earlier than longer ones, and therefore they will receive pheromone reinforcement more quickly. These are the two main facts that make possible for the ants to find shortest paths. Marc Heissenbüttel University of Berne http://www.iam.unibe.ch/ Berne, 2002-04-03

Table of Contents Introduction Meta-heuristic Ant Based Control (ABC) AntNet Ants-based Routing in Mobile Ad Hoc Networks Conclusion and Open Issues

Introduction Nature as a model for computer scientists Social insects simple behavior by limited individuals but together can solve complex tasks “Finding shortest path” applied to “Traveling Salesman Problem”, routing in networks,... Stigmergy ~ “Communication through the environment” Characterized by modification of physical environment local nature of released information Lay down trail of pheromones, follow trail with certain probability Computer scientists have been inspired by nature and biological system for al long time, probably one of the best known are Neural-Networks. Perhaps, less well-known, but not less interesting, are the approaches inspired by social insect behavior (ants, termites). These insects are rather unintelligent individuals with only limited abilities in terms of memory, sensing the environment. But nevertheless together they are able to solve astonishing complex tasks. Some keyworks here are division of labor, co-operative transport, brood sort and finding shortest pathes (e.g. between the nest and a food source). The way ants find the shortes path has first been adapted to problems like TSP, lately also for routing in computer networks. And the results were very encouraging; in some simulation they outperformed a lot of today’s used routing algorithms (in many respects). This is actually what we are trying to do and where we intend to go on. To develop further this approach and adapt it for the scenarios of the terminode networks. Let me explain how ants manage to fulfill this task. Ants seem to move randomly while foraging and looking for food, nevertheless they are capable of finding the shortest path, e.g. between the nest and the food source. Keep in mind: The individuals are not aware of the problem as a whole. Their behavior is somehow only stimulated by what other do or what others have done. This stimulus they encouter is through the environment.

Ants finding the shortest Path Food Source Nest ? Let me make it more clear with an example. Nest- Food Source, two pathes offered Two ants, no pheromones subsequent ant detects at this moment twice as much pheromone on the lower path than on the upper. Consequently, the ant would take twice as likely the lower path. Blocking and Shortcut problem: Although pheromones evaporate, too slow in real nature to find the shorter path Solved by our artifical ants by stronger evaporation of the pheromones and the reinforcement of the found path depending on the length (quality) of the path for longer pathes, it’s more difficult to maintain the pheromones

Artificial Ants Adapt the ants foraging behavior to artificial multi-agent system choosing appropriate state variables only local access to these variables for artificial ants Similarities population of concurrent and asynchronous entities real ants deposit pheromone, artificial ants change numeric information stochastic decision policy Differences internal state amount of pheromone is a function of the quality of the solution timing in pheromone laying extra capabilities (e.g. look ahead, local optimization) Global information not available in Networking, but in TSP, but not used Stigmergetic model of communication in general, and the one inspired by the ants foraging behaviour in particular, is an interesting model for artifical multi-agent systems applied to the solution of difficult optimization problems above-mentioned characteristics of stigmergy can easily be extended to artifical ants by (i) association to problem states appropriate state variables Bsp. Mit TSP ...asynchronous entites globally cooperating to find good solution to the task under consideration. Each artifical ant could build feasible solution, high quality solutions are the result of the cooperation among the individual of the whole colony. Cooperate by pheromone laying. ...numeric information locally stored in the problem’s state variables they visit. Discrete world, discrete state, cp TSP Internal state <-> like memory of the ant, remember visited states Artifical ants deposit an amount of pheromone which is a function of the quality of the solution found, counterpart in reality, more pheromone when richer food source. Aritifical ants update pheromone trails only after having generated a solution (cp. Last point)

“Foraging ant” meta-heuristic initialize_ant () while (current_state  target_state) A = read_local_pheromone-table() P = compute_transition_probabilities (A, M, problem_constraints) next_state = apply_ant_decision_policy (P, problem_constraints) move_to_next_state (next_state) if (step-by-step_pheromone_update) update_pheromone_table() // deposit pheromone on visited arc update_ant_memory() if (delayed_pheromone_update) evaluate_solution() update_pheromone_tables() // deposit pheromone on ALL visited arcs die() First explain by means of TSP -ant memory - pheromone table (probabilistic tasble) for ants to decide to which next state to go to, pheromone evaporation pheromone table sometime, like in ACO, probabilities P is function of phreomone table (clear), ants memory (allready visited cities), problem constraints (every city only be visited once) next state = ants decision policy (choose city with highest probability, other local heuristic) step by step: only at dest. Node, or all intermediate nodes delayed: clear with TSP(centralized), networking (backward ants) these ants-algorithms, because of their concurrent, independet and adaptive behavior, are particular suitable for distributed, stochastic, non-stationary problems like routing.

Ant-Based Control (ABC) I Pheromone tables each table has an entry for every destination and neighbour Pheromone laying ~ “updating routing table” updating row for Dest. s when arriving from source node s over i in j ants are launched from any node to any other node (random) cost-symmetrical links required 1 2 3 4 First attempt 1996 applied to model of BT telephone network -> circuit switched -> symmetrical links every switch has fixed capacity of possible phone calls ants no memory, exept source and destination node p is new probability and delta p is the probability (or pheromone increase) again probaility because the sum remains 1 exponential increase and decrease, helps lower probabilities One needs to realize that the pheromone table by which an individual ant is influenced, is a different table than the pheromone table that will be updated by this ant

Ant-Based Control (ABC) II Find short routes, but avoid heavily congested nodes delay ants at congested nodes make pheromone increase dependent of ant’s age Calls operate independently of ants deterministic (always neighbour with highest probability is chosen) Noise to overcome blocking and shortcut problem Noise factor f ant choosing path purely random with prob. f with prob. (1-f) choosing path according to pheromone tables Delay has two effects: - the increasing of the neighbour routing table for congested node is delayed, and therefore alternatives choices can increase rapidly - the ants are older, therefore have less effect on the pheromone tables Calls and ants dynamically interact with each other. New calls influence load of network (spare capacity) and therefore the ants. Ants influence the pheromone tables which in turn determine the routing of new calls. Need to avoid “freezing” of the routes that remain static for a long time One way of doing this is by adding an exploration probability (noise). Ensure that even apparently useless routes are used occasionally

AntNet I Node 3 Packet-switched network routing Node 2 cost-asymmetrical links Three kind of packets forward ant backward ant data Two data structures at node k routing table Tk array as model of traffic distribution Node 2 A Node 1 Packet-switched: - links are cost-asymmetrical, - packets can follow different paths Forward ants: delaid in queues, keep track of the path followed and the quality (delay, ...) Backward ants: follow same path in reverse direction, update routing table Data: Pheromone table same as with ABC Array: for valuate the ant trip times -> how much pheromone is laid need to be relative to networkstatus because poor trip time T under low congestion conditions can be an excellent one underhigh traffic load Dest.

AntNet II (Algorithm) forward ant Fs->d launched with d according to traffic patterns forward ant keeps track of path and traffic conditions cycle detection possible selection of next hop as function of Tk and queues of the links ln system more reactive At destination d, forward ant Fs->d generates backward ant Bd->s and transfers all its memory to it Backward ant same path in reverse direction not in same link queues as data packets and forward ants Updating the two data structures Tk and Mk for destination d At source s, backward ant dies forward ant, more important to nodes where a lot of traffic is sent memory: for backward ant, avoiding fluctuations to propagte the collected information faster in the network

AntNet III (Differences to ABC) Real trip times Additional data structure Pheromone is deposited delayed backward ant cost-asymmetrical links Use of local heuristics Data packets are routed probabilistic multipath routing for updating pheromone tables (evaluate path goodness), real trip times experienced are used,

Ants-based Routing in Mobile Ad Hoc Networks Not possible to save all nodes in routing table node K only maintains entries for areas Ai,j and neighboring nodes Nk Areas of different size One pheromone trail per area Evaporation is a function of node’s velocity Ants are sent to random coordinates within area A2,1 A1,1 A1,8 A2,2 A1,2 N1 All nodes within an area are gathered together (1 pheromone trail) Important: Not whole area is divide in section Just the view of each node, and keeps to be the same when moving Pheromone Evaporation as a function of the node’s speed K N2 N4 ... N3 A2,3 ...

Ants-based Routing in Mobile Ad Hoc Networks Link costs asymmetrical, no backward ant possible Link costs transferred from neighbouring nodes by data packets moving in opposite direction Not possible to use pheromone trails for ants (only data packets) Traffic as a approximation for pheromone trails S D

Ants-based Routing in Mobile Ad Hoc Networks Node only needs knowledge of its position and the destination Ants keep track of intermediate nodes coordinates recursively merge coordinates Updating not only node at destination, but also others Evaporation, Size of the Cell, ... as a function of the velocity Associativity as link cost factor

Summary and Open Issues Outperformed a lot of today’s used algorithms in a variety of problems High level of redundancy and fault tolerance Multipath routing Well suited for dynamic, decent-ralized problems Little routing overhead ... Deals efficiently with topology changes? Scalability in terms of # of nodes and geographical coverage area? Battery utilization -> sleep mode Asymmetrical links Combination with existing schemes proactive, reactive ...