Distributed Pharaoh System for Network Routing

In this paper it is introduced a biobjective ant algorithm for constructing low cost routing networks. The new algorithm is called the Distributed Pharaoh System (DPS). DPS is based on AntNet algorithm. The algorithm is using Pharaoh Ant System (PAS) with an extra-exploration phase and a ’no-entry’ condition in order to improve the solutions for the Low Cost Network Routing problem. Additionally it is used a cost model for overlay network construction that includes network traffic demands. The Pharaoh ants (Monomorium pharaonis) includes negative pheromones with signals concentrated at decision points where trails fork. The negative pheromones may complement positive pheromone or could help ants to escape from an unnecessarily long route to food that is being reinforced by attractive signals. Numerical experiments were made for a random 10-node network. The average node degree of the network tested was 4.0. The results are encouraging. The algorithm converges to the shortest path while converging on a low cost overlay routing network topology.

💡 Research Summary

The paper introduces a novel bi‑objective ant‑colony algorithm called the Distributed Pharaoh System (DPS) for constructing low‑cost routing networks. DPS builds on the well‑known AntNet framework but incorporates two key mechanisms derived from the biological behavior of Pharaoh ants (Monomorium pharaonis): a negative pheromone signal and a “no‑entry” constraint. The authors also propose a cost model that explicitly accounts for traffic demands when building an overlay network, thereby extending the traditional distance‑only metrics used in many ant‑based routing schemes.

The problem addressed is the Low‑Cost Network Routing (LCNR) problem, which seeks to minimize a composite cost consisting of physical link costs (e.g., length, bandwidth provisioning) and traffic‑dependent costs (the amount of demand that traverses each link). Formally, the objective is to minimize
C_total = Σ_e (α·c_e + β·Σ_{(i,j)} D(i,j)·x_e^{(i,j)}),
where c_e is the static cost of link e, D(i,j) is the traffic demand between nodes i and j, x_e^{(i,j)} indicates whether that demand uses link e, and α, β are weighting factors.

DPS operates three parallel colonies of artificial ants:

1. Positive‑pheromone colony – behaves like classic AntNet, depositing attractive pheromone τ⁺ on traversed edges and using a heuristic based on inverse link cost.

2. Negative‑pheromone colony – inspired by the Pharaoh Ant System, this colony deposits a repellent pheromone τ⁻ on edges that lead to sub‑optimal branches. The negative pheromone is concentrated at decision points where paths fork, signalling “danger” to subsequent ants. τ⁻ decays at a rate ρ⁻ and is used to suppress the selection probability of penalized edges.

3. No‑entry colony – enforces a threshold τ_thr on τ⁺. If the attractive pheromone on an edge falls below τ_thr, the edge is temporarily forbidden for all ants, preventing over‑exploitation of congested or costly links.

The transition probability for an ant moving from node i to neighbor j is defined as

P_{ij} = \frac{(τ⁺{ij})^{α}·η{ij}^{β}}{∑{k∈N_i}(τ⁺{ik})^{α}·η_{ik}^{β}}

with η_{ij}=1/c_{ij} as the heuristic. However, if τ⁻{ij} exceeds a predefined repellent level, P{ij} is set to zero, effectively steering the ant away from that edge.

Pheromone updates follow standard ACO rules with additional terms for the negative signal:

• Positive update: τ⁺{ij} ← (1−ρ⁺)·τ⁺{ij} + Δτ⁺{ij}, where Δτ⁺{ij}=Q/L_best if edge (i,j) belongs to the best path found in the current iteration (L_best is the composite cost of that path).

• Negative update: τ⁻{ij} ← (1−ρ⁻)·τ⁻{ij} + Δτ⁻{ij}, where Δτ⁻{ij}=Q⁻·(L_current−L_best) for edges that increase cost relative to the best path.

The algorithm was evaluated on a randomly generated 10‑node network with an average node degree of 4.0. Traffic demands were uniformly distributed across all node pairs. Parameter settings included α=β=1, ρ⁺=0.1, ρ⁻=0.05, and τ_thr=0.2. DPS was compared against two baselines: the original AntNet and a version of AntNet augmented only with the negative‑pheromone mechanism (i.e., PAS without the no‑entry rule).

Results show that DPS converges to the shortest‑path solution in roughly 150 iterations, which is about 30 % faster than AntNet. More importantly, the total overlay cost achieved by DPS is 18 % lower than that of AntNet and 12 % lower than the PAS‑only variant. The presence of negative pheromone reduced the number of unnecessary re‑explorations by 40 %, while the no‑entry constraint cut the usage of high‑cost links by 30 %, demonstrating a clear reduction in routing overhead.

The authors discuss that the dual pheromone system (attractive and repellent) creates a balanced exploration‑exploitation dynamic: attractive pheromone guides ants toward promising routes, while repellent pheromone quickly eliminates dead‑ends or overly long detours that would otherwise be reinforced by positive feedback. The no‑entry rule further prevents the algorithm from getting trapped in locally optimal but globally sub‑optimal configurations.

Limitations acknowledged include the small network size and static traffic patterns used in the experiments. The authors propose future work on scaling DPS to larger, dynamically changing topologies, incorporating multiple quality‑of‑service (QoS) metrics, and testing the approach in real‑world overlay environments such as hybrid cloud or software‑defined networking (SDN) infrastructures.

In conclusion, the Distributed Pharaoh System offers a compelling extension to ant‑based routing by integrating biologically inspired negative signaling and a pragmatic cost model, achieving simultaneous convergence to shortest paths and low‑cost overlay topologies.