Firefly Algorithm Analysis

The pairwise global network alignment is the typical alignment between two biological network, in search of maximal sequence, topological and biological similarity among them. Let the two biological PPI networks namely N1(V1, E1) and N2(V2, E2) with V1, E1 and V2, E2 as the set of nodes which represents the proteins and set of edges which represents the interactions between the proteins in networks respectively. Let m=|V1| and n=|V2| which represents the number of elements in V. Always the network alignment should happen when |V1| ≤ |V2| where all the nodes in V1 can be mapped with V2. The alignment of two networks N1 and N2 is defined as an injective function f: V1 → V2, where each and every element of V1 is mapped uniquely with an element

The firefly optimization algorithm is a swarm intelligence and a novel meta-heuristic optimization algorithm inspired by the flashing behavior of the population of fireflies. It was proposed by Xin-She Yang (2008) and it has been evidenced to be an effective optimization algorithm to search the global optima. Each firefly signifies a network alignment between two networks that gives a candidate solution. The communication among the fireflies is directed by the following rules: Every fireflies are unisex so they are attracted to other fireflies irrespective of their sex. The distance and brightness directs the attractiveness. The attractiveness of a firefly is directly proportional to its brightness. Hence for any two fireflies, the lesser brighter firefly will move towards the brighter firefly. As their distance increases between these two fireflies, both the attractiveness and brightness will be decreased as they are directly proportional. If none of the firefly is brighter than a specific firefly, then it will travel randomly. The brightness of a firefly is denoted as light intensity (I) is affected by the value of the objective