Variable Neighborhood Search for Partitioning Sparse Biological Networks into the Maximum Edge-Weighted k-Plexes

Abstract

In a network, a k-plex represents a subset of n vertices where the degree of each vertex in the subnetwork induced by this subset is at least n − k. The maximum edge-weight k-plex partitioning problem (Max-EkPP) is to find the k-plex partitioning in edge-weighted network, such that the sum of edge weights is maximal. The Max-EkPP has an important role in discovering new information in large sparse biological networks. We propose a variable neighborhood search (VNS) algorithm for solving Max-EkPP. The VNS implements a local search based on the 1-swap first improvement strategy and the objective function that takes into account the degree of every vertex in each partition. The objective function favors feasible solutions, also enabling a gradual increase in terms of objective function value when moving from slightly infeasible to barely feasible solutions.A comprehensive experimental computation is performed on real metabolic networks and other benchmark instances from literature. Comparing to the integer linear programming method from literature, our approach succeeds to find all known optimal solutions. For all other instances, the VNS either reaches previous best known solution or improves it. The proposed VNS is also tested on a large-scaled dataset which was not previously considered in literature.

Robust dynamic community detection with applications to human brain functional networks

“…First, there can be a multiplicity of plexes among a given set of nodes, and thus there is flexibility in representation. One approach might be to adopt the recentlyintroduced notion of a maximal edge-weighted plex 53 . Second, it is necessary to equip the edges between the same nodes at different network time points with an appropriate notion of an edge weight.…”

Topological Variable Neighborhood Search

“…Among the existing derivative-free optimization methods, two classes of algorithms can be distinguished: metaheuristics (with stochastic nature) and mathematical programming methods (with deterministic nature). As explained in [10], due to their simplicity and attractive nature-inspired interpretations (such as Genetic Algorithms ( [11], [12], [13] and [14]), Variable Neighbourhood Search ( [15], [16], [17], [18] and [19]), Electromagnetism-like metaheuristics ( [20] and [21]), etc. The former are used by a wide community of engineers and practitioners to solve real-world problems, while the latter are actively studied in academia due to their interesting theoretical properties, including guaranteed convergence.…”

Topologically sensitive metaheuristics

“…VNS is successfully used for solving various NP-hard problems of great practical importance [8] (location problems, graph coloring problems [9], knapsack and packing problems, vehicle routing problems). VNS is also successfully applied to Data mining domain, to design problems in communication and problems in biosciences and chemistry [10]. VNS consists of the following steps:…”