Solving the incremental graph drawing problem by multiple neighborhood solution-based tabu search algorithm

Abstract

With the advent of the era of big data, more and more complex networks and knowledge based systems require data visualization for analysis and presentation, where graphs have become a standard representation model. Graph drawing addresses the problems of constructing geometric representations of graphs to make them easy to analyze. In this paper we aim to reduce the edge crossing number in the context of the incremental graph drawing problem (IGDP), in which we want to preserve the layout of a graph over successive drawings to present complex networks or knowledge-based systems. Specifically, we propose a metaheuristic algorithm called multiple neighborhood solution-based tabu search (MNSB-TS) by combining a solution-based tabu strategy and a multiple neighborhood structure for solving the incremental graph drawing problem. Our MNSB-TS approach introduces four neighborhood operators to accompany the solution-based tabu strategy for determining the tabu status of each neighbor solution. Extensive computational experiments on public benchmark instances demonstrate that the proposed MNSB-TS is highly competitive in comparison with the state-of-the-art heuristics and the exact optimization solver Gurobi. Key components of the approach are analyzed to evaluate their impact on algorithm performance and learn which search mechanisms are better suited for incremental graph drawing.