An iterative local search approach based on fitness landscapes analysis for the delay-constrained multicast routing problem

This paper presents the first fitness landscape analysis on the delay-constrained least-cost multicast routing problem (DCLC-MRP), a well-known NP-hard problem. Although the problem has attracted an increasing research attention over the past decade in telecommunications and operational research, little research has been conducted to analyze the features of its underlying landscape. Two of the most commonly used landscape analysis techniques, the fitness distance correlation analysis and the autocorrelation analysis, have been applied to analyze the global and local landscape features for DCLC-MRPs. A large amount of simulation experiments on a set of problem instances generated based on the benchmark Steiner tree problems in the OR-library reveals that the landscape of the DCLC-MRP is highly instance dependent with different landscape features. Different delay bounds also affect the distribution of solutions in the search space. The autocorrelation analysis on the benchmark instances of different sizes and delay bounds shows the impact of different local search heuristics and neighborhood structures on the fitness distance landscapes of the DCLC-MRP. The delay bound constraint in the DCLC-MRP has shown a great influence on the underlying landscape characteristic of the problem. Based on the fitness landscape analysis, an iterative local search (ILS) approach is proposed in this paper for the first time to tackle the DCLC-MRP. Computational results demonstrate the effectiveness of the proposed ILS algorithm for the problem in comparison with other algorithms in the literature.