ALBERT

Description: In this paper, a discrete moth–flame optimization algorithm for community detection (DMFO-CD) is proposed. The representation of solution vectors, initialization, and movement strategy of the continuous moth–flame optimization are purposely adapted in DMFO-CD such that it can solve the discrete community detection. In this adaptation, locus-based adjacency representation is used to represent the position of moths and flames, and the initialization process is performed by considering the community structure and the relation between nodes without the need of any knowledge about the number of communities. Solution vectors are updated by the adapted movement strategy using a single-point crossover to distance imitating, a two-point crossover to calculate the movement, and a single-point neighbor-based mutation that can enhance the exploration and balance exploration and exploitation. The fitness function is also defined based on modularity. The performance of DMFO-CD was evaluated on eleven real-world networks, and the obtained results were compared with five well-known algorithms in community detection, including GA-Net, DPSO-PDM, GACD, EGACD, and DECS in terms of modularity, NMI, and the number of detected communities. Additionally, the obtained results were statistically analyzed by the Wilcoxon signed-rank and Friedman tests. In the comparison with other comparative algorithms, the results show that the proposed DMFO-CD is competitive to detect the correct number of communities with high modularity.

Description: This paper considers a variant of the Vehicle Routing Problem with Time Windows, with site dependencies, multiple depots and outsourcing costs. This problem is the basis for many technician routing problems. Having both site-dependency and time window constraints lresults in difficulties in finding feasible solutions and induces highly constrained instances. Matheuristics based on Mixed Integer Linear Programming compact formulations are firstly designed. Column Generation matheuristics are then described by using previous matheuristics and machine learning techniques to stabilize and speed up the convergence of the Column Generation algorithm. The computational experiments are analyzed on public instances with graduated difficulties in order to analyze the accuracy of algorithms for ensuring feasibility and the quality of solutions for weakly to highly constrained instances. The results emphasize the interest of the multiple types of hybridization between mathematical programming, machine learning and heuristics inside the Column Generation framework. This work offers perspectives for many extensions of technician routing problems.