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• An auxiliary algorithm is proposed to construct initial stage of the MCDM methods. • A multi-objective fuzzy optimization model is formulated. • An extensive comparative analysis is conducted in terms of the addressed methods. • The stability and validity of the results are tested and discussed. • Key findings and managerial insights are provided. This paper examines the performances of the multi-criteria decision-making (MCDM) methods and optimization model in solving multi-attribute shortest path problems such as the safest shortest path under a fuzzy environment. To the best of the knowledge of the authors, this is the first study performing comparative analysis on finding the multi-attribute shortest path by employing well-known techniques in terms of computational effort and results in a fuzzy environment. To this end, the safest shortest path problem, where the risk and distance values concerning arcs on a directed network are defined as triangular fuzzy numbers, is handled. The solution process is carried out under two main headings: (i) To start the solution with MCDM methods, an auxiliary algorithm that constructs a fuzzy decision matrix is proposed. Then, Fuzzy-Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS), Fuzzy Simple Additive Weighting (F-SAW), and Fuzzy Evaluation Based on Distance from Average Solution (F-EDAS), that are fuzzy-based MCDM methods, are employed to rank the alternative paths. (ii) A multi-objective fuzzy optimization model is formulated, and the most reasonable paths are obtained considering different α-cut levels. Following that, comparative analysis is performed through a set of scenarios considering the different weights of the criteria to see the variability in the rankings. Besides, the addressed fuzzy-based MCDM methods are compared in terms of computational complexity. Overall, the main findings and managerial insights regarding the effectiveness and performance of the methods discussed in the solution process are provided. [ABSTRACT FROM AUTHOR]

• Definition of the Shared Resource-Constrained Multi-Shortest Path Problem, SRMSPP. • A parallelizable matheuristic to solve the SRMSPP. • Instances with thousands of networks and millions of arcs are solved. • The SRMSPP can be applied to some Scheduling Problems. We tackle the problem of finding, for each network within a collection, the shortest path between two given nodes, while not exceeding the limits of a set of shared resources. We present an integer programming (IP) formulation of this problem and propose a parallelizable matheuristic consisting of three phases: (1) generation of feasible solutions, (2) combination of solutions, and (3) solution improvement. We show that the shortest paths found with our procedure correspond to the solution of some type of scheduling problems such as the Air Traffic Flow Management (ATFM) problem. Our computational results include finding optimal solutions to small and medium-size ATFM instances by applying Gurobi to the IP formulation. We use those solutions to assess the quality of the output produced by our proposed matheuristic. For the largest instances, which correspond to actual flight plans in ATFM, exact methods fail and we assess the quality of our solutions by means of Lagrangian bounds. Computational results suggest that the proposed procedure is an effective approach to the family of shortest path problems that we discuss here. [ABSTRACT FROM AUTHOR]

• Stratified sampling reduces genotype diversify thus reducing exploration time. • Opposition-Based guessing increases initial population fitness. • Path Length diversity is more important during the initialization phase. • The repair function can introduce diversity to population. Initialization is the first and a major step in the implementation of evolutionary algorithms (EAs). Although there are many common general methods to initialize EAs such as the pseudo-random number generator (PRNG), there is no single method that can fit every problem. This study provides a new, flexible, diversity-aware, and easy-to-implement initialization method for a genetic algorithm for the shortest path problem. The proposed algorithm, called stratified opposition-based sampling (SOBS), considers phenotype and genotype diversity while striving to achieve the best fitness for the initialization population. SOBS does not depend on a specific type of sampling, because the main goal is to stratify the sampling space. SOBS aims at an initial population with higher fitness and diversity in the phenotype and genotype. To investigate the performance of SOBS, four network models were used to simulate real-world networks. Compared with the most frequently used initialization method, that is, PRNG, SOBS provides more accurate solutions, better running time with less memory usage, and an initial population with higher fitness. Statistical analysis showed that SOBS yields solutions with higher accuracy in 68–100% of the time. Although this study was focused on the genetic algorithm, it can be applied to other population-based EAs that solve the shortest path problem and use the same direct population representation such as particle swarm optimization (PSO). [ABSTRACT FROM AUTHOR]