Team Orienteering Problem with Time Windows (TOPTW) is an extension of the well-known Orienteering Problem (OP). In this study we introduces Team Orienteering Problem with Time Windows and Fuzzy Scores (TOPTWFS) which aims to maximize the total collected scores represented by normal triangular fuzzy numbers (TFNs) at the visiting points. For solving the proposed fuzzy model we developed a Genetic Algorithm (GA) where each phenotype is split into P sub-tours so as to define the maximum number of nodes that can be visited while the genotype is represented as a permutation of N elements. Consequently, the GA is coupled with 8 heuristics commonly used on routing problems for running away from local optima in order to improve the solution quality. Furthermore, the solution approach incorporates a new way to deal with Linear Programming Problems with Fuzzy Parameters in the Objective Function by using different defuzzification and fuzzy ranking methods to evaluate the phenotypes. Finally, by applying non-parametric test, the experimental results show how the performance of the algorithm change due to the evaluation of method selected allowing to compare its efficacy and effectiveness.

Team Orienteering Problem with Time Windows (TOPTW) is an extension of the well-known Orienteering Problem (OP). In this study we introduces Team Orienteering Problem with Time Windows and Fuzzy Scores (TOPTWFS) which aims to maximize the total collected scores represented by normal triangular fuzzy numbers (TFNs) at the visiting points. For solving the proposed fuzzy model we developed a Genetic Algorithm (GA) where each phenotype is split into P sub-tours so as to define the maximum number of nodes that can be visited while the genotype is represented as a permutation of N elements. Consequently, the GA is coupled with 8 heuristics commonly used on routing problems for running away from local optima in order to improve the solution quality. Furthermore, the solution approach incorporates a new way to deal with Linear Programming Problems with Fuzzy Parameters in the Objective Function by using different defuzzification and fuzzy ranking methods to evaluate the phenotypes. Finally, by applying non-parametric test, the experimental results show how the performance of the algorithm change due to the evaluation of method selected allowing to compare its efficacy and effectiveness.

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