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This study proposes a novel fuzzy programming optimization model for tugboat scheduling, directly considering multiple berthing bases, time windows, and operational uncertainties. The uncertainties in the required number of tugboats, the earliest start time, the latest start time, the processing time, and the start and end locations of each task are directly captured in the proposed fuzzy optimization model. The objective of the presented formulation is to minimize the total cost of fuel and delays. According to the characteristics of the problem, a Grey Wolf Optimization algorithm based on random probability encoding and custom genetic operators is proposed. The proposed algorithm, LINGO, the canonical Grey Wolf Optimization algorithm, and particle swarm optimization were used to compare and analyze the results of several examples. The results validate the efficiency of the proposed algorithm against the alternative exact and metaheuristics methods. Moreover, the findings from the conducted sensitivity analysis show the applicability of the developed fuzzy programming model for different confidence interval levels.
Li et al. (Thu,) studied this question.