The system under investigation contains a single refinery, a unique distribution center, and a multiproduct pipeline. The basic aim is to plan the optimal sequence for pumping products to achieve financial benefit and satisfy the customers with on-time delivery. In this study, some restrictions (such as batch sizing, discharging rate, forbidden sequences, and settling periods) are considered and the problem is formulated as a MILP model. Although the multiproduct pipeline scheduling problem has high time complexity, meta-heuristic algorithms have been used rarely in the literature. Another contribution of this work is to develop several meta-heuristic algorithms to solve the proposed MILP effectively. Therefore, as a novelty, some classical meta-heuristics like population-based simulated annealing and population-based variable neighborhood search are hybridized by the gravitational search algorithm for obtaining better performance. Parameters of the algorithms are tuned by an optimization problem and then all algorithms are compared by numerical examples. The achieved results demonstrate the validity of the model and the efficient performance of the proposed algorithms against exact methods. These algorithms also lead to better solutions in much lower computational time. Among them, the hybrid algorithm obtained by combining the SA and GSA meta-heuristics are superior to the other algorithms.

中文翻译：

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含延误惩罚的多产品输油管道调度问题的数学公式和混合元启发式算法

被调查的系统包含一个炼油厂、一个独特的配送中心和一个多产品管道。基本目标是规划泵送产品的最佳顺序，以实现经济效益并按时交货满足客户。在本研究中，考虑了一些限制（如批量大小、卸料率、禁止序列和沉降期），并将问题表述为 MILP 模型。尽管多产品流水线调度问题具有很高的时间复杂度，但元启发式算法在文献中很少使用。这项工作的另一个贡献是开发了几种元启发式算法来有效地解决所提出的 MILP。因此，作为一种新鲜事物，一些经典的元启发式算法，如基于种群的模拟退火和基于种群的变量邻域搜索，通过引力搜索算法进行混合以获得更好的性能。通过优化问题调整算法的参数，然后通过数值例子比较所有算法。所取得的结果证明了模型的有效性和所提出算法相对于精确方法的高效性能。这些算法还可以在更短的计算时间内获得更好的解决方案。其中，结合SA和GSA元启发式得到的混合算法优于其他算法。通过优化问题调整算法的参数，然后通过数值例子比较所有算法。所取得的结果证明了模型的有效性和所提出算法对精确方法的有效性能。这些算法还可以在更短的计算时间内获得更好的解决方案。其中，结合SA和GSA元启发式得到的混合算法优于其他算法。通过优化问题调整算法的参数，然后通过数值例子比较所有算法。所取得的结果证明了模型的有效性和所提出算法对精确方法的有效性能。这些算法还可以在更短的计算时间内获得更好的解决方案。其中，结合SA和GSA元启发式得到的混合算法优于其他算法。