In this paper the proposed constrained gravitational search algorithm (CGSA) is extended and used to solve multi-reservoir operation optimization problem. Tow constrained versions of GSA named partially constrained GSA (PCGSA) and fully constrained GSA (FCGSA) are outlined to solve this optimization problem. In the PCGSA, the problem constraints are partially satisfied, however, in the FCGSA, all the problem constraints are implicitly satisfied by providing the search space for each agent which contains only feasible solution and hence leading to smaller search space for each agent. These proposed constrained versions of GSA are very useful when they are applied to solve large scale multi-reservoir operation optimization problem. The constrained versions of GSA are formulated here for both possible variables of the problem means considering water release or storage volumes as the decision variables of the problem and therefore first and second formulations of these algorithms are proposed. The proposed algorithms are used to solve the well-known four and ten reservoir operation optimization problems and the results are presented and compared with those of original form of the GSA and any available results in the literature. The results indicate the superiority of the proposed algorithms and especially FCGSA over existing methods to optimally solve large scale multi-reservoir operation optimization problem.

中文翻译：

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求解多油藏优化问题的约束重力搜索算法的推广

在本文中，所提出的约束引力搜索算法（CGSA）被扩展并用于解决多水库操作优化问题。概述了称为部分约束 GSA (PCGSA) 和完全约束 GSA (FCGSA) 的两个约束 GSA 版本以解决此优化问题。在 PCGSA 中，部分满足问题约束，而在 FCGSA 中，通过为每个代理提供仅包含可行解的搜索空间，从而导致每个代理的搜索空间更小，从而隐式满足所有问题约束。这些提议的 GSA 约束版本在应用于解决大规模多水库运行优化问题时非常有用。此处针对问题的两个可能变量制定了 GSA 的约束版本，这意味着将排水量或蓄水量视为问题的决策变量，因此提出了这些算法的第一个和第二个公式。所提出的算法被用来解决众所周知的四和十油藏操作优化问题，并给出结果并与原始形式的 GSA 和文献中的任何可用结果进行比较。结果表明，所提出的算法，尤其是 FCGSA 优于现有方法，以最优地解决大规模多水库运行优化问题。所提出的算法被用来解决众所周知的四和十个油藏操作优化问题，并给出结果并与原始形式的 GSA 和文献中的任何可用结果进行比较。结果表明，所提出的算法，尤其是 FCGSA 优于现有方法，以最优地解决大规模多水库运行优化问题。所提出的算法被用来解决众所周知的四和十个油藏操作优化问题，并给出结果并与原始形式的 GSA 和文献中的任何可用结果进行比较。结果表明，所提出的算法，尤其是 FCGSA 优于现有方法，以最优地解决大规模多水库运行优化问题。