In this paper, a new multi-objective approach is suggested, known as multi-objective backtracking search algorithm (MOBSA) in order to formulate and solve the optimal power flow (OPF) problem in power systems. Many objective functions are considered like fuel cost, power losses, and voltage deviation. The structure of the proposed method is simple and has one control parameter. In addition, MOBSA is able to solve the highly constrained objectives. A fuzzy membership technique is integrated into the BSA algorithm to extract the best compromise solution from all the obtained Pareto optimal solutions. Furthermore, the capability of the MOBSA approach is evaluated and verified for bi- and tri-objectives, and tested on three standard IEEE power systems, small network 30-bus, medium network 57-bus, and large network 118-bus test systems. The obtained results reveal that the proposed method is efficient to generate well-distributed Pareto optimal non-dominated solutions. Likewise, the comparison analysis with some re-implemented methods as MODE, SPEA, MALO, and those found in the literature as MOABC/D, QOTLBO, NSGA-II and NSMOGSA, assured the superiority, effectiveness, and robustness of MOBSA.

中文翻译：

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一种新的多目标最优潮流的元启发式规划

在本文中，提出了一种新的多目标方法，称为多目标回溯搜索算法 (MOBSA)，以制定和解决电力系统中的最优潮流 (OPF) 问题。考虑了许多目标函数，例如燃料成本、功率损耗和电压偏差。该方法结构简单，控制参数只有一个。此外，MOBSA 能够解决高度受限的目标。模糊隶属度技术被集成到 BSA 算法中，以从所有获得的帕累托最优解中提取最佳折衷解。此外，MOBSA 方法的能力针对双目标和三目标进行了评估和验证，并在三个标准 IEEE 电力系统、小型网络 30 总线、中型网络 57 总线和大型网络 118 总线测试系统上进行了测试。获得的结果表明，所提出的方法可以有效地生成分布良好的帕累托最优非支配解。同样，与一些重新实现的方法如 MODE、SPEA、MALO 和文献中的 MOABC/D、QOTLBO、NSGA-II 和 NSMOGSA 的比较分析，保证了 MOBSA 的优越性、有效性和鲁棒性。