The efficient development of an oil field mostly depends on a comprehensive optimization of subsurface flow. To account for several discrete or even contradicting objectives, multi-objective optimization (MOO) approach presents multiple optimum solutions for decision-making processes. There are excessive degrees of freedom in any optimization problem of the life-cycle of water-flooding to optimize the short-term performance during the process. Choosing each strategy has a different impact on the long-term reservoir performance. Thus, in this study, we have utilized two different model-based algorithms based on multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II) methods with some modifications to plan the short- and long-term production strategies simultaneously in water-flooded reservoirs. These algorithms are both population-based techniques, in which the Pareto-ranking approach is combined with the inherent search towards the optimal solution for a multi-criterion optimization problem. Maximizing the long-term Net Present Value (LNPV) and short-term (discounted) NPV (SNPV) are the objectives to be met in the investigated MOO problems. To address the imperfect Pareto front obtained in MOO problems, some modifications have been added to the utilized algorithms, including using a modified comparison operator in the NSGA-II method and employing the crowding distance parameter in the leader selection process together with a revised archive controller as well as a dynamic boundary search to MOPSO algorithm. By these means, the entire Pareto fronts are actively generated, which covers the complete solutions area through both algorithms. To validate the developed approaches, two benchmark water-flooded reservoir models have been employed. In the first case, the optimization parameters are the wells injection rates in the Egg benchmark reservoir model. In the second one, we have adjusted the opening values of the inflow control valves (ICV) of smart wells in the water-flooding process of a layered reservoir with a five-spot pattern. The effect of the trading-off between Pareto elitism and diversity on the final results is investigated for both algorithms. Results illustrate that the competitive values of the NPV functions, LNPV and SNPV pairs, lying on the obtained Pareto front, provide a promising criterion to improve the decision-making process. A comparison of various methods shows that for both case-studies, MOPSO can strongly propose a production strategy that more appropriately optimizes SNPV and LNPV compared to the NSGA-II as well as compared to some previous efforts published in the literature. A high rate of convergence, together with the logical Pareto front having enough diversity and uniformity, and also the independency of the final solution on the initial guess, are the main advantages of MOPSO in comparison with other approaches.

油田的有效开发主要取决于地下流量的全面优化。为了解决几个离散甚至矛盾的目标，多目标优化（MOO）方法为决策过程提供了多个最佳解决方案。在注水生命周期的任何优化问题中都存在过度的自由度，以优化过程中的短期性能。选择每种策略对油藏的长期性能有不同的影响。因此，在这项研究中，我们利用了基于多目标粒子群优化（MOPSO）和非支配排序遗传算法II（NSGA-II）的两种不同的基于模型的算法，并对它们进行了一些修改以计划短期和长期注水油藏的同时生产策略。这些算法都是基于人口的技术，其中帕累托排序方法与针对多准则优化问题的最优解决方案的内在搜索相结合。最大化长期净现值（LNPV）和短期（折现）NPV（SNPV）是要研究的MOO问题中要实现的目标。为了解决在MOO问题中获得的不完美的帕累托阵线，已对所使用的算法进行了一些修改，包括在NSGA-II方法中使用经过修改的比较算子，以及在领导者选择过程中使用拥挤距离参数以及经修订的存档控制器以及对MOPSO算法的动态边界搜索。通过这些方式，将主动生成整个帕累托前沿，并通过两种算法覆盖整个解决方案领域。为了验证已开发的方法，已使用了两个基准水淹储层模型。在第一种情况下，优化参数是Egg基准储层模型中的井注入速率。在第二篇文章中，我们在具有五点模式的分层油藏注水过程中，调整了智能井的进水控制阀（ICV）的开度。对于这两种算法，都研究了帕累托精英主义和多样性之间的权衡取舍对最终结果的影响。结果表明，NPV函数，LNPV和SNPV对的竞争价值位于获得的Pareto前沿，为改善决策过程提供了有希望的标准。各种方法的比较表明，对于两种案例研究，与NSGA-II以及与文献中先前发表的一些努力相比，MOPSO可以强烈建议一种生产策略，该策略可以更适当地优化SNPV和LNPV。与其他方法相比，MOPSO的主要优点是，较高的收敛速度以及具有足够多样性和统一性的逻辑Pareto前沿，以及最终解决方案在初始猜测时的独立性。