Water resources management often involves models that simulate physical/chemical processes to make predictions of future system behavior. These predictions often contain uncertainty that must be considered in order to make robust decisions. The quantification of this uncertainty is often not conducted in practice due to computational limitations and a lack of flexible software capabilities. To bridge this gap, we have developed a heuristic, multi-objective, model-independent optimization methodology using TCP/IP network communications for parallel run management on high-performance computing systems. The proposed optimization methodology is based on Particle Swarm Optimization (PSO), where the memory-like nature of PSO makes it ideal for tracing a Pareto front that graphically illustrates the trade-off between competing objective functions. Although the focus of this study is on addressing the likelihood of an undesirable or contested model prediction, the proposed methodology can be extended to any multi-objective optimization context, and is also able to handle inequality constraints that reflect additional conditions that must be met along the front. We have demonstrated the algorithm on two important real-world case studies. The first case study involved water allocation issues in Antelope Valley, California, USA, where the uncertainty in total natural recharge into the valley has raised significant debates over water management. The second case study involved the re-injection of coal seam gas co- produced water into deep aquifers in the Surat Basin, Queensland, Australia, where the potential impact of an undesired mobilization of arsenic concentrations needed to be understood and managed. This case study required a highly nonlinear field-scale reactive transport model, and an inequality constraint was also necessary to maintain consistency with a laboratory-scale geochemical model. The efficiency at which the proposed methodology solved these complex case studies demonstrates its effectiveness for a broad range of applications.